{ "title": "Sacred Geometry Atlas geometry analysis", "generatedBy": "scripts/analyze-geometry.js", "asOf": "2026-08-23", "units": "meters", "method": { "purpose": "Calculate transparent ratios and simple geometric comparisons from the current Atlas inputs.", "constantsCompared": [ { "name": "1:1", "value": 1 }, { "name": "3:2", "value": 1.5 }, { "name": "φ", "value": 1.618033988749895 }, { "name": "√2", "value": 1.4142135623730951 }, { "name": "√3", "value": 1.7320508075688772 }, { "name": "2:1", "value": 2 }, { "name": "3:1", "value": 3 }, { "name": "4:1", "value": 4 } ], "fractionDenominatorLimit": 24, "toleranceForWithinFivePercent": 0.05, "warning": "A close ratio is a candidate pattern, not proof of design intent or authorship. Schematic inputs remain schematic outputs." }, "summary": { "recordCount": 24, "evidenceFieldCounts": { "reference-dimension": 7, "schematic": 137 }, "constructorAttribution": "not-determined-by-geometry" }, "records": [ { "id": "basilica", "index": "01", "name": "Basilica of Sant'Apollinare in Classe", "typology": "Basilica", "place": "Ravenna, Italy", "currentGeometryEvidence": { "length": "reference-dimension", "span": "reference-dimension", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 56, "span": 30, "height": 18, "radius": 15, "module": 8, "bayCount": 7, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [ { "field": "length", "label": "overall basilica length", "value": 56, "unit": "m", "scope": "published whole-building dimension", "sourceUrl": "https://whc.unesco.org/en/list/788/" }, { "field": "span", "label": "overall basilica width", "value": 30, "unit": "m", "scope": "published whole-building dimension", "sourceUrl": "https://whc.unesco.org/en/list/788/" } ], "ratios": { "lengthToSpan": 1.866667, "heightToSpan": 0.6, "radiusToSpan": 0.5, "moduleToSpan": 0.266667, "lengthToModule": 7 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.866667, "simpleFraction": { "numerator": 28, "denominator": 15, "value": 1.866667, "absoluteError": 0 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.066666, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.077721, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.153664, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.6, "simpleFraction": { "numerator": 3, "denominator": 5, "value": 0.6, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.4, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.575736, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.6, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.266667, "simpleFraction": { "numerator": 4, "denominator": 15, "value": 0.266667, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.733333, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.811438, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.822222, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 7, "simpleFraction": { "numerator": 7, "denominator": 1, "value": 7, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.75, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.333333, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2.5, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 7, "lengthToModuleNearestInteger": 7, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 1680, "envelopeVolume": 30240, "sectionRatio": 0.6, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [ "length", "span" ], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "gothic", "index": "02", "name": "Notre-Dame de Chartres Cathedral", "typology": "Gothic", "place": "Chartres, France", "currentGeometryEvidence": { "length": "reference-dimension", "span": "schematic", "height": "reference-dimension", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 130.2, "span": 34, "height": 37.5, "radius": 17, "module": 11.5, "bayCount": 8, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [ { "field": "length", "label": "overall cathedral length", "value": 130.2, "unit": "m", "scope": "published overall length", "sourceUrl": "https://www.cathedrale-chartres.org/en/cathedrale/monument/architecture/the-13th-century-cathedral/" }, { "field": "height", "label": "vault height", "value": 37.5, "unit": "m", "scope": "published nave vault height; not external height", "sourceUrl": "https://www.cathedrale-chartres.org/en/cathedrale/monument/architecture/the-13th-century-cathedral/" }, { "field": "nave-span", "label": "nave span", "value": 16.4, "unit": "m", "scope": "published nave span; the Atlas span field remains schematic", "sourceUrl": "https://www.cathedrale-chartres.org/en/cathedrale/monument/architecture/the-13th-century-cathedral/" } ], "ratios": { "lengthToSpan": 3.829412, "heightToSpan": 1.102941, "radiusToSpan": 0.5, "moduleToSpan": 0.338235, "lengthToModule": 11.321739 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 3.829412, "simpleFraction": { "numerator": 88, "denominator": 23, "value": 3.826087, "absoluteError": 0.003325 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.042647, "withinFivePercent": true }, { "name": "3:1", "target": 3, "relativeError": 0.276471, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.914706, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.102941, "simpleFraction": { "numerator": 21, "denominator": 19, "value": 1.105263, "absoluteError": 0.002322 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.102941, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.220103, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.264706, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.338235, "simpleFraction": { "numerator": 1, "denominator": 3, "value": 0.333333, "absoluteError": 0.004902 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.661765, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.760832, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.77451, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 11.321739, "simpleFraction": { "numerator": 249, "denominator": 22, "value": 11.318182, "absoluteError": 0.003557 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1.830435, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 2.773913, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 4.66087, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 11.321739, "lengthToModuleNearestInteger": 11, "lengthToModuleIntegerResidual": 0.321739, "bayModuleCoverage": 0.706605, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 4426.8, "envelopeVolume": 166005, "sectionRatio": 1.102941, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [ "length", "height" ], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "byzantine", "index": "03", "name": "Hosios Loukas Katholikon", "typology": "Central plan", "place": "Distomo, Greece", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 30, "span": 30, "height": 25, "radius": 4.5, "module": 7.5, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1, "heightToSpan": 0.833333, "radiusToSpan": 0.15, "moduleToSpan": 0.25, "lengthToModule": 4 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1, "simpleFraction": { "numerator": 1, "denominator": 1, "value": 1, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.292893, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.333333, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.833333, "simpleFraction": { "numerator": 5, "denominator": 6, "value": 0.833333, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.166667, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.410745, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.444445, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.15, "simpleFraction": { "numerator": 3, "denominator": 20, "value": 0.15, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.85, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.893934, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.9, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.25, "simpleFraction": { "numerator": 1, "denominator": 4, "value": 0.25, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.75, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.823223, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.833333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 4, "simpleFraction": { "numerator": 4, "denominator": 1, "value": 4, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0, "withinFivePercent": true }, { "name": "3:1", "target": 3, "relativeError": 0.333333, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 4, "lengthToModuleNearestInteger": 4, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 900, "envelopeVolume": 22500, "sectionRatio": 0.833333, "radialReachRatio": 0.15 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "baroque", "index": "04", "name": "Sant'Andrea al Quirinale", "typology": "Baroque", "place": "Rome, Italy", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 30, "span": 22, "height": 20, "radius": 11, "module": 5.5, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.363636, "heightToSpan": 0.909091, "radiusToSpan": 0.5, "moduleToSpan": 0.25, "lengthToModule": 5.454545 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.363636, "simpleFraction": { "numerator": 15, "denominator": 11, "value": 1.363636, "absoluteError": 0 }, "nearestConstants": [ { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.035764, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.090909, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.157227, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.909091, "simpleFraction": { "numerator": 10, "denominator": 11, "value": 0.909091, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.090909, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.357176, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.393939, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.25, "simpleFraction": { "numerator": 1, "denominator": 4, "value": 0.25, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.75, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.823223, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.833333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 5.454545, "simpleFraction": { "numerator": 60, "denominator": 11, "value": 5.454545, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.363636, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.818182, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1.727273, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 5.454545, "lengthToModuleNearestInteger": 5, "lengthToModuleIntegerResidual": 0.454545, "bayModuleCoverage": 0.733333, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 660, "envelopeVolume": 13200, "sectionRatio": 0.909091, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "stave", "index": "05", "name": "Borgund Stave Church", "typology": "Timber", "place": "Lærdal, Norway", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 18, "span": 10, "height": 16, "radius": 5, "module": 3.6, "bayCount": 5, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.8, "heightToSpan": 1.6, "radiusToSpan": 0.5, "moduleToSpan": 0.36, "lengthToModule": 5 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.8, "simpleFraction": { "numerator": 9, "denominator": 5, "value": 1.8, "absoluteError": 0 }, "nearestConstants": [ { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.03923, "withinFivePercent": true }, { "name": "2:1", "target": 2, "relativeError": 0.1, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.112461, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.6, "simpleFraction": { "numerator": 8, "denominator": 5, "value": 1.6, "absoluteError": 0 }, "nearestConstants": [ { "name": "φ", "target": 1.618033988749895, "relativeError": 0.011146, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.066667, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.07624, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.36, "simpleFraction": { "numerator": 5, "denominator": 14, "value": 0.357143, "absoluteError": 0.002857 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.64, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.745442, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.76, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 5, "simpleFraction": { "numerator": 5, "denominator": 1, "value": 5, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.25, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.666667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1.5, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 5, "lengthToModuleNearestInteger": 5, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 180, "envelopeVolume": 2880, "sectionRatio": 1.6, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "concrete", "index": "06", "name": "Church of the Light", "typology": "Modern", "place": "Ibaraki, Osaka, Japan", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 18, "span": 6.5, "height": 6.5, "radius": 3.25, "module": 4.5, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.769231, "heightToSpan": 1, "radiusToSpan": 0.5, "moduleToSpan": 0.692308, "lengthToModule": 4 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.769231, "simpleFraction": { "numerator": 36, "denominator": 13, "value": 2.769231, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.076923, "withinFivePercent": false }, { "name": "4:1", "target": 4, "relativeError": 0.307692, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.384615, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1, "simpleFraction": { "numerator": 1, "denominator": 1, "value": 1, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.292893, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.333333, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.692308, "simpleFraction": { "numerator": 9, "denominator": 13, "value": 0.692308, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.307692, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.510464, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.538461, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 4, "simpleFraction": { "numerator": 4, "denominator": 1, "value": 4, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0, "withinFivePercent": true }, { "name": "3:1", "target": 3, "relativeError": 0.333333, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 4, "lengthToModuleNearestInteger": 4, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 117, "envelopeVolume": 760.5, "sectionRatio": 1, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "san-vitale", "index": "07", "name": "Basilica of San Vitale", "typology": "Byzantine", "place": "Ravenna, Italy", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 32, "span": 28, "height": 24, "radius": 14, "module": 4, "bayCount": 8, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.142857, "heightToSpan": 0.857143, "radiusToSpan": 0.5, "moduleToSpan": 0.142857, "lengthToModule": 8 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.142857, "simpleFraction": { "numerator": 8, "denominator": 7, "value": 1.142857, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.142857, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.191878, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.238095, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.857143, "simpleFraction": { "numerator": 6, "denominator": 7, "value": 0.857143, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.142857, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.393908, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.428571, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.142857, "simpleFraction": { "numerator": 1, "denominator": 7, "value": 0.142857, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.857143, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.898985, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.904762, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 8, "simpleFraction": { "numerator": 8, "denominator": 1, "value": 8, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.666667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 8, "lengthToModuleNearestInteger": 8, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 896, "envelopeVolume": 21504, "sectionRatio": 0.857143, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "hagia-sophia", "index": "08", "name": "Hagia Sophia", "typology": "Byzantine", "place": "Istanbul, Türkiye", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 60, "span": 42, "height": 35, "radius": 21, "module": 10, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.428571, "heightToSpan": 0.833333, "radiusToSpan": 0.5, "moduleToSpan": 0.238095, "lengthToModule": 6 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.428571, "simpleFraction": { "numerator": 10, "denominator": 7, "value": 1.428571, "absoluteError": 0 }, "nearestConstants": [ { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.010152, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.047619, "withinFivePercent": true }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.117095, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.833333, "simpleFraction": { "numerator": 5, "denominator": 6, "value": 0.833333, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.166667, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.410745, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.444445, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.238095, "simpleFraction": { "numerator": 5, "denominator": 21, "value": 0.238095, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.761905, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.831641, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.84127, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 6, "simpleFraction": { "numerator": 6, "denominator": 1, "value": 6, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.5, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 6, "lengthToModuleNearestInteger": 6, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 0.666667, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 2520, "envelopeVolume": 88200, "sectionRatio": 0.833333, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "speyer", "index": "09", "name": "Speyer Cathedral", "typology": "Romanesque", "place": "Speyer, Germany", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 100, "span": 40, "height": 30, "radius": 20, "module": 12.5, "bayCount": 8, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.5, "heightToSpan": 0.75, "radiusToSpan": 0.5, "moduleToSpan": 0.3125, "lengthToModule": 8 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.5, "simpleFraction": { "numerator": 5, "denominator": 2, "value": 2.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.166667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.25, "withinFivePercent": false }, { "name": "4:1", "target": 4, "relativeError": 0.375, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.75, "simpleFraction": { "numerator": 3, "denominator": 4, "value": 0.75, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.25, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.46967, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.5, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.3125, "simpleFraction": { "numerator": 5, "denominator": 16, "value": 0.3125, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.6875, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.779029, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.791667, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 8, "simpleFraction": { "numerator": 8, "denominator": 1, "value": 8, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.666667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 8, "lengthToModuleNearestInteger": 8, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 4000, "envelopeVolume": 120000, "sectionRatio": 0.75, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "durham", "index": "10", "name": "Durham Cathedral", "typology": "Romanesque", "place": "Durham, England", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 100, "span": 35, "height": 28, "radius": 17.5, "module": 11, "bayCount": 9, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.857143, "heightToSpan": 0.8, "radiusToSpan": 0.5, "moduleToSpan": 0.314286, "lengthToModule": 9.090909 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.857143, "simpleFraction": { "numerator": 20, "denominator": 7, "value": 2.857143, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.047619, "withinFivePercent": true }, { "name": "4:1", "target": 4, "relativeError": 0.285714, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.428572, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.8, "simpleFraction": { "numerator": 4, "denominator": 5, "value": 0.8, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.2, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.434315, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.466667, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.314286, "simpleFraction": { "numerator": 6, "denominator": 19, "value": 0.315789, "absoluteError": 0.001503 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.685714, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.777766, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.790476, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 9.090909, "simpleFraction": { "numerator": 100, "denominator": 11, "value": 9.090909, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1.272727, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 2.030303, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3.545454, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 9.090909, "lengthToModuleNearestInteger": 9, "lengthToModuleIntegerResidual": 0.090909, "bayModuleCoverage": 0.99, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 3500, "envelopeVolume": 98000, "sectionRatio": 0.8, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "santiago", "index": "11", "name": "Cathedral of Santiago de Compostela", "typology": "Romanesque", "place": "Santiago de Compostela, Spain", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 90, "span": 45, "height": 26, "radius": 22.5, "module": 10, "bayCount": 9, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2, "heightToSpan": 0.577778, "radiusToSpan": 0.5, "moduleToSpan": 0.222222, "lengthToModule": 9 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2, "simpleFraction": { "numerator": 2, "denominator": 1, "value": 2, "absoluteError": 0 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0, "withinFivePercent": true }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.154701, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.236068, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.577778, "simpleFraction": { "numerator": 11, "denominator": 19, "value": 0.578947, "absoluteError": 0.001169 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.422222, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.591449, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.614815, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.222222, "simpleFraction": { "numerator": 2, "denominator": 9, "value": 0.222222, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.777778, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.842865, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.851852, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 9, "simpleFraction": { "numerator": 9, "denominator": 1, "value": 9, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1.25, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 2, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3.5, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 9, "lengthToModuleNearestInteger": 9, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 4050, "envelopeVolume": 105300, "sectionRatio": 0.577778, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "reims", "index": "12", "name": "Notre-Dame de Reims Cathedral", "typology": "Gothic", "place": "Reims, France", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 100, "span": 35, "height": 40, "radius": 17.5, "module": 11, "bayCount": 9, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.857143, "heightToSpan": 1.142857, "radiusToSpan": 0.5, "moduleToSpan": 0.314286, "lengthToModule": 9.090909 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.857143, "simpleFraction": { "numerator": 20, "denominator": 7, "value": 2.857143, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.047619, "withinFivePercent": true }, { "name": "4:1", "target": 4, "relativeError": 0.285714, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.428572, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.142857, "simpleFraction": { "numerator": 8, "denominator": 7, "value": 1.142857, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.142857, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.191878, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.238095, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.314286, "simpleFraction": { "numerator": 6, "denominator": 19, "value": 0.315789, "absoluteError": 0.001503 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.685714, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.777766, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.790476, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 9.090909, "simpleFraction": { "numerator": 100, "denominator": 11, "value": 9.090909, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1.272727, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 2.030303, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3.545454, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 9.090909, "lengthToModuleNearestInteger": 9, "lengthToModuleIntegerResidual": 0.090909, "bayModuleCoverage": 0.99, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 3500, "envelopeVolume": 140000, "sectionRatio": 1.142857, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "cologne", "index": "13", "name": "Cologne Cathedral", "typology": "Gothic", "place": "Cologne, Germany", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 120, "span": 40, "height": 48, "radius": 20, "module": 11.5, "bayCount": 10, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 3, "heightToSpan": 1.2, "radiusToSpan": 0.5, "moduleToSpan": 0.2875, "lengthToModule": 10.434783 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 3, "simpleFraction": { "numerator": 3, "denominator": 1, "value": 3, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0, "withinFivePercent": true }, { "name": "4:1", "target": 4, "relativeError": 0.25, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.5, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.2, "simpleFraction": { "numerator": 6, "denominator": 5, "value": 1.2, "absoluteError": 0 }, "nearestConstants": [ { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.151472, "withinFivePercent": false }, { "name": "1:1", "target": 1, "relativeError": 0.2, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.2, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.2875, "simpleFraction": { "numerator": 2, "denominator": 7, "value": 0.285714, "absoluteError": 0.001786 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.7125, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.796707, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.808333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 10.434783, "simpleFraction": { "numerator": 240, "denominator": 23, "value": 10.434783, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1.608696, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 2.478261, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 4.217391, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 10.434783, "lengthToModuleNearestInteger": 10, "lengthToModuleIntegerResidual": 0.434783, "bayModuleCoverage": 0.958333, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 4800, "envelopeVolume": 230400, "sectionRatio": 1.2, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "monreale", "index": "14", "name": "Monreale Cathedral", "typology": "Norman-Arab", "place": "Monreale, Sicily, Italy", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 72, "span": 32, "height": 26, "radius": 16, "module": 9, "bayCount": 7, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.25, "heightToSpan": 0.8125, "radiusToSpan": 0.5, "moduleToSpan": 0.28125, "lengthToModule": 8 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.25, "simpleFraction": { "numerator": 9, "denominator": 4, "value": 2.25, "absoluteError": 0 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.125, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.25, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.299038, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.8125, "simpleFraction": { "numerator": 13, "denominator": 16, "value": 0.8125, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.1875, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.425476, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.458333, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.28125, "simpleFraction": { "numerator": 5, "denominator": 18, "value": 0.277778, "absoluteError": 0.003472 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.71875, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.801126, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.8125, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 8, "simpleFraction": { "numerator": 8, "denominator": 1, "value": 8, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 1, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.666667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 3, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 8, "lengthToModuleNearestInteger": 8, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 0.875, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 2304, "envelopeVolume": 59904, "sectionRatio": 0.8125, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "saint-denis", "index": "15", "name": "Basilica Cathedral of Saint-Denis", "typology": "Gothic", "place": "Saint-Denis, France", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 75, "span": 30, "height": 34, "radius": 15, "module": 10, "bayCount": 7, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.5, "heightToSpan": 1.133333, "radiusToSpan": 0.5, "moduleToSpan": 0.333333, "lengthToModule": 7.5 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.5, "simpleFraction": { "numerator": 5, "denominator": 2, "value": 2.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.166667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.25, "withinFivePercent": false }, { "name": "4:1", "target": 4, "relativeError": 0.375, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.133333, "simpleFraction": { "numerator": 17, "denominator": 15, "value": 1.133333, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.133333, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.198613, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.244445, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.333333, "simpleFraction": { "numerator": 1, "denominator": 3, "value": 0.333333, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.666667, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.764298, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.777778, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 7.5, "simpleFraction": { "numerator": 15, "denominator": 2, "value": 7.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.875, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.5, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2.75, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 7.5, "lengthToModuleNearestInteger": 8, "lengthToModuleIntegerResidual": 0.5, "bayModuleCoverage": 0.933333, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 2250, "envelopeVolume": 76500, "sectionRatio": 1.133333, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "urnes", "index": "16", "name": "Urnes Stave Church", "typology": "Timber", "place": "Luster, Norway", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 18, "span": 8, "height": 13, "radius": 4, "module": 3.5, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.25, "heightToSpan": 1.625, "radiusToSpan": 0.5, "moduleToSpan": 0.4375, "lengthToModule": 5.142857 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.25, "simpleFraction": { "numerator": 9, "denominator": 4, "value": 2.25, "absoluteError": 0 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.125, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.25, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.299038, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.625, "simpleFraction": { "numerator": 13, "denominator": 8, "value": 1.625, "absoluteError": 0 }, "nearestConstants": [ { "name": "φ", "target": 1.618033988749895, "relativeError": 0.004305, "withinFivePercent": true }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.061806, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.083333, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.4375, "simpleFraction": { "numerator": 7, "denominator": 16, "value": 0.4375, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5625, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.690641, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.708333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 5.142857, "simpleFraction": { "numerator": 36, "denominator": 7, "value": 5.142857, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.285714, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.714286, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1.571429, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 5.142857, "lengthToModuleNearestInteger": 5, "lengthToModuleIntegerResidual": 0.142857, "bayModuleCoverage": 0.777778, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 144, "envelopeVolume": 1872, "sectionRatio": 1.625, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "kizhi", "index": "17", "name": "Church of the Transfiguration, Kizhi Pogost", "typology": "Timber", "place": "Kizhi Island, Karelia, Russia", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 30, "span": 18, "height": 25, "radius": 9, "module": 5, "bayCount": 6, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.666667, "heightToSpan": 1.388889, "radiusToSpan": 0.5, "moduleToSpan": 0.277778, "lengthToModule": 6 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.666667, "simpleFraction": { "numerator": 5, "denominator": 3, "value": 1.666667, "absoluteError": 0 }, "nearestConstants": [ { "name": "φ", "target": 1.618033988749895, "relativeError": 0.030057, "withinFivePercent": true }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.037749, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.111111, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.388889, "simpleFraction": { "numerator": 25, "denominator": 18, "value": 1.388889, "absoluteError": 0 }, "nearestConstants": [ { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.017907, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.074074, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.141619, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.277778, "simpleFraction": { "numerator": 5, "denominator": 18, "value": 0.277778, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.722222, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.803581, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.814815, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 6, "simpleFraction": { "numerator": 6, "denominator": 1, "value": 6, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.5, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 6, "lengthToModuleNearestInteger": 6, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 540, "envelopeVolume": 13500, "sectionRatio": 1.388889, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "san-giorgio", "index": "18", "name": "Basilica of San Giorgio Maggiore", "typology": "Renaissance", "place": "Venice, Italy", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 55, "span": 28, "height": 24, "radius": 14, "module": 9, "bayCount": 6, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.964286, "heightToSpan": 0.857143, "radiusToSpan": 0.5, "moduleToSpan": 0.321429, "lengthToModule": 6.111111 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.964286, "simpleFraction": { "numerator": 47, "denominator": 24, "value": 1.958333, "absoluteError": 0.005953 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.017857, "withinFivePercent": true }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.134081, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.213996, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.857143, "simpleFraction": { "numerator": 6, "denominator": 7, "value": 0.857143, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.142857, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.393908, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.428571, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.321429, "simpleFraction": { "numerator": 7, "denominator": 22, "value": 0.318182, "absoluteError": 0.003247 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.678571, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.772715, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.785714, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 6.111111, "simpleFraction": { "numerator": 55, "denominator": 9, "value": 6.111111, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.527778, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.037037, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2.055556, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 6.111111, "lengthToModuleNearestInteger": 6, "lengthToModuleIntegerResidual": 0.111111, "bayModuleCoverage": 0.981818, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 1540, "envelopeVolume": 36960, "sectionRatio": 0.857143, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "redentore", "index": "19", "name": "Il Redentore", "typology": "Renaissance", "place": "Venice, Italy", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 55, "span": 24, "height": 25, "radius": 12, "module": 8, "bayCount": 6, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 2.291667, "heightToSpan": 1.041667, "radiusToSpan": 0.5, "moduleToSpan": 0.333333, "lengthToModule": 6.875 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.291667, "simpleFraction": { "numerator": 55, "denominator": 24, "value": 2.291667, "absoluteError": 0 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.145833, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.236111, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.323095, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.041667, "simpleFraction": { "numerator": 25, "denominator": 24, "value": 1.041667, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.041667, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.26343, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.305555, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.333333, "simpleFraction": { "numerator": 1, "denominator": 3, "value": 0.333333, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.666667, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.764298, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.777778, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 6.875, "simpleFraction": { "numerator": 55, "denominator": 8, "value": 6.875, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.71875, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 1.291667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 2.4375, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 6.875, "lengthToModuleNearestInteger": 7, "lengthToModuleIntegerResidual": 0.125, "bayModuleCoverage": 0.872727, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 1320, "envelopeVolume": 33000, "sectionRatio": 1.041667, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "st-pauls", "index": "20", "name": "St Paul's Cathedral", "typology": "Baroque", "place": "London, England", "currentGeometryEvidence": { "length": "reference-dimension", "span": "reference-dimension", "height": "reference-dimension", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 169.2, "span": 75, "height": 111.6, "radius": 30, "module": 12, "bayCount": 8, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [ { "field": "length", "label": "cathedral length", "value": 169.2, "unit": "m", "scope": "published length including western steps", "sourceUrl": "https://www.cityoflondon.gov.uk/assets/Services-Environment/ed-htb34-protected-views-spd.pdf" }, { "field": "span", "label": "greatest breadth", "value": 75, "unit": "m", "scope": "published greatest breadth", "sourceUrl": "https://www.cityoflondon.gov.uk/assets/Services-Environment/ed-htb34-protected-views-spd.pdf" }, { "field": "height", "label": "overall height", "value": 111.6, "unit": "m", "scope": "published height above pavement to top of cross", "sourceUrl": "https://www.cityoflondon.gov.uk/assets/Services-Environment/ed-htb34-protected-views-spd.pdf" } ], "ratios": { "lengthToSpan": 2.256, "heightToSpan": 1.488, "radiusToSpan": 0.4, "moduleToSpan": 0.16, "lengthToModule": 14.1 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 2.256, "simpleFraction": { "numerator": 52, "denominator": 23, "value": 2.26087, "absoluteError": 0.00487 }, "nearestConstants": [ { "name": "2:1", "target": 2, "relativeError": 0.128, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.248, "withinFivePercent": false }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.302502, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.488, "simpleFraction": { "numerator": 34, "denominator": 23, "value": 1.478261, "absoluteError": 0.009739 }, "nearestConstants": [ { "name": "3:2", "target": 1.5, "relativeError": 0.008, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.052175, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.080365, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.4, "simpleFraction": { "numerator": 2, "denominator": 5, "value": 0.4, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.6, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.717157, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.733333, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.16, "simpleFraction": { "numerator": 3, "denominator": 19, "value": 0.157895, "absoluteError": 0.002105 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.84, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.886863, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.893333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 14.1, "simpleFraction": { "numerator": 141, "denominator": 10, "value": 14.1, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 2.525, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 3.7, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 6.05, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 14.1, "lengthToModuleNearestInteger": 14, "lengthToModuleIntegerResidual": 0.1, "bayModuleCoverage": 0.567376, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 12690, "envelopeVolume": 1416204, "sectionRatio": 1.488, "radialReachRatio": 0.4 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [ "length", "span", "height" ], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "karlskirche", "index": "21", "name": "Karlskirche", "typology": "Baroque", "place": "Vienna, Austria", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 45, "span": 30, "height": 30, "radius": 15, "module": 8, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.5, "heightToSpan": 1, "radiusToSpan": 0.5, "moduleToSpan": 0.266667, "lengthToModule": 5.625 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.5, "simpleFraction": { "numerator": 3, "denominator": 2, "value": 1.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:2", "target": 1.5, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.06066, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.072949, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1, "simpleFraction": { "numerator": 1, "denominator": 1, "value": 1, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.292893, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.333333, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.266667, "simpleFraction": { "numerator": 4, "denominator": 15, "value": 0.266667, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.733333, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.811438, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.822222, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 5.625, "simpleFraction": { "numerator": 45, "denominator": 8, "value": 5.625, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.40625, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.875, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1.8125, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 5.625, "lengthToModuleNearestInteger": 6, "lengthToModuleIntegerResidual": 0.375, "bayModuleCoverage": 0.711111, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 1350, "envelopeVolume": 40500, "sectionRatio": 1, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "ronchamp", "index": "22", "name": "Chapelle Notre-Dame-du-Haut", "typology": "Modern", "place": "Ronchamp, France", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 25, "span": 16, "height": 14, "radius": 8, "module": 5, "bayCount": 4, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1.5625, "heightToSpan": 0.875, "radiusToSpan": 0.5, "moduleToSpan": 0.3125, "lengthToModule": 5 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1.5625, "simpleFraction": { "numerator": 25, "denominator": 16, "value": 1.5625, "absoluteError": 0 }, "nearestConstants": [ { "name": "φ", "target": 1.618033988749895, "relativeError": 0.034322, "withinFivePercent": true }, { "name": "3:2", "target": 1.5, "relativeError": 0.041667, "withinFivePercent": true }, { "name": "√3", "target": 1.7320508075688772, "relativeError": 0.09789, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.875, "simpleFraction": { "numerator": 7, "denominator": 8, "value": 0.875, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.125, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.381282, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.416667, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.3125, "simpleFraction": { "numerator": 5, "denominator": 16, "value": 0.3125, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.6875, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.779029, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.791667, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 5, "simpleFraction": { "numerator": 5, "denominator": 1, "value": 5, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 0.25, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 0.666667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 1.5, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 5, "lengthToModuleNearestInteger": 5, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 0.8, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 400, "envelopeVolume": 5600, "sectionRatio": 0.875, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "brasilia", "index": "23", "name": "Cathedral of Brasília", "typology": "Modern", "place": "Brasília, Brazil", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 40, "span": 40, "height": 30, "radius": 20, "module": 2.5, "bayCount": 16, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 1, "heightToSpan": 0.75, "radiusToSpan": 0.5, "moduleToSpan": 0.0625, "lengthToModule": 16 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 1, "simpleFraction": { "numerator": 1, "denominator": 1, "value": 1, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.292893, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.333333, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 0.75, "simpleFraction": { "numerator": 3, "denominator": 4, "value": 0.75, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.25, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.46967, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.5, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.0625, "simpleFraction": { "numerator": 1, "denominator": 16, "value": 0.0625, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.9375, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.955806, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.958333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 16, "simpleFraction": { "numerator": 16, "denominator": 1, "value": 16, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 3, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 4.333333, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 7, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 16, "lengthToModuleNearestInteger": 16, "lengthToModuleIntegerResidual": 0, "bayModuleCoverage": 1, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 1600, "envelopeVolume": 48000, "sectionRatio": 0.75, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." }, { "id": "thorncrown", "index": "24", "name": "Thorncrown Chapel", "typology": "Contemporary", "place": "Eureka Springs, Arkansas, USA", "currentGeometryEvidence": { "length": "schematic", "span": "schematic", "height": "schematic", "radius": "schematic", "module": "schematic", "bayCount": "schematic" }, "geometryInputs": { "length": 25, "span": 8, "height": 12, "radius": 4, "module": 2, "bayCount": 12, "units": "m for dimensions; count for bayCount" }, "publishedMeasurements": [], "ratios": { "lengthToSpan": 3.125, "heightToSpan": 1.5, "radiusToSpan": 0.5, "moduleToSpan": 0.25, "lengthToModule": 12.5 }, "ratioPatterns": [ { "name": "lengthToSpan", "observed": 3.125, "simpleFraction": { "numerator": 25, "denominator": 8, "value": 3.125, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:1", "target": 3, "relativeError": 0.041667, "withinFivePercent": true }, { "name": "4:1", "target": 4, "relativeError": 0.21875, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 0.5625, "withinFivePercent": false } ] }, { "name": "heightToSpan", "observed": 1.5, "simpleFraction": { "numerator": 3, "denominator": 2, "value": 1.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "3:2", "target": 1.5, "relativeError": 0, "withinFivePercent": true }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.06066, "withinFivePercent": false }, { "name": "φ", "target": 1.618033988749895, "relativeError": 0.072949, "withinFivePercent": false } ] }, { "name": "radiusToSpan", "observed": 0.5, "simpleFraction": { "numerator": 1, "denominator": 2, "value": 0.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.5, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.646447, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.666667, "withinFivePercent": false } ] }, { "name": "moduleToSpan", "observed": 0.25, "simpleFraction": { "numerator": 1, "denominator": 4, "value": 0.25, "absoluteError": 0 }, "nearestConstants": [ { "name": "1:1", "target": 1, "relativeError": 0.75, "withinFivePercent": false }, { "name": "√2", "target": 1.4142135623730951, "relativeError": 0.823223, "withinFivePercent": false }, { "name": "3:2", "target": 1.5, "relativeError": 0.833333, "withinFivePercent": false } ] }, { "name": "lengthToModule", "observed": 12.5, "simpleFraction": { "numerator": 25, "denominator": 2, "value": 12.5, "absoluteError": 0 }, "nearestConstants": [ { "name": "4:1", "target": 4, "relativeError": 2.125, "withinFivePercent": false }, { "name": "3:1", "target": 3, "relativeError": 3.166667, "withinFivePercent": false }, { "name": "2:1", "target": 2, "relativeError": 5.25, "withinFivePercent": false } ] } ], "moduleChecks": { "lengthToModule": 12.5, "lengthToModuleNearestInteger": 13, "lengthToModuleIntegerResidual": 0.5, "bayModuleCoverage": 0.96, "bayModuleCoverageNote": "This tests the supplied Atlas module against the supplied bay count; it does not establish the historical construction grid." }, "derivedReadings": { "floorArea": 200, "envelopeVolume": 2400, "sectionRatio": 1.5, "radialReachRatio": 0.5 }, "constructorFinding": { "result": "not-determined-by-geometry", "confidence": "not-applicable", "explanation": "Ratios, symmetry, modules, and curve fits can test a geometric hypothesis but cannot identify the historical designer, mason, carpenter, engineer, or construction team. Attribution must come from documentary, archival, epigraphic, or institutional evidence.", "geometryEvidenceFields": [], "documentaryEvidenceRequired": true }, "interpretation": "Pattern calculations are exploratory because the Atlas inputs are schematic; do not report these ratios as surveyed dimensions." } ] }