{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.dividing-ratio","code":"thing-q2400901","url":"https://ver.cy/models/thing/q2400901/","name":"dividing ratio","alternateNames":[],"kind":"thing","status":"published","version":"0.2.0-wave.2","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.REL"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In geometry, the ratio in which a point divides a line segment, expressed as the quotient of the lengths of the two parts, used to locate points by the section formula, to define internal and external division, harmonic division and cross-ratios, and to describe special divisions such as the golden section; the dividing ratio is basic to coordinate geometry, projective geometry and constructions.","purpose":"Let an agent explain the dividing ratio of a segment and the section formula, support locating points and solving construction problems, describe special ratios and projective generalisations, and support learning in geometry.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Ratio of lengths","Section formula","Signed for external division","Projective invariants"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What the dividing ratio is.","layers":[{"id":"concept","name":"Concept","description":"Concept and formula.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is the dividing ratio of a point on a segment, and how does the section formula give coordinates?","kind":"definition"},{"text":"Is internal or external division meant?","kind":"boundary"}]}]},{"id":"kinds","name":"Kinds","description":"Internal, external and harmonic.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Kinds.","questions":[{"text":"How do internal, external and harmonic division differ, and what is the cross-ratio?","kind":"definition"},{"text":"Which entry fits projective geometry?","kind":"action"}]}]}]},{"id":"apply","name":"Apply","description":"Problems and constructions.","layers":[{"id":"locate","name":"Locate","description":"Locating points.","findings":[{"id":"locate-finding","name":"Locate","description":"Location.","questions":[{"text":"Where is the point dividing this segment in a given ratio, in coordinates or by construction?","kind":"action"},{"text":"Which entry fits coordinate geometry?","kind":"action"}]}]},{"id":"theorems","name":"Theorems","description":"Theorems using ratios.","findings":[{"id":"theorems-finding","name":"Theorems","description":"Theorems.","questions":[{"text":"How do theorems such as those of Menelaus and Ceva use dividing ratios?","kind":"provenance"},{"text":"Which entry fits triangle geometry?","kind":"action"}]}]}]},{"id":"special","name":"Special","description":"Special ratios.","layers":[{"id":"golden","name":"Golden","description":"The golden section.","findings":[{"id":"golden-finding","name":"Golden","description":"Golden.","questions":[{"text":"What is the golden section, and what does evidence say about its claimed occurrences in art and nature, with findings attributed?","kind":"provenance"},{"text":"Which findings are contested?","kind":"boundary"}]}]},{"id":"projective","name":"Projective","description":"Projective invariance.","findings":[{"id":"projective-finding","name":"Projective","description":"Projective.","questions":[{"text":"Why is the cross-ratio invariant under projection, and how is it used?","kind":"provenance"},{"text":"Which entry fits cross-ratio?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"History and teaching.","layers":[{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did Greek and later geometers treat the division of segments?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]},{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can dividing ratios be taught?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain the dividing ratio and the section formula.","Locate points by internal and external division, stating the sign convention.","Describe harmonic division and the golden section accurately."],"mustNot":["Mix ratio conventions without saying which one is used.","Make sign errors in external division without checking.","Present mystical claims about the golden section as mathematical fact.","Present homework answers as the student's own work when that would be dishonest."],"requiresHuman":["Relying on a computed division point in surveying or construction."]},"ethics":{"considerations":["Myths about the golden ratio are widely spread as fact; accuracy matters.","Help with learning should build understanding, not replace it."],"affectedParties":["Students","Designers","Surveyors"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q121960184","type":"parent","note":"registry parent class"},{"target":"ratio of lengths","type":"related","note":"category"},{"target":"irrational","type":"related","note":"the golden ratio as an irrational dividing ratio"},{"target":"point","type":"related","note":"points dividing segments"},{"target":"triangle","type":"related","note":"cevians dividing sides in ratios"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.dividing-ratio","Wikidata: Q2400901 (https://www.wikidata.org/wiki/Q2400901)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Quotient of the two parts of a divided segment","Internal, external, harmonic, golden","A proportion equates two ratios; a scale factor scales a whole figure","Not physical; a ratio."]},"capabilities":{"applicability":"required","items":["explain the concept and formula","support point location","describe special ratios","support learning"]},"hazards":{"applicability":"required","items":["Sign errors in external division","Confusing ratio conventions","Mystical claims about the golden section"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","Curriculum standards for geometry","No regulation of the concept"]},"context":{"applicability":"required","items":["Ratio in which a point divides a segment.","internal division","external division","harmonic division","the golden section","cross-ratio in projective geometry"]}},"sources":[{"title":"Wikidata item Q2400901: dividing ratio","url":"https://www.wikidata.org/wiki/Q2400901","note":"identity and sense of the item"},{"title":"Section formula","url":"https://en.wikipedia.org/wiki/Section_formula","note":"Coordinates of a point dividing a line segment in a specified ratio."}],"openQuestions":["Should the golden ratio be a separate entry?","How should geometry resources be linked?","How should construction methods be linked?"],"resources":{"spec":"/models/things/publications/thing-q2400901/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q2400901/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T06:07:38Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"filled","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"filled","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T12:51:17+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane XCT: no invented physical properties."},"score":1.0}}