{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.triangle","code":"thing-q19821","url":"https://ver.cy/models/thing/q19821/","name":"triangle","alternateNames":["pink triangle","Orthologic triangles","central triangle","non-equilateral triangle","circumscribed triangle","derived triangle","oblique triangle","Karpman drama triangle","acute or obtuse triangle","inscribed triangle","desmic mate","triangle character"],"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.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"A polygon with three edges and three vertices, the simplest polygon and a two-dimensional simplex, classified by sides as equilateral, isosceles or scalene and by angles as acute, right or obtuse, with properties such as the angle sum of 180 degrees in Euclidean geometry and many special centres and derived triangles; the triangle is fundamental in geometry, trigonometry, engineering and symbolism.","purpose":"Let an agent explain triangle types and properties, solve triangle problems, apply triangles in construction and trigonometry, and describe symbolic uses with attribution.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Simplest polygon","Rigid shape","Classified by sides and angles","Basis of trigonometry"],"structure":{"bundles":[{"id":"classify","name":"Classify","description":"Types of triangle.","layers":[{"id":"type","name":"Type","description":"Which type.","findings":[{"id":"type-finding","name":"Type","description":"Type.","questions":[{"text":"What type of triangle is this by sides and angles?","kind":"definition"},{"text":"Is it a special triangle with known ratios?","kind":"definition"}]}]},{"id":"exists","name":"Exists","description":"Can it exist.","findings":[{"id":"exists-finding","name":"Exists","description":"Existence.","questions":[{"text":"Can a triangle with these sides or angles exist, by the triangle inequality and angle sum?","kind":"boundary"},{"text":"Is it unique?","kind":"boundary"}]}]}]},{"id":"solve","name":"Solve","description":"Calculations.","layers":[{"id":"measure","name":"Measure","description":"Sides, angles and area.","findings":[{"id":"measure-finding","name":"Measure","description":"Measurement.","questions":[{"text":"What are the unknown sides, angles and area of this triangle?","kind":"measurement"},{"text":"Which rule applies, such as sine or cosine rule?","kind":"definition"}]}]},{"id":"centres","name":"Centres","description":"Triangle centres.","findings":[{"id":"centres-finding","name":"Centres","description":"Centres.","questions":[{"text":"Where are the centroid, circumcentre, incentre and orthocentre of this triangle?","kind":"measurement"},{"text":"Which theorems relate them?","kind":"definition"}]}]}]},{"id":"apply","name":"Apply","description":"Applications.","layers":[{"id":"structures","name":"Structures","description":"Triangles in engineering.","findings":[{"id":"structures-finding","name":"Structures","description":"Engineering.","questions":[{"text":"Why are triangles used in trusses and frames?","kind":"definition"},{"text":"How is triangulation used in surveying and graphics?","kind":"definition"}]}]},{"id":"geometries","name":"Geometries","description":"Non-Euclidean triangles.","findings":[{"id":"geometries-finding","name":"Geometries","description":"Non-Euclidean.","questions":[{"text":"How do spherical and hyperbolic triangles differ from Euclidean ones?","kind":"definition"},{"text":"When does this matter in practice?","kind":"boundary"}]}]}]},{"id":"culture","name":"Culture","description":"Symbolism and teaching.","layers":[{"id":"symbols","name":"Symbols","description":"Symbolic triangles.","findings":[{"id":"symbols-finding","name":"Symbols","description":"Symbolism.","questions":[{"text":"What do triangle symbols mean in this context, such as warning signs, religious symbols or the pink triangle in LGBTQ history, as described by the communities and historians concerned?","kind":"provenance"},{"text":"Are meanings attributed rather than assumed?","kind":"boundary"}]}]},{"id":"teach","name":"Teach","description":"Teaching triangles.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can triangle properties be taught with constructions and proofs?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Calculate the properties of triangles and show the working.","Classify triangles by sides and angles."],"mustNot":["Present a wrong calculation as correct in structural, surveying or navigation work.","Do a student's graded work in a way that breaks the rules of their course.","Attach mystical or pseudoscientific powers to the shape as if established."],"requiresHuman":["Using triangulation results to set a legal boundary."]},"ethics":{"considerations":["Geometric errors in surveying and engineering can cause disputes and failures.","Mathematics teaching should build understanding, not bypass it."],"affectedParties":["Students","Engineers and surveyors"]},"owners":{"steward":"Nobody owns the concept: held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q117307846","type":"parent","note":"registry parent class"},{"target":"Q331350","type":"parent","note":"registry parent class"},{"target":"Q37555","type":"parent","note":"registry parent class"},{"target":"Q4903575","type":"parent","note":"registry parent class"},{"target":"Q85292517","type":"parent","note":"registry parent class"},{"target":"polygon","type":"related","note":"category"},{"target":"simplex","type":"related","note":"category"},{"target":"truss","type":"related","note":"triangulated structures"},{"target":"line segment","type":"related","note":"edges"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.triangle","Wikidata: Q19821 (https://www.wikidata.org/wiki/Q19821)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Three sides and three vertices","Angle sum of 180 degrees in the plane","A quadrilateral has four sides","A three-sided figure."]},"capabilities":{"applicability":"required","items":["classify triangles","solve for sides, angles and area","explain centres and theorems","describe applications and symbolism"]},"hazards":{"applicability":"required","items":["Applying Euclidean rules to curved surfaces","Ambiguous case errors in solving triangles","Misattributing symbolic meanings"]},"interfaces":{"applicability":"required","items":["ISO 80000-2 notation","No regulation"]},"context":{"applicability":"required","items":["Geometry, measurement and structure.","equilateral, isosceles and scalene triangles","acute, right and obtuse triangles","special triangles such as 30-60-90","derived triangles and triangle centres","spherical and hyperbolic triangles"]}},"sources":[{"title":"Wikidata item Q19821: triangle","url":"https://www.wikidata.org/wiki/Q19821","note":"identity and sense of the item"},{"title":"Wikipedia: Triangle","url":"https://en.wikipedia.org/wiki/Triangle","note":"general description of the item"}],"openQuestions":["Should trigonometry be a separate entry?","How should geometry resources be linked?","How should symbolic uses be attributed?"],"resources":{"spec":"/models/things/publications/thing-q19821/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q19821/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T20:18:40Z","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 2026-10-06T19:51:56+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}}