{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.circle","code":"thing-q17278","url":"https://ver.cy/models/thing/q17278/","name":"circle","alternateNames":["parallel marker","circle of latitude","tropic","color wheel","spinning pinwheel","unit circle","triangle circles","circumscribed circle","Hart circle","Rrakota","Droz-Farny circle","Soddy circle"],"kind":"thing","status":"published","version":"0.2.0-wave.1","language":"en","classifiers":{"family":"Thing Registry","category":"Cross-cutting context","entryKind":"thing","plane":"XCT","domain":["XCT.QLT"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The set of all points in a plane at a fixed distance, the radius, from a centre point; its circumference is 2 pi r and its area pi r squared, and the unit circle underlies trigonometry; the word also names circles of latitude and circular shapes such as colour wheels.","purpose":"Let an agent explain circles by definition, formulas, theorems and applications, and separate geographic and other senses.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Constant distance from centre","Special conic section","Defines pi","Symmetric in every direction"],"structure":{"bundles":[{"id":"measure","name":"Measure","description":"Formulas.","layers":[{"id":"formulas","name":"Formulas","description":"Circumference and area.","findings":[{"id":"formulas-finding","name":"Formulas","description":"Formulas.","questions":[{"text":"What are the circumference and area for this radius?","kind":"measurement"},{"text":"How precise should pi be?","kind":"boundary"}]}]},{"id":"arcs","name":"Arcs","description":"Arcs and sectors.","findings":[{"id":"arcs-finding","name":"Arcs","description":"Arcs and sectors.","questions":[{"text":"What are the arc length and sector area for this angle?","kind":"measurement"},{"text":"Is the angle in radians?","kind":"boundary"}]}]}]},{"id":"theory","name":"Theory","description":"Theorems.","layers":[{"id":"theorems","name":"Theorems","description":"Circle theorems.","findings":[{"id":"theorems-finding","name":"Theorems","description":"Circle theorems.","questions":[{"text":"Which circle theorem applies here, such as the inscribed angle theorem?","kind":"definition"},{"text":"How is it proved?","kind":"definition"}]}]},{"id":"unit","name":"Unit circle","description":"Trigonometry.","findings":[{"id":"unit-finding","name":"Unit circle","description":"Unit circle.","questions":[{"text":"How does the unit circle define sine and cosine?","kind":"definition"},{"text":"What are the values at key angles?","kind":"measurement"}]}]}]},{"id":"applications","name":"Applications","description":"Uses.","layers":[{"id":"engineering","name":"Engineering","description":"Design.","findings":[{"id":"engineering-finding","name":"Engineering","description":"Engineering.","questions":[{"text":"How are circles used in wheels, gears and pipes?","kind":"definition"},{"text":"Which tolerances apply?","kind":"provenance"}]}]},{"id":"geography","name":"Geography","description":"Circles of latitude.","findings":[{"id":"geography-finding","name":"Geography","description":"Circles of latitude.","questions":[{"text":"What are circles of latitude and the tropics?","kind":"definition"},{"text":"Where are they located?","kind":"provenance"}]}]}]},{"id":"senses","name":"Senses","description":"Disambiguation.","layers":[{"id":"social","name":"Social","description":"Social circles.","findings":[{"id":"social-finding","name":"Social","description":"Social sense.","questions":[{"text":"Is a social circle or group meant?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]},{"id":"design","name":"Design","description":"Colour wheels and icons.","findings":[{"id":"design-finding","name":"Design","description":"Design sense.","questions":[{"text":"Is a colour wheel or a loading icon meant?","kind":"boundary"},{"text":"Which entry fits?","kind":"action"}]}]}]}]},"agentConduct":{"may":["Compute circle properties and explain them.","Distinguish the geometric circle from circles of latitude and other uses of the word."],"mustNot":["Present approximations of pi as exact.","Claim to have squared the circle or present disproven results as valid."],"requiresHuman":["Relying on calculations for a design used by people."]},"ethics":{"considerations":["Accurate mathematics underlies engineering and teaching.","Misleading claims about famous problems can deceive learners."],"affectedParties":["Students and teachers","Users of designs"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q1155211","type":"parent","note":"registry parent class"},{"target":"Q1192156","type":"parent","note":"registry parent class"},{"target":"Q124255","type":"parent","note":"registry parent class"},{"target":"Q1541599","type":"parent","note":"registry parent class"},{"target":"Q15974976","type":"parent","note":"registry parent class"},{"target":"Q204352","type":"parent","note":"registry parent class"},{"target":"conic section","type":"related","note":"category"},{"target":"angular measure","type":"related","note":"angles"},{"target":"trigonometry","type":"related","note":"field"},{"target":"orbit","type":"related","note":"circular orbits"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.circle","Wikidata: Q17278 (https://www.wikidata.org/wiki/Q17278)"]},"properties":{"applicability":"not-applicable","items":["circumference: 2 pi r - formula","area: pi r squared - formula"]},"recognition":{"applicability":"optional","items":["Constant radius from a centre","Symbol pi in formulas","Ellipses have two foci","A round closed curve, as in wheels, coins and drawings."]},"capabilities":{"applicability":"required","items":["calculate circumference, area and arc length","use the unit circle in trigonometry","explain circle theorems","separate other senses of circle"]},"hazards":{"applicability":"required","items":["Confusing radius and diameter","Rounding pi too early"]},"interfaces":{"applicability":"required","items":["No specific regulation"]},"context":{"applicability":"required","items":["Geometry, trigonometry, engineering and design.","unit circle","great and small circles","circles of latitude","inscribed and circumscribed circles","circle packing"]}},"sources":[{"title":"Wikidata item Q17278: circle","url":"https://www.wikidata.org/wiki/Q17278","note":"identity and sense of the item"},{"title":"Wikipedia: Circle","url":"https://en.wikipedia.org/wiki/Circle","note":"general description of the item"}],"openQuestions":["Should circle theorems be separate entries?","How should geographic circles be linked?","How should other senses be split off?"],"resources":{"spec":"/models/things/publications/thing-q17278/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q17278/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-11T14:24:29Z","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 2026-10-06T19:51:55+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}}