{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.base-q2553861","code":"thing-q2553861","url":"https://ver.cy/models/thing/q2553861/","name":"base","alternateNames":["tunc"],"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.QTY"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"In geometry, the side or face of a figure on which it is considered to stand or from which its height is measured, such as the base of a triangle, parallelogram or trapezoid, the base faces of a prism or cylinder, the base of a pyramid or cone, and the bases of a frustum; the choice of base is often conventional, and formulas for area and volume are expressed in terms of base and height, with the word also used for the base of a logarithm or number system in other senses.","purpose":"Let an agent explain the base of a geometric figure and its role in area and volume formulas, support calculations, separate the geometric sense from bases of numbers, logarithms and chemistry, and support learning.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Conventional choice","Paired with height","Formula role","Two- and three-dimensional"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a base is.","layers":[{"id":"concept","name":"Concept","description":"Concept.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is the base of a geometric figure, how is it chosen, and how does it pair with height?","kind":"definition"},{"text":"Is the geometric base or a number, logarithm or chemical base meant?","kind":"boundary"}]}]},{"id":"figures","name":"Figures","description":"Bases of figures.","findings":[{"id":"figures-finding","name":"Figures","description":"Figures.","questions":[{"text":"What are the bases of triangles, parallelograms, trapezoids, prisms, pyramids, cylinders, cones and frustums?","kind":"definition"},{"text":"Which entry fits a specific figure?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Calculations.","layers":[{"id":"area","name":"Area","description":"Area formulas.","findings":[{"id":"area-finding","name":"Area","description":"Area.","questions":[{"text":"How are areas computed from base and height for this figure?","kind":"action"},{"text":"Which entry fits area?","kind":"action"}]}]},{"id":"volume","name":"Volume","description":"Volume formulas.","findings":[{"id":"volume-finding","name":"Volume","description":"Volume.","questions":[{"text":"How are volumes of prisms, pyramids, cylinders and cones computed from base area and height?","kind":"action"},{"text":"Which entry fits volume?","kind":"action"}]}]}]},{"id":"other","name":"Other","description":"Other senses.","layers":[{"id":"numbers","name":"Numbers","description":"Bases of number systems and logarithms.","findings":[{"id":"numbers-finding","name":"Numbers","description":"Numbers.","questions":[{"text":"What are the base of a number system and the base of a logarithm?","kind":"definition"},{"text":"Which entry fits numeral systems?","kind":"action"}]}]},{"id":"chemistry","name":"Chemistry","description":"Chemical bases.","findings":[{"id":"chemistry-finding","name":"Chemistry","description":"Chemistry.","questions":[{"text":"What is a base in chemistry, and how does it differ from the geometric sense?","kind":"definition"},{"text":"Which entry fits acids and bases?","kind":"action"}]}]}]},{"id":"learn","name":"Learn","description":"Teaching.","layers":[{"id":"teach","name":"Teach","description":"Teaching.","findings":[{"id":"teach-finding","name":"Teach","description":"Teaching.","questions":[{"text":"How can base and height be taught to avoid orientation misconceptions?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]},{"id":"history","name":"History","description":"History.","findings":[{"id":"history-finding","name":"History","description":"History.","questions":[{"text":"How did the terminology of base and height develop in geometry?","kind":"provenance"},{"text":"Which references are standard?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Identify the base of a figure and use it consistently with the matching height in calculations.","Explain that any side or face can serve as a base depending on orientation."],"mustNot":["Mix up the geometric base with the base of a number system or a chemical base.","Pair a base with a height that is not perpendicular to it in an area or volume formula.","Present a computed area or volume without stating which base was used."],"requiresHuman":["Relying on computed dimensions for construction or manufacturing decisions."]},"ethics":{"considerations":["Small errors in basic geometry propagate into wrong measurements and costs.","Clear teaching of fundamentals affects who succeeds in mathematics."],"affectedParties":["Students","Teachers","People relying on calculations"]},"owners":{"steward":"Nobody: a mathematical concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q3847020","type":"parent","note":"registry parent class"},{"target":"Q815741","type":"parent","note":"registry parent class"},{"target":"facet","type":"related","note":"category"},{"target":"geometric shape","type":"related","note":"category"},{"target":"plane","type":"related","note":"bases lying in planes"},{"target":"triangle","type":"related","note":"a figure with a base"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.base-q2553861","Wikidata: Q2553861 (https://www.wikidata.org/wiki/Q2553861)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Side or face from which height is measured","Triangles, prisms, pyramids, cones","Number base, logarithm base and chemical base are other senses","Not physical; a designated side or face of a shape."]},"capabilities":{"applicability":"required","items":["explain the geometric base","support calculations","separate other senses","support learning"]},"hazards":{"applicability":"required","items":["Confusing senses of base","Mismatching base and height in formulas","Assuming the base must be at the bottom"]},"interfaces":{"applicability":"required","items":["Mathematical terminology conventions","No regulation"]},"context":{"applicability":"required","items":["The side or face from which a figure height is measured.","bases of triangles and quadrilaterals","bases of prisms and cylinders","bases of pyramids and cones","bases of frustums","bases in coordinate and solid geometry"]}},"sources":[{"title":"Wikidata item Q2553861: base","url":"https://www.wikidata.org/wiki/Q2553861","note":"identity and sense of the item"},{"title":"Wikipedia: Base (geometry)","url":"https://en.wikipedia.org/wiki/Base_%28geometry%29","note":"general description of the item"}],"openQuestions":["Should other senses of base be separate entries?","How should geometry resources be linked?","How should formula references be linked?"],"resources":{"spec":"/models/things/publications/thing-q2553861/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q2553861/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T03:20:15Z","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 2026-10-06T19:51:57+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}}