{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.plane","code":"thing-q17285","url":"https://ver.cy/models/thing/q17285/","name":"plane","alternateNames":["bisector plane","real plane","plane in physical space","elliptic plane","rectifying plane","axis/plane of symmetry (akin to the mirror's surface)","fault plane","origin plane","projection plane","Laplace plane","normal plane","tangent plane"],"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 flat two-dimensional surface extending infinitely in all directions, one of the basic objects of Euclidean geometry, determined by three non-collinear points, a line and a point outside that line, or two intersecting or distinct parallel lines, and appearing as the real plane of coordinate geometry, the complex plane, planes in physical space, and special planes such as bisector, symmetry and rectifying planes; planes are described by linear equations in three dimensions and are fundamental in geometry, physics and engineering.","purpose":"Let an agent explain the plane as a geometric object, support equations and calculations involving planes, describe special planes and their uses, and separate this sense from aircraft and other meanings.","scope":{"in":[],"out":[],"boundaries":[]},"distinguishingFeatures":["Two-dimensional","Flat","Linear equation","Fundamental object"],"structure":{"bundles":[{"id":"understand","name":"Understand","description":"What a plane is.","layers":[{"id":"concept","name":"Concept","description":"Concept and determination.","findings":[{"id":"concept-finding","name":"Concept","description":"Concept.","questions":[{"text":"What is a plane, and how is it determined by points, lines or a normal vector?","kind":"definition"},{"text":"Is the geometric plane or another sense meant?","kind":"boundary"}]}]},{"id":"equations","name":"Equations","description":"Equations.","findings":[{"id":"equations-finding","name":"Equations","description":"Equations.","questions":[{"text":"How are planes described by linear equations and vector forms in three dimensions?","kind":"definition"},{"text":"Which entry fits analytic geometry?","kind":"action"}]}]}]},{"id":"compute","name":"Compute","description":"Calculations.","layers":[{"id":"calculate","name":"Calculate","description":"Plane calculations.","findings":[{"id":"calculate-finding","name":"Calculate","description":"Calculations.","questions":[{"text":"How are distances, intersections and angles involving this plane computed?","kind":"action"},{"text":"Which entry fits vector geometry?","kind":"action"}]}]},{"id":"transform","name":"Transform","description":"Transformations.","findings":[{"id":"transform-finding","name":"Transform","description":"Transformations.","questions":[{"text":"How do reflections, rotations and projections act on and with planes?","kind":"definition"},{"text":"Which entry fits geometric transformations?","kind":"action"}]}]}]},{"id":"special","name":"Special","description":"Special planes.","layers":[{"id":"kinds","name":"Kinds","description":"Named planes.","findings":[{"id":"kinds-finding","name":"Kinds","description":"Named.","questions":[{"text":"What are symmetry, bisector, rectifying, osculating and other named planes, and where are they used?","kind":"definition"},{"text":"Which entry fits differential geometry?","kind":"action"}]}]},{"id":"noneuclidean","name":"Non-Euclidean","description":"Non-Euclidean planes.","findings":[{"id":"noneuclidean-finding","name":"Non-Euclidean","description":"Non-Euclidean.","questions":[{"text":"How do the elliptic and hyperbolic planes differ from the Euclidean plane?","kind":"definition"},{"text":"Which entry fits non-Euclidean geometry?","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 the concept of the plane develop from Euclid to modern geometry?","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 planes be taught in geometry courses?","kind":"action"},{"text":"Which misconceptions arise?","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain planes in geometry, their equations and properties.","Compute plane intersections and distances, stating precision."],"mustNot":["Confuse the geometric plane with an aircraft or a tool.","Hide numerical errors in plane calculations used in engineering or surveying.","Present an approximation as exact."],"requiresHuman":["Using computed geometry in safety-critical design."]},"ethics":{"considerations":["Geometry errors propagate into structures people rely on.","Teaching should be accurate for learners."],"affectedParties":["Learners","Engineers","Surveyors"]},"owners":{"steward":"Nobody: an abstract concept held in common.","roles":[],"masterSystems":[]},"relations":[{"target":"Q1541599","type":"parent","note":"registry parent class"},{"target":"Q211548","type":"parent","note":"registry parent class"},{"target":"Q222032","type":"parent","note":"registry parent class"},{"target":"Q3505239","type":"parent","note":"registry parent class"},{"target":"Q657586","type":"parent","note":"registry parent class"},{"target":"Q66539726","type":"parent","note":"registry parent class"},{"target":"two-dimensional space","type":"related","note":"category"},{"target":"geometric primitive","type":"related","note":"category"},{"target":"line","type":"related","note":"lines lie in planes"},{"target":"imaginary","type":"related","note":"the complex plane"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.plane","Wikidata: Q17285 (https://www.wikidata.org/wiki/Q17285)"]},"properties":{"applicability":"not-applicable","items":[]},"recognition":{"applicability":"optional","items":["Flat surface extending infinitely","Determined by three points","An aircraft and a woodworking plane are other senses","Not physical; an idealised flat surface."]},"capabilities":{"applicability":"required","items":["explain the geometric plane","support equations and calculations","describe special planes","separate other senses"]},"hazards":{"applicability":"required","items":["Confusing senses of plane","Errors in plane equations and normals","Confusing plane and surface"]},"interfaces":{"applicability":"required","items":["Mathematical notation conventions","No regulation"]},"context":{"applicability":"required","items":["Flat two-dimensional geometric surface.","Euclidean plane","coordinate and complex planes","planes in three-dimensional space","special planes such as symmetry and bisector planes","non-Euclidean planes such as the elliptic plane"]}},"sources":[{"title":"Wikidata item Q17285: plane","url":"https://www.wikidata.org/wiki/Q17285","note":"identity and sense of the item"},{"title":"Wikipedia: Euclidean plane","url":"https://en.wikipedia.org/wiki/Euclidean_plane","note":"general description of the item"}],"openQuestions":["Should the complex plane be a separate entry?","How should geometry resources be linked?","How should other senses be separated?"],"resources":{"spec":"/models/things/publications/thing-q17285/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q17285/spec.json"],"providers":["Claude"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T03:14:16Z","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 2026-10-07T10:10:26+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}}