plane
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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What a plane is.
Concept
Concept and determination.
Concept
Concept.
- What is a plane, and how is it determined by points, lines or a normal vector? definition
- Is the geometric plane or another sense meant? boundary
Equations
Equations.
Equations
Equations.
- How are planes described by linear equations and vector forms in three dimensions? definition
- Which entry fits analytic geometry? action
Compute Calculations.
Calculate
Plane calculations.
Calculate
Calculations.
- How are distances, intersections and angles involving this plane computed? action
- Which entry fits vector geometry? action
Transform
Transformations.
Transform
Transformations.
- How do reflections, rotations and projections act on and with planes? definition
- Which entry fits geometric transformations? action
Special Special planes.
Kinds
Named planes.
Kinds
Named.
- What are symmetry, bisector, rectifying, osculating and other named planes, and where are they used? definition
- Which entry fits differential geometry? action
Non-Euclidean
Non-Euclidean planes.
Non-Euclidean
Non-Euclidean.
- How do the elliptic and hyperbolic planes differ from the Euclidean plane? definition
- Which entry fits non-Euclidean geometry? action
Learn History and teaching.
History
History.
History
History.
- How did the concept of the plane develop from Euclid to modern geometry? provenance
- Which references are standard? provenance
Teach
Teaching.
Teach
Teaching.
- How can planes be taught in geometry courses? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- 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
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Two-dimensional
- Flat
- Linear equation
- Fundamental object
What robots and AI may and may not do Filled
Must not
- 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.
Only with a human decision
- Using computed geometry in safety-critical design.
May
- Explain planes in geometry, their equations and properties.
- Compute plane intersections and distances, stating precision.
Moral aspects Filled
- Geometry errors propagate into structures people rely on.
- Teaching should be accurate for learners.
Who is affected
- Learners
- Engineers
- Surveyors
Owners Filled
Steward
Nobody: an abstract concept held in common.
Links to other meta-models Filled
parent
- Q1541599 - registry parent class
- Q211548 - registry parent class
- Q222032 - registry parent class
- Q3505239 - registry parent class
- Q657586 - registry parent class
- Q66539726 - registry parent class
related
- two-dimensional space - category
- geometric primitive - category
- line - lines lie in planes
- imaginary - the complex plane
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.plane
- Wikidata: Q17285 (https://www.wikidata.org/wiki/Q17285)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Flat surface extending infinitely
- Determined by three points
- An aircraft and a woodworking plane are other senses
- Not physical; an idealised flat surface.
Capabilities and actions required Filled
- explain the geometric plane
- support equations and calculations
- describe special planes
- separate other senses
Hazards and failure modes required Filled
- Confusing senses of plane
- Errors in plane equations and normals
- Confusing plane and surface
Standards and interfaces required Filled
- Mathematical notation conventions
- No regulation
Context of use required Filled
- 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 Filled
- Wikidata item Q17285: plane - identity and sense of the item
- Wikipedia: Euclidean plane - general description of the item
Open questions
- Should the complex plane be a separate entry?
- How should geometry resources be linked?
- How should other senses be separated?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q17285/spec.json