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.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
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.
A flat two-dimensional surface extending infinitely in all directions, one of the basic objects of geometry, determined by three non-collinear points, a line and a point, or two intersecting or 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, rectifying and elliptic planes; planes are described by linear equations in three dimensions and are fundamental in geometry, physics and engineering.
What it is for: Flat two-dimensional geometric surface.
It can be explain the geometric plane; support equations and calculations; describe special planes; separate other senses.
Distinguishing features
Two-dimensional
Flat
Linear equation
Fundamental object
What it looks like
Not physical; an idealised flat surface.
How it is recognised
Flat surface extending infinitely
Determined by three points
An aircraft and a woodworking plane are other senses
Related models
is a kind of - category
is a kind of - category
is related to - lines lie in planes
is related to - the complex plane
In practice
Families and kinds
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
Standards and regulation
Mathematical notation conventions
No regulation
Failure modes and hazards
Confusing senses of plane
Errors in plane equations and normals
Confusing plane and surface
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.plane-2
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a plane is.
Geometry.
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.
Practice.
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.
Context.
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.
Education.
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
What the second pass must settle
- Should the complex plane be a separate entry?
- How should geometry resources be linked?
- How should other senses be separated?