cone
Let an agent define cones and their kinds, compute volume, surface area and sections, relate cones to conic sections, and describe uses of the cone concept in physics and other fields.
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 define cones and their kinds, compute volume, surface area and sections, relate cones to conic sections, and describe uses of the cone concept in physics and other fields.
A three-dimensional geometric figure that tapers from a flat base, usually a circle, to a point called the apex, with a surface formed by lines from the apex to the base boundary, including right and oblique circular cones, elliptic cones and double cones extending through the apex; cones appear as solids in geometry and engineering, as conic sections when cut by planes, and in physics as light cones and Mach cones.
What it is for: A basic solid in geometry with wide applications.
It can be define kinds of cone; compute volume and area; relate to conic sections; describe uses in physics and engineering.
Distinguishing features
Apex and base
Ruled surface
Conic sections
Physical analogues
What it looks like
A solid with a circular base tapering to a point, like a party hat or funnel.
Physical character
volume: one third base area times height formula
lateral area of right circular cone: pi r l formula - l is slant height
How it is recognised
Base tapering to an apex
Right, oblique, elliptic and double cones
Pyramids have polygonal bases; cylinders do not taper
Related models
is a kind of - in registry terms
is a kind of - in registry terms
yields - when cut by a plane
is related to - the polygonal analogue
In practice
Families and kinds
right and oblique circular cones
elliptic cones
double cones and cones in projective geometry
truncated cones or frustums
open and closed cones in topology and convex analysis
light cones and Mach cones in physics
Standards and regulation
ISO 80000-2 notation for geometry
Failure modes and hazards
Confusing slant height with height
Confusing cone senses across fields
Errors with oblique cones
Also called
Where this came from
wikidata · CC0 1.0
Also registered as vr.tr.cone-plant
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Define What a cone is.
Definition.
Definition
Definition and kinds.
Definition
Definition.
- What is a cone, and what kinds exist? definition
- Is the solid a cone, a pyramid, a cylinder or a frustum? boundary
Sections
Conic sections.
Sections
Sections.
- How do plane cuts of a cone give circles, ellipses, parabolas and hyperbolas? definition
- Which entry fits conic section? action
Compute Computation.
Computation.
Volume
Volume and area.
Volume
Volume.
- How are volume, surface area and slant height computed for cones and frustums? action
- What are the values for the cone in question? measurement
Coordinates
Equations.
Coordinates
Coordinates.
- How are cones described by equations in coordinates? action
- Which entry fits quadric surface? action
Fields Cones across fields.
Application.
Physics
Light and Mach cones.
Physics
Physics.
- What are light cones in relativity and Mach cones in supersonic flow? provenance
- Which entry fits the specific physics concept? action
Mathematics
Cones in topology and analysis.
Mathematics
Mathematics.
- What are cones in topology, convex analysis and projective geometry? provenance
- Which references are standard? provenance
Context Uses and teaching.
Context.
Uses
Engineering and everyday uses.
Uses
Uses.
- Where do cones appear in engineering, design and everyday objects? provenance
- Which entry fits the specific application? action
Teach
Teaching.
Teach
Teaching.
- How are cones taught, and which misconceptions arise? provenance
- Which sources are cited? provenance
What the second pass must settle
- Should light cone and conic section be separate primary entries?
- How should geometry references be linked?
- The registry entry has merged aliases naming physics and topology senses; should they be split off?