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.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Define What a cone is.
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.
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.
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.
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
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.QLT
- Other names and narrower kinds
- double cone, light cone, Elliptic cone, Mach cone, closed cone, open cone
What it is Filled
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.
Why it exists Filled
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.
Distinguishing features Filled
- Apex and base
- Ruled surface
- Conic sections
- Physical analogues
What robots and AI may and may not do Filled
Must not
- Confuse slant height with height in calculations.
- Apply right cone formulas to oblique cones without saying so.
- Present results without units or checks where they feed into engineering or manufacturing.
- Mix the geometric sense with traffic cones, pine cones or retinal cones.
Only with a human decision
- Using a computed cone dimension in a structure, container or part that must be safe.
May
- Explain the geometry of cones, including volume, surface area and conic sections.
- Compute cone dimensions for designs supplied by a user, stating units and assumptions.
Moral aspects Filled
- Calculation errors can carry into products and structures.
- Clear teaching helps students who struggle with geometry.
Who is affected
- Students
- Engineers and makers
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q1541599 - registry parent class
- Q937946 - registry parent class
related
- solid figure - in registry terms
- geometric primitive - in registry terms
- conic section - when cut by a plane
- pyramid - the polygonal analogue
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.cone
- Wikidata: Q42344 (https://www.wikidata.org/wiki/Q42344)
Direct properties not applicable Not applicable
- volume: one third base area times height formula
- lateral area of right circular cone: pi r l formula - l is slant height
Plane XCT: no invented physical properties.
Recognition optional Filled
- Base tapering to an apex
- Right, oblique, elliptic and double cones
- Pyramids have polygonal bases; cylinders do not taper
- A solid with a circular base tapering to a point, like a party hat or funnel.
Capabilities and actions required Filled
- define kinds of cone
- compute volume and area
- relate to conic sections
- describe uses in physics and engineering
Hazards and failure modes required Filled
- Confusing slant height with height
- Confusing cone senses across fields
- Errors with oblique cones
Standards and interfaces required Filled
- ISO 80000-2 notation for geometry
Context of use required Filled
- A basic solid in geometry with wide applications.
- 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
Sources Filled
- Wikidata item Q42344: cone - identity and sense of the item
- Wikipedia: Cone - general description of the item
Open questions
- 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?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q42344/spec.json