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Cone

In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the apex or vertex.

Measurement, Overview & Projective geometry

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Explore the main themes, entities and connections around Cone. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Overview

32 related topics

Projective geometry

9 related topics

Further terminology

8 related topics

Measurements and equations

2 related topics

Key facts & relationships

High-confidence facts extracted from structured source data. Use them as anchors for further research.

Euler char.
2
Faces
1 circular face and 1 conic surface
Surface area
πr2 + πrℓ
Symmetry group
O(2)
Type
Solid figure
Volume
(πr2h)/3

Topics to explore

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Overview

Further terminology

Measurements and equations

Proof (no calculus)

Projective geometry

Generalizations

Advanced semantic analysis

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Map overview Semantic statistics

Cone

Nodes68
Edges67
Triples59
Avg. degree1.97
Density0.029412
Components1

How this topic connects Entity context

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Cone

Top relations

is a · 9
Cone → cone with an elliptical base, distance from any point on the circle of its base to the apex via a line segment along the surface of the cone, maximum angle between two generatrix lines, radius of its base, same as for any circle, solid object, straight line passing through the apex about which the cone has a circular symmetry, surface created by the set of lines passing through a vertex and every point on a boundary, three-dimensional figure that tapers smoothly from a flat base
related to External links · 9
Cone → An, Cone An, Double Cone, Eric, Generalized Cone, Maths Is FunPaper, MathWorld, Spinning Cone, Weisstein
related to Step 3: Cavalieri's principle finishes the proof · 8
Cone → Ah, At, By Cavalieri's, Hence, Proof, The, Therefore From, Volume
related to Projective geometry · 6
Cone → According, Halsted, In, Intuitively, Steiner, This
related to Idea of the proof · 5
Cone → Cavalieri's, Conclude, Show, The, Then
related to Further terminology · 4
Cone → Dandelin, For, In, The
related to Generalizations · 3
Cone → An, In, The
related to Proof (no calculus) · 3
Cone → Cavalieri's, It, The
related to Step 1: cross-sections of a cone · 3
Cone → Because, Consider, Slice
see also · 3
Cone → BiconeCone, Conic, DemocritusElliptic

Important terminology Word statistics

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Important terminology

base apex circular area surface displaystyle right height circle called pyramid geometry lines axis volume solid radius line plane conic

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
ConeEuler char.21.00infobox
ConeFaces1 circular face and 1 conic surface1.00infobox
ConeSurface areaπr2 + πrℓ1.00infobox
ConeSymmetry groupO(2)1.00infobox
ConeTypeSolid figure1.00infobox
ConeVolume(πr2h)/31.00infobox
Coneis athree-dimensional figure that tapers smoothly from a flat base0.90text
Coneis asolid object0.90text
Coneis astraight line passing through the apex about which the cone has a circular symmetry0.90text
Coneis aradius of its base0.90text
Coneis amaximum angle between two generatrix lines0.90text
Coneis acone with an elliptical base0.90text
Coneis asurface created by the set of lines passing through a vertex and every point on a boundary0.90text
Coneis adistance from any point on the circle of its base to the apex via a line segment along the surface of the cone0.90text
Coneis asame as for any circle0.90text

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