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Sphere

A sphere (from Ancient Greek σφαῖρα (sphaîra) 'ball') is a surface analogous to the circle, a curve. In solid geometry, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. That given point is the center of the sphere, and the distance r is the sphere's radius. The earliest known mentions of…

History, Basic terminology & Properties

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Key facts & relationships

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Euler char.
2
Surface area
4πr2
Symmetry group
O(3)
Type
Smooth surface Algebraic surface

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Overview

Basic terminology

Equations

Properties

Treatment by area of mathematics

Curves on a sphere

Generalizations

History

Gallery

Regions

Notes and references

Advanced semantic analysis

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Map overview Semantic statistics

Sphere

Nodes209
Edges208
Triples205
Avg. degree1.99
Density0.009569
Components1

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Sphere

Top relations

related to Further reading · 34
Sphere → Abraham Adrian, Advanced Engineering Mathematics, Advanced Methods, Albert, An Alphabetical Journey Through, An Introduction, Analytic Geometry, April, Bibcode, Dover, Dunham, Erwin, Frederick, Great Proofs, Higher Geometry, ISBN, January, John, Kreyszig, Mathematical Snapshots
related to Properties of the sphere · 33
Sphere → All, Also, Any, Apollonius, At, Circular, David Hilbert, Each, Euler, For, Gaussian, Geodesics, Geometry, Hence, Imagination, In, It, Many, Meissner, Numerous
is a · 19
Sphere → 2-sphere, boundary of a, circle of radius rS2, fundamental surface in many fields of mathematics, important concept in astronomy, inverse image of a one-point set under the continuous function, one with the smallest surface area, only embedded surface that lacks boundary or singularities with constant positive mean curvature, only surface that lacks a boundary with constant, quadric surface, same as the area of the cross section of the circumscribing cylinder, set of points that are all at the same distance r from a given point in three-dimensional space, shorter segment of the great circle that includes the points.Many theorems from classical geometry hold true for spherical geometry as well, smooth surface with constant Gaussian curvature at each point equal to 1/r2, solid of maximum volume.Archimedes wrote about the problem of dividing a sphere into segments whose volumes are in a given ratio, special type of ellipsoid of revolution, sphere with unit radius, spherical conic, surface called the real projective plane
related to history · 15
Sphere → Archimedes, Archimedes's On, Cnidus, Cylinder, Dionysodorus, Euclid, Euclid's Elements, Eudoxus, Greeks, Quhi, The, XI, XII, XIII, Zenodorus
related to Gallery · 11
Sphere → An, Australian, Deck, Einstein, England, Gravity Probe, It, July, King, Spheres, This
related to Loxodrome · 10
Sphere → Earth, East, For, In, Loxodromes, Mercator, North, South, Two, West
related to Enclosed volume · 9
Sphere → Archimedes, BCE, Cavalieri's, CCFFCC, Cylinder, F0F2F5, In, On, This
related to Spherical geometry · 9
Sphere → Also, Euclidean, For, In, Many, Measuring, On, Spherical, The
related to Differential geometry · 8
Sphere → Also, As, Gauss, Gauss's Theorema Egregium, Gaussian, The, Therefore, This
related to Basic terminology · 6
Sphere → As, Diameters, If, Like, Radius, Two

Important terminology Word statistics

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Important terminology

surface points plane circle radius spherical spheres volume center two point area curvature also called constant geometry given distance intersection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
SphereEuler char.21.00infobox
SphereSurface area4πr21.00infobox
SphereSymmetry groupO(3)1.00infobox
SphereTypeSmooth surface Algebraic surface1.00infobox
SphereVolume.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:cent…1.00infobox
Sphereis aset of points that are all at the same distance r from a given point in three-dimensional space0.90text
Sphereis afundamental surface in many fields of mathematics0.90text
Sphereis aimportant concept in astronomy0.90text
Sphereis asphere with unit radius0.90text
Sphereis aboundary of a0.90text
Sphereis aquadric surface0.90text
Sphereis asame as the area of the cross section of the circumscribing cylinder0.90text
Sphereis aspecial type of ellipsoid of revolution0.90text
Sphereis aone with the smallest surface area0.90text
Sphereis aonly embedded surface that lacks boundary or singularities with constant positive mean curvature0.90text
Sphereis aonly surface that lacks a boundary with constant0.90text
Sphereis ashorter segment of the great circle that includes the points.Many theorems from classical geometry hold true for spherical geometry as well0.90text
Sphereis asmooth surface with constant Gaussian curvature at each point equal to 1/r20.90text
Sphereis asurface called the real projective plane0.90text
Sphereis aspherical conic0.90text
Sphereis acircle of radius rS20.90text
Sphereis a2-sphere0.90text
Sphereis ainverse image of a one-point set under the continuous function0.90text
Sphereis asolid of maximum volume.Archimedes wrote about the problem of dividing a sphere into segments whose volumes are in a given ratio0.90text

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