Linked from

The 40 pages that link to Sphere, each with the reason it gives.

• CircleCompared with: It extends the circle’s equal-distance definition from a plane into space.

• Euler characteristicRelated: Its Euler characteristic is two, matching the boundary of any convex polyhedron.

• ArchimedesRelated: Archimedes proved the sphere's surface area and volume in relation to its enclosing cylinder.

• Gaussian curvatureBroader topic: Its two principal curvatures have the same sign, giving positive Gaussian curvature.

• Riemannian manifoldBroader topic: Its induced metric gives a standard example of constant positive curvature.

• Great circleNarrower topic: A great circle is defined by slicing this surface with a central plane.

• Simply connected spaceRelated: Spheres of dimension at least two are simply connected, unlike the circle.

• RadiusNarrower topic: A sphere has radii from its center to its surface, extending the circle idea into space.

• ManifoldBroader topic: The sphere is a compact surface that cannot be covered by one coordinate chart.

• Surface areaBroader topic: Its surface area is four times the area of a great circle.

• Direct imaging of exoplanetsRelated: Its coronagraphs and adaptive optics support direct searches for exoplanets and disks.

• Magnus effectRelated: A spinning sphere provides a standard geometry for measuring lateral force.

• TorusCompared with: Unlike the torus, every loop on a sphere contracts to a point.

• Banach–Tarski paradoxRelated: The construction first exploits rotational symmetries on the sphere.

• Direct imagingBroader topic: Its observations have produced detailed images of exoplanets and circumstellar disks.

• Oblate spheroidCompared with: A sphere has no polar flattening or equatorial bulge.

• HemisphereNarrower topic: A hemisphere is formed by dividing a sphere through its center.

• Rhumb lineNarrower topic: The classical rhumb line is defined on a spherical model of Earth.

• Stereographic projectionNarrower topic: The projection begins with a sphere and sends its surface points to a plane.

• ConeCompared with: A sphere has no base or apex, unlike a cone’s pointed, one-sided form.

• Theorema EgregiumBroader topic: Its positive curvature cannot be removed by bending it into a flat plane without stretching.

• Unit sphereNarrower topic: The unit sphere is the special case with center at the origin and radius one.

• SteradianRelated: The unit’s definition measures a patch on a sphere centered at the angle’s vertex.

• Figure of the EarthCompared with: A sphere is simpler than Earth’s figure but ignores polar flattening.

• Flat torusCompared with: A sphere cannot carry a smooth metric of zero curvature everywhere while retaining its usual topology.

• Surface of revolutionBroader topic: Rotating a semicircle around its diameter generates a sphere.

• Borsuk–Ulam theoremNarrower topic: The theorem applies to spheres in every positive dimension.

• Cartan–Hadamard theoremCompared with: Positive curvature and multiple geodesics prevent the theorem's global exponential-map conclusion.

• Earth ellipsoidCompared with: A sphere ignores polar flattening that Earth ellipsoids explicitly model.

• Hairy ball theoremNarrower topic: The theorem concerns tangent fields on spheres of even dimension.

• Pappus's centroid theoremRelated: A semicircle’s area and centroid path recover the sphere’s volume.

• Solid geometryBroader topic: The sphere is the basic example of a solid defined by a curved boundary.

• 3-sphereNarrower topic: The 3-sphere extends the familiar sphere by one ambient dimension.

• Azimuthal equidistant projectionNarrower topic: The classic form of the projection maps distances measured over a spherical Earth.

• Monge's theoremNarrower topic: The theorem extends from circles to spheres without changing its collinearity conclusion.

• Square degreeRelated: Solid-angle area is measured on a sphere centered at the observation point.

• Carathéodory conjectureBroader topic: Every point on a sphere is umbilic, so it satisfies the claim non-isolatedly.

• Hubble volumeNarrower topic: The Hubble volume applies the sphere’s volume formula to the Hubble radius.

• Measurement geometry (colorimetry)Broader topic: The family that d/8 belongs to, contrasted with directional designs.

• Pappus's area theoremRelated: A semicircle rotated about its diameter generates a sphere whose area the theorem recovers.