Sphere

A sphere is the set of points in three-dimensional space at a fixed distance from a center. Its radius is that fixed distance.

Euclidean space: A space with flat geometry governed by Euclid’s parallel postulate and distance rules. A sphere is defined here using ordinary three-dimensional Euclidean distance.
Sphere equation: An equation describing points at a fixed distance from a center in Cartesian coordinates. It translates the defining equal-distance condition into coordinates.
Earth: The third planet from the Sun, an oblate spheroid shaped by rotation and gravity. Earth is often approximated as a sphere in maps and basic calculations.
Circle: The set of points in a plane at a fixed distance from a center. A circle is the two-dimensional counterpart of a sphere.
Distance: A measure of how far apart two points are. Every point on a sphere has the same distance from its center.
Spherical coordinates: A coordinate system that locates points using radial distance and two angles. Its radial coordinate makes the sphere a constant-radius surface.
Celestial sphere: An imaginary sphere centered on an observer, onto which celestial objects are projected. It uses spherical geometry to describe apparent positions in the sky.
Ellipsoid: A quadric surface formed by scaling a sphere by different factors along three perpendicular axes. Unequal axis lengths remove the sphere’s uniform radius.
Center (geometry): A point equidistant from the relevant boundary points of a geometric figure. The sphere’s fixed distance is measured outward from this defining point.
Surface area: The total area covering the boundary of a three-dimensional object. A sphere of radius r has surface area 4πr².

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