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A sphere is a surface in solid geometry such that all straight lines falling upon it from one particular point inside it are equal.

In the words of Euclid:

When, the diameter of a semicircle remaining fixed, the semicircle is carried round and restored again to the same position from which it began to be moved, the figure so comprehended is a sphere.

(The Elements: Book $\text{XI}$: Definition $14$)


That point is called the center of the sphere.


A radius of a sphere is a straight line segment whose endpoints are the center and the surface of the sphere.

The radius of a sphere is the length of one such radius.


Thus a sphere is the three-dimensional equivalent of the circle.

Every point on the sphere is at the same distance from its center.


The diameter of a sphere is the length of any straight line drawn from a point on the surface to another point on the surface through the center.


By definition, a sphere is made by turning a semicircle around a straight line.

That straight line is called the axis of the sphere.

In the words of Euclid:

The axis of the sphere is the straight line which remains fixed about which the semicircle is turned.

(The Elements: Book $\text{XI}$: Definition $15$)


As the sphere is defined here, it is specified as being the surface only, that is, not the inside.

Also see

  • Results about spheres can be found here.