Definition:Sphere/Geometry

Definition

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.

Center

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.

Diameter

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.

Axis

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.

Note

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.