# 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.