# 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**.

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

### Center

That point is called the **center** of the sphere.

### Radius

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.

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

## Note

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

## Sources

- 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next): Entry:**sphere** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**sphere**