Definition:Sphere/Geometry
Definition
A sphere is the locus of all points which are a fixed distance from a distinguished point.
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 distinguished 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.
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.
Also see
- Results about spheres can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): sphere
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): sphere
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): sphere