# Base

A two-dimensional figure's side or a three-dimensional figure's face by which the figure is measured or named.

Example:

## Meaning

The word *base* has several meaning in mathematics depending on the context in which it arises. Most of the uses are related to the common meaning of base as a *starting point* or *building block*.

In geometry, for example, a student may say that the area of a rectangle is equal to the length of its base times its height. In this case, *base* refers to one side of the rectangle, typically the side oriented most nearly horizontally from the perspective of the viewer.

In algebra, a student may wish to compute 3^{2}. In this case, the number 3 is the *base* and the number 2 is the power. More generally, when describing the expression *b*^{a} we call *b* the base.

In arithmetic (or number theory), the word *base* is related to place value and how a number is represented. Students in elementary school learn to use the *base 10* system. Here, each place value is a power of 10. In contrast, computers represent information as numbers written to *base 2*. Here, each place value is a power of 2 (and the only allowable digits are 0 and 1). Of course, numbers can be written to other bases as well.

The word *base* occurs when describing mathematical induction. Proofs by mathematical induction are often conceived in two steps: a *base case* followed by an inductive step.