Definition:Square Number/Definition 1

Definition

An integer $n$ is classified as a square number if and only if:

$\exists m \in \Z: n = m^2$

where $m^2$ denotes the integer square function.

Euclid's Definition

In the words of Euclid:

A square number is equal multiplied by equal, or a number which is contained by two equal numbers.

(The Elements: Book $\text{VII}$: Definition $18$)

Examples of Square Numbers

The first few square numbers are as follows:

Sequence of Square Numbers

The sequence of square numbers, for $n \in \Z_{\ge 0}$, begins:

$0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, \ldots$

Also see

• Equivalence of Definitions of Square Number

Sources

• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): square number