Definition:Plane Number

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A plane number is the product of two (natural) numbers.

In the words of Euclid:

And, when two numbers having multiplied one another make some number, the number so produced is called plane, and its sides are the numbers which have multiplied one another.

(The Elements: Book $\text{VII}$: Definition $16$)


The side of a plane number is one of the (natural) numbers which are its divisors.


A example of a plane number is $6 = 2 \times 3$.

Its divisors $2$ and $3$ are its sides.

Similar Numbers

Let $m$ and $n$ be plane numbers.


$m = p_1 \times p_2$ where $p_1 \le p_2$
$n = q_1 \times q_2$ where $q_1 \le q_2$

Then $m$ and $n$ are similar if and only if:

$p_1 : q_1 = p_2 : q_2$

Also see