Definition:Commensurable in Square Only

Definition
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers.

Then $a$ and $b$ are commensurable in square only iff:
 * $\left ({\dfrac a b}\right)^2$ is rational.

but:
 * $\dfrac a b$ is irrational.

That is, such that:
 * $a$ and $b$ are commensurable in square

but:
 * $a$ and $b$ are incommensurable in length.



and:

Also known as
When used in the context of linear measure, the term incommensurable in length only can also be used for this concept.

Also see

 * Definition:Commensurable
 * Definition:Incommensurable


 * Definition:Commensurable in Square
 * Definition:Incommensurable in Square