Definition:Apotome/Fifth Apotome

Definition
Let $a, b \in \R_{>0}$ be (strictly) positive real numbers such that $a - b$ is an apotome.

Then $a - b$ is a fifth apotome iff $b \in \Q$ and $\dfrac {\sqrt {a^2 - b^2}} a \notin \Q$.



Example
When $a = \sqrt {13}$ and $b = 3$:

Therefore $\sqrt {13} - 3$ is a fifth apotome.