Definition:Apotome/Fifth Apotome

Definition
Let $a$ and $b$ be two positive real numbers, such that $a - b$ is an apotome.

Then $a - b$ is a fifth apotome iff $b \in \Q$ and $\frac {\sqrt {a^2 - b^2}} a \not \in \Q$.



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

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