Definition:Apotome/Fourth 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 fourth apotome iff $a \in \Q$ and $\dfrac {\sqrt {a^2 - b^2}} a \notin \Q$.



Example
When $a = 3$ and $b = \sqrt 2$,

Therefore $3 - \sqrt 2$ is a fourth apotome.