Definition:Apotome/Second 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 second apotome iff $b \in \Q$ and $\dfrac {\sqrt {a^2 - b^2}} a \in \Q$, where $\Q$ denotes the set of all rational numbers.



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

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