Fourth Apotome/Example

Example of Fourth Apotome
Let $a, b \in \set {x \in \R_{>0} : x^2 \in \Q}$ be two rationally expressible numbers such that $a - b$ is an apotome.

By definition, $a - b$ is a fourth apotome :
 * $(1): \quad a \in \Q$
 * $(2): \quad \dfrac {\sqrt {a^2 - b^2}} a \notin \Q$

where $\Q$ denotes the set of rational numbers.

Let $a = 3$ and $b = \sqrt 2$.

Then:

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