Definition:Apotome/Third Apotome

Definition
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.

Then $a - b$ is a third apotome :
 * $(1): \quad a \notin \Q$
 * $(2): \quad b \notin \Q$
 * $(3): \quad \dfrac {\sqrt {a^2 - b^2}} a \in \Q$

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



Also see

 * Definition:First Apotome
 * Definition:Second Apotome
 * Definition:Fourth Apotome
 * Definition:Fifth Apotome
 * Definition:Sixth Apotome