Definition:Apotome of Medial/First Apotome

Definition
Let $a, b \in \set {x \in \R_{>0} : x^2 \in \Q}$ be two rationally expressible numbers such that $a > b$ be in the forms:
 * $a = k^{1/4} \rho$
 * $b = k^{3/4} \rho$

where:
 * $\rho$ is a rational number
 * $k$ is a rational number whose square root is irrational.

Then $a - b$ is a first apotome of a medial.

Also see

 * First Apotome of Medial is Irrational


 * Definition:Apotome


 * Definition:Medial


 * Definition:Second Apotome of Medial