Definition:Side of Rational plus Medial Area

Definition
Let $a, b \in \R_{>0}$ be in the forms:
 * $a = \dfrac \rho {\sqrt {2 \left({1 + k^2}\right)} } \sqrt{\sqrt {1 + k^2} + k}$
 * $b = \dfrac \rho {\sqrt {2 \left({1 + k^2}\right)} } \sqrt{\sqrt {1 + k^2} - k}$

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

Then $a + b$ is the side of the sum of (two) medial areas.

Also see

 * Construction of Components of Side of Rational plus Medial Area


 * Side of Rational plus Medial Area is Irrational