Definition:Medial Area

Definition

A medial area is an area which is equal to the square on a medial straight line.

Thus an area $A$ is medial if and only if it is of the form:

$A = \rho^2 \sqrt k$

where:

$\rho$ is a rational number

$k$ is a rational number whose square root is irrational.

In the words of Euclid:

From this it is manifest that an area commensurable with a medial area is medial.

(The Elements: Book $\text{X}$: Proposition $23$ : Porism)

Also see

• Medial is Irrational