Definition:Rational Line Segment

Definition
A rational line segment is a line segment the square of whose length is a rational number of units of area.

In other words, a rational line segment is a line segment whose length belongs to the set $\left\{{x \in \R_{>0} : x^2 \in \Q}\right\}$.



Also known as
This is also known as a rational straight line.

Euclid's Definition of Rational
Note that this usage of rational differs from the contemporary definition of rational number.

Let $AB$ be a straight line whose length $\rho$ is a rational number of units.

Then a straight line whose length $\rho \sqrt k$, where $k$ is an integer, is also rational straight line.

Thus, to, a straight line of length $\sqrt 2$ is defined as a rational straight line, despite the fact that its length is an irrational number of units.

Also see

 * Definition:Irrational Line Segment