Definition:Irrational Line Segment

Definition

An irrational line segment is a line segment such that the square of whose length is an irrational number of units of area.

In the words of Euclid:

With these hypotheses, it is proved that there exist straight lines infinite in multitude which are commensurable and incommensurable respectively, some in length only, and others in square also, with an assigned straight line. Let then the assigned straight line be called rational, and those straight lines which are commensurable with it, whether in length and in square or square only, rational, but those which are incommensurable with it irrational.

(The Elements: Book $\text{X}$: Definition $3$)

Also known as

This is also known as an irrational straight line.

Also see

• Definition:Squarely Irrational Number
• Definition:Rational Line Segment