English: Straightedge and compass construction of the length
, given the length
and the unit length. The proof relies on
Thales's theorem (blue circle) to obtain a right triangle with hypothenuse length
, and on the
Pythagorean theorem to set up equations about its height and side lengths, viz.
(from the left triangle; trivially satisfied),
(from the right triangle; trivially satisfied), and
(from the big triangle). Their unique positive solution is
.