To construct your own Wheel of Theodorus using Euclidean tools, follow the steps described and illustrated below.
1. Construct right triangle ABC, with base = 1 unit and height = 1 unit.
2. Using hypotenuse AB as the base of the next triangle, construct a perpendicular to line AB through point A.
3. Mark off 1 unit as the height of right triangle DBA.
4. Construct triangle DBA.
5. Continue using the hypotenuse of the newly constructed right triangle as the base of the next triangle iteration. The height should continue to be 1 unit.
6. Continue constructing your “Wheel of Theodorus” until the final picture is pleasing to the eye.
7. What is the length of the hypotenuse of the final right triangle? Explain or show how you know using the Pythagorean theorem.