Quadratrix of Hippias
Hippias of Elis (460 - 400 BC) was a statesman and a philosopher. His only contribution to mathematics is the invention of Quadratrix of Hippias - a special curve that can be used for squaring a circle.
Quadratrix of Hippias can be obtained as follows:
Let ABCD be a unit square. Using the slider in the above diagram to change the value of t from 0 to 1, the red line segment will rotate about B and the blue line segment will slide down, both at constant speed. The intersection point F will trace out the Quadratrix of Hippias. Check the box to show the curve.
When , , from which the length can be constructed easily by straightedge and compass.