Lunulae de hippocrates biography

Geometric construction

In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.

Equivalently, it is a non-convex plane region bounded by one 180-degree circular arc and one 90-degree circular arc. It was the first curved figure to have its exact area calculated mathematically.^[1]

History

Hippocrates wanted to solve the classic problem of squaring the circle, i.e.

constructing a square by means of straightedge and compass, having the same area as a given circle.^[2][3] He proved that the lune bounded by the arcs labeled E and F in the figure has the same area as triangle ABO.

This afforded some hope of solving the circle-squaring problem, since the lune is bounded only by arcs of circles. Heath concludes that, in proving his result, Hippocrates was also the f