Archimedes is the first mathematician known to have studied the properties of this shape. He named it an arbelos, the Greek word for a shoemaker?s knife.
The shape is made from three semicircles defined such that the sum of the diameters of the two smaller semicircles is equal to the diameter of the largest semicircle.
There is a relationship between the perimeter of the arbelos and the radii of the semicircles; also between the area of the arbelos and the radii of the semicircles. The purpose of this activity, which has been developed from an old Scottish Standard Grade Investigation, is to investigate these relationships and conjecture a formal relationship between them.
A lesson using this activity is described by Allan Duncan in a booklet entitled Inspired Connections in Maths Lessons. For a pdf version of the entire booklet please click here.