its gnomon8. There is good reason to believe that this triangle was especially studied by the Pythagoreans; for it lies at the root of many interesting geometrical constructions, such as the regular pentagon, and the mystical ãpentalpha,ã and a whole range of other curious figures beloved of the ancient mathematicians9. {512}
If we take any one of these figures, for instance the isosceles triangle which we have just described, and add to it (or subtract from it) in succession a series of gnomons, so converting it into larger and larger (or smaller and smaller) triangles all similar to the first, we find that