The Science of the Shulba: A Study in Early Hindu Geometry c11.87

c11.87

The latter part of this rule appears rather to be obscure. How to break up an irregular pentagon into squares? Mahīdhara has failed to grasp the matter accurately and hence made a worse confusion.² I think Kātyāyana has in view a pentagon of the shape *ABCDE* in which *CP*=*PD*=*AM* and *BC*=*MP*=*ED*=*CP*/2 (Fig. 42); *or* in which *CP*, *PD*, *AM*, *BC*, *MP*, *ED* are all equal (Fig. 43). We find description of bricks of these shapes in the *Śulba* of Baudhāyana¹ and they are ordinarily called *haṁsamukhī* ("of the shape of the mouth of a goose"). Obviously a pentagon of that kind can be easily transformed into two or three squares of equal size. So that by combining the transformed squares we can find a square equal to the sum or difference of two or more pentagons.