LIU HUI’S PROOF OF THE THEOREM OF BĀUDHAYANA
Liu Hui lived in the third century CE. His proof was given in algorithmic form and corresponds to the figure below. It starts with a rectangle of 3 by 4 (HIGD). The diagonal (HG) is 5. Draw a square on this diagonal (GHFF). By this ‘piling up of rectangles’ (as the Chinese put it), visible inspection shows that the theorem holds: 3-4-5 is not only a ‘Pythagorean triple’ of numbers but a ‘Pythagoraean triangle’ in geometry: the square on 3 is AMIH, on 4 is MBFL and on 5 is GHEF. The reader may be able to see this but for moderns the algebraic notation a2 + b2 = c2 is not only much easier, but it is generally applicable: to other triples of integers, to rational, real numbers, etc. But algebra did not exist in 263 CE.
