Chinese interest in right-angled triangles

Abstract

This paper traces briefly the discovery of the Pythagorean theorem and the contradictory views about the origin of the famous problem. The earliest evidence of the theorem goes back to a cuneiform text of the Old Babylonian period (c. 1900 to 1600 B.C.). In the East, the theorem is found to have been applied in the Sulba-sutras (c. 800 to 500 B.C.) by the Vedic Hindus, but with no geometric proof given by them. In China, a discussion of the theorem is found in the Chou-pi suan-ching (c. 5th century B.C. to 3rd century B.C.). Chao Chün-ch'ing (c. 3rd century A.D.), the first to comment on the text, gave an algebraic treatment of the theorem involving quadratic equations. This ‘proof’ of the theorem is also found in Bhaskara II's work in the 12th century A.D., giving rise to the question of possible transmission. Finally, this paper surveys Chinese interest in right-angled and similar triangles in three other old Chinese texts, namely, the Chiu-chang suan-shu, Hai-tao suan-ching and Chang Ch'iu-chien suan-ching, and concludes that Chinese interest in the right-angled triangles was mainly practical, for the purposes of surveying.