35
Chinese Foundation of Japanese Math
Plate 2.3. Illustrating the Pythagorean theorem with a broken bamboo stalk, this famous problem from Nine Chapters was published in many subsequent books. The version shown here comes from Yang Hu’s Xiangjie Jiuzhang Suanfa of a.d. 1261.
A bamboo stalk 10 syaku high is broken at a point Q so that the top of the stalk falls over and touches the ground at a point T. The distance from the root P to T is 3 syaku. Find the distance PQ. This is a famous problem, which first appeared in the Jiu zhang and then in a number of Chinese books, including Yang Hu’s Xiangjie Jiuzhang Suanfa of a.d. 1261, and Cheng Da-Wei’s 1593 Suanfa Tong Zong. The answer follows directly from the Pythagorean theorem: If x is the distance PQ, then x 2 + 32 = (10 − x)2. Solving for x gives x = 91/20 = 4 + 11/20 syaku.