The Jiuzhang suanshu is an ancient Chinese mathematics text of 246 problems. Some

Chapter 9, Problem 22

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The Jiuzhang suanshu is an ancient Chinese mathematics text of 246 problems. Some solutions use the gou gu, the Chinese name for what we call the Pythagorean Theorem. The gou gu reads (gou) 2 + (gu) 2 = (xian) 2 . Here is a gou gu problem translated from the ninth chapter of Jiuzhang. A rope hangs from the top of a pole with three chih of it lying on the ground. When it is tightly stretched so that its end just touches the ground, it is eight chih from the base of the pole. How long is the rope?

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