1c+-+Hsuan-thu+(1000+BC+-+1+AD)

The Hsuan-thu is one of the oldest known proofs of the Pythagorean Theorem. As such, it came "long before Pythagoras received the credit for its conception (Swetz, 1993, p. 149)." The diagram is contained within the text of the Zhou Bi Suan Zing (or Chou Pei Suan Ching), a Chinese collection of 246 problems. The collection of problems and solutions spans 1000 years and is probably the work of several men of differing periods (Boyer, 1991, p. 195).

media type="custom" key="6288525" Created using GeoGebra 3.2.40.0 GeoGebra - Dynamic Mathematics for Everyone []

This figure is similar to the one drawn by Bhaskara II. The proof, however, is different. 1. Slide the "Rotation" slider all the way to the right. Does this suggest a relationship?

2. Check the "Show Hints" checkbox. From here, using only the variables a, b, and c note: a. The area of the outer square, b. the area of the four triangles, and c. the area of the inner square.

3. Use the relations established to prove the Pythagorean Theorem: a 2 + b 2 = c 2.

4. Experiment with the sliders for a and b. Note what happens when a > b and, then, when b > a. Does the equation you derived still hold? Why or why not?