Study Questions


  1. Is the hsuan-thu actually square, and if so, why? Hint: use the sum of angles rules.
  2. Are you satisfied that the construction of the hsuan-thu constitutes a proof of the Pythagorean theorem? If so, try to write down your reasons. What about a right triangle with two sides equal?
  3. Put together the four identical copies of the right triangle in another way, and derive the formula for the area of a right triangle. Hint: use the Pythagorean theorem.
  4. Geometric algebra: derive from the hsuan-thu the formula,
    (a + b)2 = a2 + 2ab + b2
  5. Geometric algebra: derive from the hsuan-thu the formula,
    (a - b)2 = a2 - 2ab + b2

Revised by Ralph Abraham, 24 Mar 2001