## Study Questions- Is the hsuan-thu actually square, and if so, why? Hint: use the sum of angles rules.
- 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?
- 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.
- Geometric algebra: derive from the hsuan-thu
the formula,
(a + b)^{2}= a^{2}+ 2ab + b^{2} - Geometric algebra: derive from the hsuan-thu
the formula,
(a - b)^{2}= a^{2}- 2ab + b^{2}
Revised by Ralph Abraham, 24 Mar 2001 |