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 = a2 + 2ab + b2
- Geometric algebra: derive from the hsuan-thu
the formula,
(a - b)2 = a2 - 2ab + b2
Revised by Ralph Abraham, 24 Mar 2001
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