The Theorem of Pythagoras


Video Segments

1.
Three questions from real life
2.
Discovering the Theorem of Pythagoras
3.
Geometric interpretation
4.
Pythagoras
5.
Applying the Theorem of Pythagoras
6.
Pythagorean triples
7.
The Chinese proof
8.
Euclid's elements
9.
Euclid's proof
10.
A dissection proof
11.
Euclid's Book VI, Proposition 31
12.
The Pythagorean Theorem in 3D

Contents

The program begins with three real-life situations that lead to the same mathematical problem:

Find the length of one side of a right triangle if the lengths of the other two sides are known.

The problem is solved by a simple computer-animated derivation of the Pythagorean theorem (based on similar triangles):

In any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs.

The algebraic formula a2 + b2 = c2 is interpreted geometrically in terms of areas of squares, and is then used to solve the three real-life problems posed earlier. Historical context is provided through stills showing Babylonian clay tablets and various editions of Euclid's Elements. Several different computer-animated proofs of the Pythagorean theorem are presented, and the theorem is extended to 3-space.


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