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Three questions from real life |
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Discovering the Theorem of Pythagoras |
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Geometric interpretation |
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Pythagoras |
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Applying the Theorem of Pythagoras |
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Pythagorean triples |
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The Chinese proof |
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Euclid's elements |
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Euclid's proof |
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A dissection proof |
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Euclid's Book VI, Proposition 31 |
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The Pythagorean Theorem in 3D |
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.