Feynman's Triangle

According to R.J. Cook & G.V. Wood (2004). Feynman's Triangle. Mathematical Gazette 88:299-302, this triangle result puzzled famous physicist Richard Feynman in a dinner conversation: For a triangle ABC in the plane, if each vertex is joined to the point (1/3) along the opposite side (measured say anti-clockwise), then area ABC = 7 x area UWV (the inner triangle formed by these lines).

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Feynman's Triangle

1. Can you prove the above result?

2. Can you generalize to find a formula for a triangle ABC in the plane, when each vertex is joined to the point (1/p), (p > 2) along the opposite side (measured say anti-clockwise)?

3. Have a look at Feynman Generalization for two dynamic sketches of special cases of Question 2 above.

4. Can you generalize the Feynman result for a triangle to a parallelogram?

5. Have a look at Feynman Parallelogram Generalization for three dynamic sketches of special cases of Question 4 above.

6. Also investigate the following variations: Feynman triangle variation and Feynman parallelogram variation


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Michael de Villiers, Sept 2009.