In the first example below, each vertex is joined to the point (1/4) along the opposite side (measured say anti-clockwise), and in the second example (1/5) along the opposite side.
Feynman triangle: 1/4 division
Feynman triangle: 1/5 division
1. Can you now 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)?
2. Read my article at Feynman's triangle: Some feedback and more
3. The result actually generalizes further for sides divided into different ratios as shown by Routh's Theorem (1896)
4. Recommended reading: Y.K. Man. (2009). On Feynman's Triangle problem and the Routh Theorem. Teaching Mathematics & its Applications, 28(1):16-20.
5. Other references:
One-seventh area triangle
Feynman's and Steiner's triangle
Michael de Villiers, Sept 2009.