Triangle variation: For a triangle ABC in the plane, if each side is divided by a point (1/p), (measured say anti-clockwise), find a formula relating the area of ABC with that of A'B'C' (triangle formed by these points). Drag the slider p to investigate.
Feynman Triangle & Parallelogram Variations
Parallelogram variation: For a parallelogram ABCD in the plane, if each side is divided by a point (1/p), (measured say anti-clockwise), find a formula relating the area of ABCD with that of A'B'C'D' (parallelogram formed by these points). Click on the 'Link to ...' button in the above sketch and drag the slider p to investigate.
What formulae did you find? Can you prove your findings? Can you prove them in more than one way?
Can you generalize further if the sides of the triangle & parallelogram are divided into different ratios?
De Villiers, M. (2005). Feedback: Feynman's Triangle (extended). The Mathematical Gazette, 89 (514), March, p. 107.
Created by Michael de Villiers, Sept 2009; modified 26 July 2021.