Iterations in Geometry, an example . Let there be given a triangle ABC and a point P. First, point P moves towards A. But half way from its original position to A it makes a turn and continues towards B. However, half way from B, it turns towards C. Half way towards C, it turns towards A, and so on. P eventually settles into cycling between three successive positions irrespective of its initial position. The simplest is probably to recognize a construction we discussed on another occasion .
Similar iterations converge for a more general N-gon.
R d , where each number can be clicked on. Clicking a little off but to the right of its vertical center line will increase the number, clicking to the left will decrease it. The formula for the area of the resulting N-gon may not be at all obvious. Alexander Bogomolny 2413135 .