New puzzle!! Like every other responsible brother-in-law, I called up my BIL this morning to check on him and his family. As is his wont, he immediately rewarded me with a puzzle which has stumped me ever since. (I think he is trying to give me a hint 🙂 ). Anyways, I got to the answer intuitively (and I am assuming it is the correct answer since he confirmed it) but for the life of me, I cannot come up with a proof for the answer.
So, here it is: Think of a circle. Now think of all the n-sided regular polygons that can fit in it (all the vertices of the regular polygon will touch the circumference of the circle). Which figure (i.e. for what value of “n” – triangle, square, pentagon, hexagon, heptagon, octagon etc etc ) will have the maximum value for the sum of squares of the sides.
As always, if you know or crack it, send a PM. I will acknowledge in the common forum.