This is truly an amazing result from Five Hundred Mathematical Challenges.
“Problem 119. Two unequal regular hexagons ABCDEF and CGHJKL touch each other at C and are so situated that F, C, and J are collinear.
Show that
(i) the circumcircle of BCG bisects FJ (at O say);
(ii) ΔBOG is equilateral.”
I wonder how anyone ever discovered this.
See the Magic Hexagons
If you will pardon the pun, this is a diabolical problem from the collection Five Hundred Mathematical Challenges.
“Problem 5. Calculate the sum
__________
It has a non-calculus solution, but that involves a bunch of manipulations that were not that evident to me, or at least I doubt if I could have come up with them. I was able to reframe the problem using one of my favorite approaches, power series (or polynomials). The calculations are a bit hairy in any case, but I was impressed that my method worked at all.
See the Number of the Beast for solutions.
