Given a regular right hexagonal prism
of edge length 1, what is the largest circle (in terms of area) that can be placed completely inside the prism?
What is the largest circle (in terms of n) that can be placed completely inside a regular right unit n-prism
If n=3 you can't do better than putting your circle on one of the square sides of the prism, so the solution is a circle of diameter 1 and an area of π/4
As n increases the prism approaches a cylinder. In a cylinder you can do no better than the circular base (picture a coin spinning in a tube.) So the limiting area as n increases is that of the circle that can be inscribed in the base. r = 1/(2tan(180/n)) A = πr^2
Posted by Jer
on 2012-07-01 14:27:19