Just today, I was making tortilla chips, and I began to wonder, what is the most efficient way to pack circular quarters onto the plane?
This sort of circle packing is most efficient for circles, but what if quarter circles are used instead of whole circles, is it still this method?
Does anyone have an answer for this? What is the most efficient way to pack quarter circles onto the plane?
I expect, but am not about to try to prove, that the optimal packing would be something like the following:
Of course, pushing each to be as tight as possible. (pardon my bad mspaint skills)
In fact, a similar packing argument allowed the ancient egyptians to derive the formula $\pi r^2$ for the area of the circle, noting that as you cut the circle into a large number of segments and alternate between pointed up and pointed down, the shape resembles a rectangle of height $r$ and width $\pi r$.