Question

How divide circle in 3 parts

Answer 1

6

Assuming that the pizza has unit radius, the area of the pizza is π and each piece has to have area π3. So it is enough to find the height of a circle segment such that its area is one third of the original circle, i.e. to solve

∫h(2−h)√−h(2−h)√1−x2−−−−−√dx−2(1−h)h(2−h)−−−−−−−√=π3

in terms of h, that with some substitution boils down to Kepler's equation(∗), i.e. to a trascendental equation that, in general, cannot be solved in explicit terms, but is easy to solve numerically by Newton's method. In our case we get h≈0.735068≈44926111, so the three slices have widths approximately proportional to 3:2:3.