1. using calculus [7] and
2. without using calculus or just looking it up [3].

Bonus. Suppose you draw a number of circles on a blank piece of paper. This divides up the paper into a number of regions whose borders are made up of circular arcs. Prove that you can colour these regions with only colours in such a way that no two regions that have a common border have the same colour, as in the example below. [1]

Department of Mathematics

Trent University