### Assignment #7

**Due: 3 February, 1998**

Find the area of the region enclosed by the ellipse `x`^{2}/`a`^{2} + `y`^{2}/`b`^{2} = 1 both
- using calculus
*[7]* and
- 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]*

Solution to Assignment #7

Department of Mathematics
Trent University

Maintained by Stefan Bilaniuk. Last updated 1998.08.22.