Assignment #7

Due: 3 February, 1998

Find the area of the region enclosed by the ellipse x2/a2 + y2/b2 = 1 both
  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]

[overlapping circles]

Solution to Assignment #7
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Maintained by Stefan Bilaniuk. Last updated 1998.08.22.