MATH 380 Assignment #5

1. Exercise 8.1 [10]

2. Prove Pappus' Theorem (well, one them...), stated below. [10]

Suppose A, B, C are distinct points on a line and A', B', C' are distinct points on another line. Let E be the intersection OF A'B and AB', F be the intersection of A'C and AC', and G be the intersection of B'C and BC'. Then E, F, and G are collinear.

3. The text tells us little enough about Hypatia, and essentially nothing about her work. Give a brief description of what she did in mathematics. Is the text's claim that Hypatia was "the first woman mathematician whose name is known" justified? [10]

Department of Mathematics

Trent University