MATH 380 Assignment #10

Do two of 1-3.

1. The priority dispute between Leibniz and Newton over who discovered calculus first was mostly carried on by other mathematicians acting on their behalf, with or without encouragement and permission. Who were some of these individuals and what did they do to further the dispute? [10]

2. In your opinion, how would the development of calculus have differed if neither Newton nor Leibniz had invented it when they did? Give you reasons! [10]

3. Felix Klein developed a model in Euclidean geometry of two-dimensional hyperbolic geometry that is somewhat similar to Poincar\'e's. Give a complete description of this model, including how hyperbolic distances and angles can be computed in it. [10]

Bonus.

What was David Hilbert's Tenth Problem? If the answer to the problem had turned out to be `yes', what might the consequences have been for Fermat's Last Theorem? [3]

Department of Mathematics

Trent University