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Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics by Robert B. Banks

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19

Making Mathematical Mountains

In this chapter and the one to follow, we are going to fabricate and analyze various kinds of mathematical mountains. To do this, we shall need some algebra and trigonometry and some analytic geometry and calculus. In addition, for problems with large numbers and diverse shapes of mountains, it will be necessary to utilize various topics of statistics and probability theory.

These are the basic mathematical tools used in the science of geomorphology: the study of the characteristics, origins, and changes of land forms.

Cones and Paraboloids

We begin our studies of the subject with a very simple mountain: a circular cone. What we want to do in this case, and in those to follow, is to determine the hypsometric ...

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