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Euler's Gem by David S. Richeson

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CHAPTER 19

COMBING THE HAIR ON A COCONUT

Let chaos storm!Let cloud shapes swarm!I wait for form.—Robert Frost, “Pertinax”1

Many scientists use mathematics as a tool to predict behavior. A scientist may have an equation or a system of equations that describes the interactions of the quantities in their model. Then they use mathematics to draw conclusions from these equations.

Often the mathematical models are differential equations. These describe the rates of change of various quantities as a function of time. For example, an ecologist might use a system of differential equations to model the population dynamics of rabbits and foxes living in a wildlife refuge driven by their predator-prey relationship. When the number of rabbits is large, the ...

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