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

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3

Slicing Things Like Pizzas and Watermelons

We Start with Pizza

Our problem begins with the supposition that you have a large pizza in front of you and you want to obtain the maximum number of pieces with a certain number of straight line slices. With one slice you get two pieces of pizza, two slices give you four pieces, and three slices get you six, right?

Not necessarily. If your third slice avoids the intersection of the first two slices, you will have a total of seven pieces.

A short pause while you get a pad of paper, a pencil, and a ruler. All set? Draw a straight line and then another that intersects the first. These are slices one and two and you have four pieces. Another line—slice three—gives seven pieces and slice four yields eleven. ...

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