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

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14

More Great Turtle Races: Logarithmic Spirals

More turtle racing: This time we shall use several or many turtles and instruct all of them to move at the same speed. So it is not really racing; as we shall see, it is more a matter of symmetrical pursuit.

We start with a configuration involving two turtles. Turtle A is located at the west end of a straight line of length a, facing east. Turtle B is at the east end facing west. When the starting gun is fired, each turtle heads directly toward the other. Obviously, the two turtles will collide at the midpoint of the line and each will have covered a distance a/2.

Since that was not too difficult we move on to the three-turtle problem. This is not as easy. As shown in figure 14.1, initially the ...

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