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Rooting through a spiral. Start with a right triangle with both legs having length 1. What is the length of the hypotenuse? Suppose we draw a line of length 1 perpendicular to the hypotenuse and then make a new triangle as illustrated. What is the length of this new hypotenuse? Suppose we continue in this manner. Describe a formula for the lengths of all the hypotenuses.
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The Heart of Mathematics: An Invitation to Effective Thinking
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