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 " wrote a paper explaining how to use convergents to find the best rational \
approximations for gear ratios. He was able to select the best gears based on \
these approximate values."
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Continued fractions further captivated the attention of most prominent \
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In certain aspects, continued fractions are a more natural mathematical \
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Keep only a limited number of terms. Start with one term and add one each \
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The first thing to notice is that by taking more terms, they get closer to \
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Then you can notice that the odd-numbered numbers are smaller than the value \
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Every infinite continued fraction is irrational, and every irrational number \
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Only real quadratic irrationals have periodic continued fraction forms:\
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