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It is in this sense that one irrational is more irrational than another.\
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You can measure the quality of these approximations by observing that\
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Suppose the denominators of the approximations can be other integers as well.\
\
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An infinite continued fraction is a continued fraction with an infinite \
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Every irrational number can be represented in one way as an infinite \
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The best rational approximations to an irrational number always lie among its \
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What do you think is the most irrational number, the one for which rational \
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The most irrational number is, in fact, a widely recognized number.\
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The continued fraction expansion of the golden ratio is the simplest of all:\
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The golden ratio appears in an array of mathematical contexts. You can find \
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The golden ratio also occurs in nature. For example, it is often used for the \
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