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Good Math by Mark C. Chu-Carroll

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10Egyptian Fractions

As math has evolved, so have people’s views of what is aesthetic in math and what is not. The ancient Greeks (from whom we got many of our mathematical notions) thought, for example, that as a matter of elegance, the only way to write fractions was as unit fractions—fractions whose numerator is 1. A fraction that was written with a numerator larger than one was considered wrong. Even today, many math books use the term vulgar fraction to refer to non-unit fractions.

Obviously, there are fractions other than the unit fractions. A unit fraction like is a reasonable quantity; but so is . So how did the Greeks handle these quantities? They represented them in a form that we refer to today as an Egyptian fraction. An Egyptian ...

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