Professor Stewart's Hoard of Mathematical Treasures (14 page)

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Authors: Ian Stewart

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Historically, different cultures handled fractions in different ways. The ancient Egyptians had a very unusual approach to fractions; in fact, they had
three
unusual approaches.

First, they had special hieroglyphs for

and

Hieroglyphs for

and

Second, they used various portions of the Eye of Horus, or Wadjet Eye, to represent 1 divided by the first six powers of 2.

Wadjet Eye (left), and fraction hieroglyphs derived from it (right).

Finally, they devised symbols for fractions of the form ‘one over something’, that is,

, and so on. Today we call these
unit fractions. The unit fraction 1/n was represented by placing a cushion-shaped hieroglyph (normally representing the letter R) over the top of the symbols for n.

Hieroglyphs for 1/1,237

(in practice the Egyptians wouldn’t have used such big numbers in a unit fraction).

However, these methods dealt only with special types of fractions, and 6 divided by 7 was still a problem. So the Egyptians expressed all other fractions as sums of distinct unit fractions, for instance