Rhind Papyrus

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates to 1650 BC. It was purchased by Henry Rhind in Egypt in 1858, and placed in the British Museum in 1864 by the estate of Henry Rhind.

A bootleg copy that listed the initial table of Egyptian fraction representations for fractions of the form and 84 practical problems/solutions was published in Germany in 1873. Hot debates between British scholars, only seeing additive contents, and German scholars, sometimes seeing higher forms of math, continued until the 1920s, when the debates simmered, nearly dying out during the 1930s and World War II.

The table shows 51 and rational numbers being converted to exact and concise Egyptian fractions, starting at 1/3 and progressing to 2/101. The most difficult cases were the conversions. They were first decoded by Hultsch in 1895, independently confirmed by Bruins in 1950, showing that a form of subtle number theory was present. Evidence suggests that early Egyptians used a form of number theory for these conversions. Egyptians used two algebraic identities to find unit fractions series.

To the ancient scribe, there was a straightforward method of finding Egyptian fractions for numbers of the form . One basic rule was first published in 2002, and states that

(1)

where . For example, to find , let , and , so

			(2)
			(3)
			(4)

as listed in the table.

There were only three fractions appearing that cannot be decomposed using this rule: 2/35, 2/91 and 2/95.

Taken together, the table and the Egyptian mathematical leather roll shows that Middle Kingdom students studied ways to convert any rational number to exact and optimal unit fraction series. Practical applications of this early number theory are explained by five Akhmim wooden tablet divisions, the Moscow Mathematical Papyrus, Kahun, the Rhind papyrus's 84 problems, and several other Middle Kingdom mathematical texts.

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