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Pages: 28. Chapters: Akhmim wooden tablets, Egyptian fraction,
Egyptian Mathematical Leather Roll, Egyptian multiplication and
division, Engel expansion, Erd s-Graham problem, Erd s-Straus
conjecture, Eye of Horus, Greedy algorithm for Egyptian fractions,
Kahun Papyri, Lahun Mathematical Papyri, Moscow Mathematical
Papyrus, Odd greedy expansion, Practical number, Primary
pseudoperfect number, Red auxiliary number, Reisner Papyrus, Rhind
Mathematical Papyrus, Rhind Mathematical Papyrus 2/n table,
Sylvester's sequence, Znam's problem. Excerpt: An Egyptian fraction
is the sum of distinct unit fractions, such as . That is, each
fraction in the expression has a numerator equal to 1 and a
denominator that is a positive integer, and all the denominators
differ from each other. The value of an expression of this type is
a positive rational number a/b; for instance the Egyptian fraction
above sums to 43/48. Every positive rational number can be
represented by an Egyptian fraction. Sums of this type, and similar
sums also including 2/3 and 3/4 as summands, were used as a serious
notation for rational numbers by the ancient Egyptians, and
continued to be used by other civilizations into medieval times. In
modern mathematical notation, Egyptian fractions have been
superseded by vulgar fractions and decimal notation. However,
Egyptian fractions continue to be an object of study in modern
number theory and recreational mathematics, as well as in modern
historical studies of ancient mathematics. For more information on
this subject, see Egyptian numerals, Eye of Horus, and Egyptian
mathematics. Eye of HorusEgyptian fraction notation was developed
in the Middle Kingdom of Egypt, altering the Old Kingdom's Eye of
Horus numeration system. Five early texts in which Egyptian
fractions appear were the Egyptian Mathematical Leather Roll, the
Moscow Mathematical Papyrus, the Reisner Papyrus, the Kahun Papyrus
and the Akhmim Wooden Tablet. A later text, the Rhind Mathematical
Papyrus, introduced improved ways of writing Egyptian fractions.
The Rhind papyrus was written by Ahmes and dates from the Second
Intermediate Period; it includes a table of Egyptian fraction
expansions for rational numbers 2/n, as well as 84 word problems.
Solutions to each problem were written out in scribal shorthand,
with the final answers of all 84 problems being expressed in
Egyptian fraction notation. 2/n tables similar to the one on the
Rhind papyrus also appear on some of the other texts. However, as
the Kahun Papyrus shows, vulgar fractions were
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