An Egyptian fraction is a finite 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 ; for instance the Egyptian fraction above sums to . Every positive rational number can be represented by an Egyptian fraction. Sums of this type, and similar sums also including and 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 In modern mathematical notation, Egyptian fractions have been superseded by vulgar fractions and decimal notation.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.
An Egyptianfraction is a finite sum of distinct unit fractions, such as 1 2 + 1 3 + 1 16 . {\displaystyle {\frac {1}{2}}+{\frac {1}{3}}+{\frac {1}{16}}...
of four, and so on. The Egyptians used Egyptianfractions c. 1000 BC. About 4000 years ago, Egyptians divided with fractions using slightly different...
for Egyptianfractions is a greedy algorithm, first described by Fibonacci, for transforming rational numbers into Egyptianfractions. An Egyptian fraction...
a sum of distinct unit fractions; these representations are called Egyptianfractions based on their use in ancient Egyptian mathematics. Many infinite...
numbers as Egyptianfractions. Fibonacci does not formally define practical numbers, but he gives a table of Egyptianfraction expansions for fractions with...
In mathematics, ancient Egyptian multiplication (also known as Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication)...
the Egyptianfractions commonly used until that time and the vulgar fractions still in use today. Fibonacci's notation differs from modern fraction notation...
continued fraction Continued Logarithms Complete quotient Computing continued fractions of square roots – Algorithms for calculating square roots Egyptian fraction –...
the symbol stand for fractions in ancient Egyptian mathematics, although this hypothesis has been challenged. The ancient Egyptian god Horus was a sky...
a rational number is a number that can be expressed as the quotient or fraction p q {\displaystyle {\tfrac {p}{q}}} of two integers, a numerator p and...
interesting feature of ancient Egyptian mathematics is the use of unit fractions. The Egyptians used some special notation for fractions such as 1/2, 1/3 and 2/3...
fractional numbers dates to prehistoric times. The Ancient Egyptians used their Egyptianfraction notation for rational numbers in mathematical texts such...
the country Egypt. Ancient Egyptian civilization followed prehistoric Egypt and coalesced around 3100 BC (according to conventional Egyptian chronology)...
ancient Egyptian mathematics. It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt; it was...
quality uncertain) but became e by Late Egyptian.[citation needed] Egyptian language Egyptian mathematics "Egyptian numerals". MacTutor - School of Mathematics...
of unit fractions that most rapidly converge to 1 are the reciprocals of Sylvester's sequence, which generate the infinite Egyptianfraction 1 = 1 2 +...
The answers were written in binary Eye of Horus quotients and exact Egyptianfraction remainders, scaled to a 1/320 factor named ro. The second half of...
including ancient Egypt, China, and India. The scribes of ancient Egypt used two different systems for their fractions, Egyptianfractions (not related to...
is now the modern country of Egypt. Egyptian civilization coalesced around 3150 BCE (according to conventional Egyptian chronology) with the political...
number Farey sequence Ford circle Stern–Brocot tree Dedekind sum Egyptianfraction Montgomery reduction Modular exponentiation Linear congruence theorem...
capital P). The Rhind Mathematical Papyrus, from around 1550 BC, has Egyptianfraction expansions of different forms for prime and composite numbers. However...
Reisner and RMP to convert vulgar fractions to unit fraction series look similar to the conversion methods used in the Egyptian Mathematical Leather Roll. Gillings...
Mathematical Papyrus after its first non-Egyptian owner, Egyptologist Vladimir Golenishchev, is an ancient Egyptian mathematical papyrus containing several...
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