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	Egyptian fraction - Wikipedia, the free encyclopedia
		That is, each fraction in the sum has a numerator equal to 1 and a denominator that is a positive integer, and all the denominators differ from each other.
		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.
		Egyptian fraction notation continued to be used into Greek times and even the middle ages (Struik 1967) despite complaints as early as Ptolemy's Almagest about the clumsiness of this notation compared to alternatives such as the Babylonian base-60 notation.
	en.wikipedia.org /wiki/Egyptian_fraction (1721 words)

	PlanetMath: unit fraction
		Such fractions are known from Egyptian mathematics where we can find a lot of special representations of the numbers as a sum of an unit fractions, which are now called Egyptian fractions.
		Many unit fractions are in the pairs of the adjacent fractions.
		This is version 7 of unit fraction, born on 2002-06-21, modified 2002-06-24.
	planetmath.org /encyclopedia/EgyptianFraction.html (310 words)

	Egyptian Fraction -- from MathWorld
		Any rational number has representations as an Egyptian fraction with arbitrarily many terms and with arbitrarily large denominators, although for a given fixed number of terms, there are only finitely many.
		Martin (1999) showed that for every positive rational number, there exist Egyptian fractions whose largest denominator is at most N and whose denominators form a positive proportion of the integers up to N for sufficiently large N.
		However, there are a number of algorithms (including the binary remainder method, continued fraction unit fraction algorithm, generalized remainder method, greedy algorithm, reverse greedy algorithm, small multiple method, and splitting algorithm) for decomposing an arbitrary fraction into unit fractions.
	users.skynet.be /fa956617/math/topics/EgyptianFraction.html (804 words)

	[No title]
		One can derive a good Egyptian fraction algorithm from continued fractions: the algorithm is quick, generates reasonably few terms, and uses fractions with very small denominators [Ble72].
		The number of terms in the Egyptian fraction representation of x/y is the sum of the odd terms after the first in the continued fraction list, which is at most x.
		As in the continued fraction method, the largest denominator in the representation of x/y is O[y^2].
	www.ics.uci.edu /~eppstein/numth/egypt/cfrac.html (2028 words)

	Good Math, Bad Math : Egyptian Fractions
		An Egyptian fraction is expressed as the sum of a finite set of unit fractions.
		I was definitely taught that it was a fraction with a non-unit numerator, and that that was the reason it was called "vulgar"; unit fractions were considered clean and elegant, but non-unit fractions were considered ugly, and thus vulgar.
		Fractions aren't perfect for every application, but they very well may be the best we'll ever have for what they are good at.
	scienceblogs.com /goodmath/2006/11/egyptian_fractions.php (2988 words)

	Egyptian Fraction -- from Wolfram MathWorld (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-10-16)
		An Egyptian fraction is a sum of positive (usually) distinct unit fractions.
		In 1202, Fibonacci published an algorithm for constructing unit fraction representations, and this algorithm was subsequently rediscovered by Sylvester (Hoffman 1998, p.
		Any fraction with odd denominator can be represented as a finite sum of unit fractions, each having an odd denominator (Starke 1952, Breusch 1954).
	mathworld.wolfram.com.cob-web.org:8888 /EgyptianFraction.html (816 words)

	Greedy algorithm for Egyptian fractions - Wikipedia, the free encyclopedia
		In mathematics, an Egyptian fraction is a representation of a natural number as a sum of unit fractions, as e.g.
		The denominator of the second unit fraction, 8, is the result of rounding 15/2 up to the next larger integer, and the remaining fraction 1/120 is what is left from 7/15 after subtracting both 1/3 and 1/8.
		As each expansion step reduces the numerator of the remaining fraction to be expanded, this method always terminates with a finite expansion; however, compared to ancient Egyptian expansions or to more modern methods, this method may produce expansions that are quite long, with large denominators.
	en.wikipedia.org /wiki/Greedy_algorithm_for_Egyptian_fractions (825 words)

	Math Lair - Egyptian Fractions (Site not responding. Last check: 2007-10-16)
		With the exception of ⅔ (two-thirds), for which the Egyptians had a special symbol (literally "one over one and a half"), they had symbols only for unit fractions (fractions that are the reciprocals of natural numbers.
		Interestingly, although the Egyptian system is much more complicated than the Babylonian system, or our modern system of having fractions with any numerator and denominator (which the ancient Chinese were able to handle), the ancient Greeks adopted the Egyptian system.
		A famous algorithm for writing any proper fraction as the sum of a finite number of distinct Egyptian fractions was first published in 1202 by Fibonacci in his book
	www.stormloader.com /ajy/egyptfract.html (513 words)

	Egyptian fraction
		A unit fraction; in other words, a fraction in which the numerator (the number on top) is 1.
		This type of fraction was the only kind used by the ancient Egyptians and appears extensively in the Rhind papyrus.
		In 1201 Fibonacci proved that every rational number can be written as a sum of Egyptian fractions.
	www.daviddarling.info /encyclopedia/E/Egyptian_fraction.html (144 words)

	The Universe of Discourse : Egyptian Fractions
		As I mentioned recently, a large part of it is a table of the values of fractions of the form 2/n for odd integers n.
		The Egyptians, at least at that time, did not have a generalized fraction notation.
		A simple algorithm for calculating this so-called "Egyptian fraction representation" is the greedy algorithm: To represent n/d, find the largest unit fraction 1/a that is less than n/d.
	blog.plover.com /math/egyptian-fractions.html (1040 words)

	Egyptian Fractions
		Best of Mathnerds: the magnificent seven asks for seven-term Egyptian fraction decompositions of 1, and describes a method for finding decompositions of any fraction using a method based on Farey sequences (essentially equivalent to the continued fraction method).
		The Distribution of Prime Primitive Roots and Dense Egyptian Fractions, dissertation by Greg Martin.
		Terrance Nevin uses greedy Egyptian fraction methods as a basis for investigating the dimensions of the Egyptian pyramids.
	www.ics.uci.edu /~eppstein/numth/egypt (1149 words)

	Title: THE EGYPTIAN MATHEMATICAL LEATHER ROLL,
		Appendix II discusses the Horus-Eye fraction method in one older sense, awkwardly computing the units of weights and measures, even when the easier Egyptian fractions are hidden within the calculation.
		This shows that in the EMLR all Egyptian fraction series were calculated to the highest accuracy, with no remainder, whenever rational numbers were considered.
		The application of these newer methods to ancient Egyptian mathematical materials tends to obscure the beautiful history of the fragmented subject of ancient Egyptian fractions.
	mathorigins.com /B_emlr050602.htm (4806 words)

	Math Games:Egyptian Fractions
		This is the simplest Egyptian fraction that requires 4 parts.
		Ten Algorithms for Egyptian Fractions entry, by David Eppstein.
		Ten Algorithms for Egyptian Fractions, Mathematica in Education and Research, 1995, p5-15.
	www.maa.org /editorial/mathgames/mathgames_07_19_04.html (782 words)

	egfrac.html
		Even though the Egyptian method of writing fractions stuck around for a long time, people were still very aware of its limitations.
		One thing that would be nice to do is take an egyptian fraction and print out an equation whose left hand side is the usual form of the fraction and whose right hand side is the fraction written as a sum of unit fractions.
		It is necessary to be able to convert an eqyptian fraction from the inert form to the active form.
	www.ms.uky.edu /~carl/ma330/html/egfrac1.html (1091 words)

	Sequence A100140: Largest Denominator of Greedy Egyptian Fraction Sum for M/N at MROB (Site not responding. Last check: 2007-10-16)
		This sequence, Sloane's A100140, gives the largest denominator in the Egyptian fraction expansion, using the "greedy" algorithm, for fractions with denominator N.
		In general when doing an Egyptian fraction expansion, you want to keep the denominators small.
		The Rhind papyrus lists Egyptian fraction expansions for all fractions of the form 2/N for odd N from 5 to 101.
	home.earthlink.net /~mrob/pub/math/seq-a100140.html (377 words)

	Pyr 1st
		Whenever a fraction was involved in a math problem, they would convert it into a sum of fractions, all with a numerator of one.
		I'll also start calling Egyptian fractions by their more modern name, unit fractions, and use the abbreviation UFR for them.
		So the calculations; (1) figuring the set of unit fractions, (2) the four diagonals and (3) the error of fit, were entered into a computer spreadsheet (Lotus 123) in 3600 rows (one row for each set).
	www.aloha.net /~hawmtn/pyr.htm (1484 words)

	Egyptian Math (Site not responding. Last check: 2007-10-16)
		So all their fractions are what we nowadays call by the name unit fractions, because 1 means "unit".
		The Egyptians had their way, perhaps rather complicated to our way of thinking, and they also used prepared tables with many simple cases already worked out in advance.
		As you might guess from looking at the solution, we need the fraction whose denominator is 84, obtained by multiplying both parts of the fraction by 12.
	www.trottermath.net /numthry/egyptmth.html (1809 words)

	Undergraduate Mathematics Research Group (Site not responding. Last check: 2007-10-16)
		The Diophantine equation of the title has its roots in the fractional numeration system of dynastic Egypt, dating from the third millennium BC.
		The study of this and related Egyptian fraction equation received a boost in the 1980's when a group of researchers at Wayne State University discovered applications of this topic to the structure theory of isolated singular points of four-dimensional topological spaces.
		The discovery of several new "perfectly weighted graphs," with application to continued fractions and to presentations of groups.
	www.math.wayne.edu /ugresearch/egyfra.html (468 words)

	Discovering Math: Rational Number Concepts - Mathematics lesson plan (grades 10-12) - DiscoverySchool.com (Site not responding. Last check: 2007-10-16)
		Definition: A fraction expressed as a sum of unit fractions, where all of the unit fractions in the sum are different
		Context: The first step in the greedy method for converting to an Egyptian fraction is to divide 23 by 11.
		Context: The study of ancient Egyptian history was made easier by translating the hieroglyphic symbols found on the walls of temples and tombs.
	school.discovery.com /lessonplans/programs/rationalNumConcepts (615 words)

	Kris' Egyptian Fraction Applet (Site not responding. Last check: 2007-10-16)
		Simply put, they are series of unit fractions that can represent any rational fraction.
		The ancient Egyptians represented all of their fractions as Egyptian fractions.
		As a project for a graduate computer operating systems class I was asked to write a program to find the Egyptian fraction of any rational fraction less than one.
	www.3rd-imperium.com /Java/Math/egypt.html (187 words)

	Akhmim Wooden Tablet
		Egyptian mathematics and its weights and measures system forever.
		fraction notion, followed by ro in the second half of the expression,
		Egyptian fractions were found in the Old Kingdom,
	akhmimwoodentablet.blogspot.com (4345 words)

	Egyptian Fractions at Math Cats (via CobWeb/3.1 planetlab-2.cs.princeton.edu) (Site not responding. Last check: 2007-10-16)
		The written record goes all the way back to 1650 B.C.: the Rhind Mathematical Papyrus contains a table of Egyptian fractions copied from another papyrus 200 years older.
		Ancient Egyptians needed to understand a lot of complex mathematics to create a table like this.
		Old Egyptian Math Cat image (drawn for Math Cats) © copyright 2003 - by Boni Cordoba Matos.
	www.mathcats.com.cob-web.org:8888 /explore/oldegyptianfractions.html (201 words)

	Math History
		The unit fraction series are known as Egyptian fraction
		Egyptian fraction data cited in the RMP and other texts.
		fractional divisors of a hekat, his feeding rates, in terms of a larger
	egyptianmath.blogspot.com (4240 words)

	The Best Egyptian Fraction - Mathematicians of the African Diaspora
		The Best Egyptian Fraction - Mathematicians of the African Diaspora
		recent work of Milo Gardner and others to understand Egyptian Fractions.
		Below is a list, found on the Rhind (Ahmes) Papyrus, used for 2/n where n is an odd n umber from 3 to 101.
	www.math.buffalo.edu /mad/Ancient-Africa/best-egyptian-fraction.html (300 words)

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