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Topic: Egyptian mathematics

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Moscow and Rhind Mathematical Papyri

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	Mathematics - MSN Encarta
		In the past mathematics was regarded as the science of quantity, whether of magnitudes, as in geometry, or of numbers, as in arithmetic, or the generalization of these two fields, as in algebra.
		Towards the middle of the 19th century mathematics came to be regarded increasingly as the science of relations, or as the science that draws necessary conclusions.
		There mathematics was dominated by arithmetic, with an emphasis on measurement and calculation in geometry and with no trace of later mathematical concepts such as axioms or proofs.
	uk.encarta.msn.com /encyclopedia_761578291/Mathematics.html (1888 words)

	Egyptian is what you can call somewhat lost in time
		The origins of Egyptian mathematics was largely dependent on the changes of climate near the end of the Stone Age, and indeed very similar to the origins of Babylonian and Chinese mathematics.
		The Egyptians ideas of teaching arithmetic, resurfaced in 20-th century British schools, as ‘modern maths’, but failed to catch on, largely because of lack of analysis related to the age of the class involved.
		Describing the Egyptian methods of multiplying and dividing, the Egyptian use of unit fractions, their employment of false position, their solution of the problem of finding the area of a circle, and many applications of mathematics to practical problems.
	home.c2i.net /greaker/comenius/9899/egyptiannumerals/mp.html (1310 words)

	History of mathematics - Wikipedia, the free encyclopedia
		In the Vedic era, mathematics was not studied for the sole purpose of science, but there are still advanced mathematics papers scattered throughout a large body of Indian texts from this period (many are of uncertain date and authorship, however, and do not follow a serious mathematical tradition).
		Greek mathematics studied from the time of the Hellenistic period (from 323 BC) refers to all mathematics of those who wrote in the Greek language, since Greek mathematics was now not only written by Greeks but also non-Greek scholars throughout the Hellenistic world, which was spread across the Eastern end of the Mediterranean.
		Even after European mathematics began to flourish during the Renaissance, European and Chinese mathematics were separate traditions, with significant Chinese mathematical output in decline, until the Jesuit missionaries in the 18th century carried mathematical ideas back and forth between the two cultures.
	en.wikipedia.org /wiki/History_of_mathematics (5387 words)

	Egyptian fraction - Wikipedia, the free encyclopedia
		An Egyptian fraction is the sum of distinct unit fractions (that is, fractions whose numerators are equal to 1) whose denominators are positive integers, and all of whose denominators differ from each other, for example
		An algorithm for calculating Egyptian fractions represented for a given rational number between 0 and 1, was developed after 800 AD Islamic mathematicians.
		Ahmes and Egyptian scribes often computed within remainder arithmetic, a fact that was not confirmed in the Akhmim Wooden Tablet, the RMP and other mathematical texts until 2005.
	en.wikipedia.org /wiki/Egyptian_fraction (1932 words)

	Mathematics in Ancient Egypt
		For the Egyptians, mathematics was mainly algorithmic in nature, aimed at performing practical everyday tasks, that is a tool for say controlling flood or measuring land.
		They used mathematics to exchange money with merchandise, to figure out wages, find the areas of fields and the volumes of granaries, calculate the quantity of material they needed for structures as well as to estimate taxes.
		Some known historians suggest that their mathematics was based on two very elementary concepts, namely a knowledge of the twice-time table and the ability to find two-third of any number whether integral or fractional, and based upon these two simple rules that the whole structure of Egyptian mathematics was founded.
	www.geocities.com /mathematics_in_ancient_egypt (315 words)

	Moscow and Rhind Mathematical Papyri Summary
		The mathematical problems contained on the papyrus are presented in a series of exercises, in form similar to a teaching text, and are formulated in a nonalgebraic rhetorical manner with little abstract notation.
		For example, the Egyptians recognized that the volume of a cylinder was quantitatively similar to the volume of a rectangular container (the volumes of both are equal to the area of their respective bases times their height).
		The ancient Egyptians did not recognize mathematics as an academic discipline in of itself; indeed, their language had no word for "mathematician." Instead, mathematics was one of the many domains of the priestly caste, which served as a tool to allow them to pursue their numerous "mysterious" interests, such as astronomy.
	www.bookrags.com /Moscow_and_Rhind_Mathematical_Papyri (2502 words)

	Projects - Annette Imhausen
		Egyptian mathematics has traditionally been seen as having reached the height of its development in the early Middle Kingdom, remaining nearly "unchanged" from that time forth.
		Due to developments in the field of history of mathematics of the last 30 years, it has only recently become obvious that many "statements" about Egyptian mathematics which were made a long time ago, and which have since then been accepted as "truths", are in fact in serious need of reassessment.
		The Rhind mathematical papyrus was last edited by a group of mathematicians (!) in 1927/28; its {\it editio princeps} remains the second edition prepared by the Egyptologist (and former mathematician) Thomas Eric Peet in 1923.
	www.annetteimhausen.com /projects.html (1982 words)

	¥°. The Oriental Mathematics : Practical Arithmatic and Mensuration
		Mathematics was one of the essencial parts in the ancient civilization.
		The Babylonians used imperishable baked clay tablets and the Egyptians used stone and papyrus, the latter fortunately being long lasting because of the unusually dry climate of the region.
		Ancient Egyptians say that the area of a circle is repeatedly taken as equal to that of the square of 8/9 of the diameter.
	library.thinkquest.org /22584/emh1100.htm (829 words)

	Ancient Greek Mathematics - Crystalinks (Site not responding. Last check: 2007-10-20)
		Greek mathematics, as that term is used in this article, is the mathematics developed from the 6th century BC to the 5th century AD around the shores of the Mediterranean.
		Mathematical developments took place in Greek-speaking centers as far apart as Sicily and Egypt, and with a high estimation of the intellectual and cultural status of mathematics (for example in the school of Plato).
		Some of the most well-known figures in Greek mathematics are Pythagoras, a shadowy figure from the isle of Samos associated partly with number mysticism and numerology, but more commonly with his theorem, and Euclid, who is known for his Elements, a canon of geometry for centuries.
	www.crystalinks.com /greekmath.html (305 words)

	$FILE (Site not responding. Last check: 2007-10-20)
		Both civilizations developed mathematics that was similar in some ways but different in others.
		The mathematics of Egypt, at least what is known from the papyri, can essentially be called applied arithmetic.
		This point, that mathematics was communicated by example, rather than by principle, is significant and is different than today's mathematics that is communicated essentially by principle with examples to illustrate principles.
	www.math.tamu.edu /~don.allen/history/egypt/egypt.html (171 words)

	K. Zahrt - Thoughts on Ancient Egyptian Mathematics
		It was as though the Egyptians had a preference for 2 / 3 since it was used in many of the problems and had its own symbol which was unrelated to 1 / 3.
		Although earlier evidence of Egyptian mathematics exist, the Rhind Mathematical Papyrus is the source most frequently quoted as an example of classical Egyptian mathematics (Gillings 260-261).
		Outside of the mathematical realm, there are other noted scholars of Egyptian history who have made comments that tend to lead one to doubt the opinions of the mathematical and science experts.
	www.iusb.edu /~journal/2000/zahrt.html (2621 words)

	Egyptian Mathematics (Site not responding. Last check: 2007-10-20)
		The oldest source of Egyptian mathematics is a royal mace dating from c.
		All Egyptian fractions are decomposed into unit fractions, where the shortest version possible is chosen, or else the version with the smallest first denominator.
		Egyptians had separate symbols for the fractions 1/2, 1/4 and 2/3 (the only non-unit fraction), but any other unit fractions had a special symbol over them to indicate they were fractions.
	www.bath.ac.uk /~ma2jc/egyptian.html (1182 words)

	Egyptian Fractions
		An Egyptian Fraction for t/b is a sum of unit fractions, all different, whose sum is t/b.
		However, the egyptian fraction produced by the greedy method may not be the shortest such fraction.
		Mathematics in the Time of the Pharaohs by Richard J Gillings, Dover, 1972 is an inexpensive and readable account of the mathematics in the Rhind Papyrus, it contents and methods.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Fractions/egyptian.html (3847 words)

	Egyptian mathematics
		However, once the Egyptians began to use flattened sheets of the dried papyrus reed as "paper" and the tip of a reed as a "pen" there was reason to develop more rapid means of writing.
		To overcome the deficiencies of their system of numerals the Egyptians devised cunning ways round the fact that their numbers were poorly suited for multiplication as is shown in the Rhind papyrus.
		Not that anyone believes that the Egyptians knew of the secant function, but it is of course just the ratio of the height of the sloping face to half the length of the side of the square base.
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Egyptian_mathematics.html (1677 words)

	Egyptian mathematics
		However, once the Egyptians began to use flattened sheets of the dried papyrus reed as "paper" and the tip of a reed as a "pen" there was reason to develop more rapid means of writing.
		To overcome the deficiencies of their system of numerals the Egyptians devised cunning ways round the fact that their numbers were poorly suited for multiplication as is shown in the Rhind papyrus.
		Not that anyone believes that the Egyptians knew of the secant function, but it is of course just the ratio of the height of the sloping face to half the length of the side of the square base.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Egyptian_mathematics.html (1677 words)

	egyptian maths
		Egyptians had their own numerals which can still be found on temples, stone monuments and decorative objects around the world.
		There must have been huge number of these papyri which were made and circulated around the country, as we have proofs that they had schools and that scribes were reasonably numerous.
		We unfortunately, only have two papyri which survived and deal with mathematics, and so almost all of our knowledge of Egyptian mathematics is based on these two surviving documents.
	www.mathsisgoodforyou.com /topicsPages/egyptianmaths/Egyptian.htm (275 words)

	Egyptian Papyri
		In the article An overview of Egyptian mathematics we looked at some details of the major Egyptian papyri which have survived.
		Although the mathematical methods we have described are found in various Egyptian documents, all the actual examples we have given so far have come from Rhind papyrus.
		This example means that the Egyptian knew the formula for the volume (although of course not in the algebraic sense which we now think of formulas).
	www-gap.dcs.st-and.ac.uk /~history/HistTopics/Egyptian_papyri.html (1769 words)

	Bryn Mawr Classical Review 2004.09.21
		What shines through most clearly in the book is perhaps this mnemonic nature of Egyptian architectural design and building praxis rather than the presence of a tangible Egyptian mathematical system which the architects drew on in their designs of monuments.
		After all, within the confines of the book, the author's mathematical focus on the pyramids is restricted to slopes alone, while the siting and orientation of the Giza group or the alignment of the shafts inside the pyramids with aspects of the night sky, all mathematical/astronomical feats, are not addressed.
		To my mind, the tendency to rule out anything 'symbolic' in the mathematical bases of Egyptian architecture, even with the dearth of evidence, and to place 'symbolism' or 'symbology' solely within the realm of the aforementioned eccentric or outdated theories is an aspect of the book that may be considered misleading.
	ccat.sas.upenn.edu /bmcr/2004/2004-09-21.html (1682 words)

	Egyptian Mathematics (Site not responding. Last check: 2007-10-20)
		The oldest source of Egyptian mathematics is a royal mace dating from c.
		All Egyptian fractions are decomposed into unit fractions, where the shortest version possible is chosen, or else the version with the smallest first denominator.
		Egyptians had separate symbols for the fractions 1/2, 1/4 and 2/3 (the only non-unit fraction), but any other unit fractions had a special symbol over them to indicate they were fractions.
	people.bath.ac.uk /ma2jc/egyptian.html (1182 words)

	Babylonian and Egyptian
		The Egyptians and the Romans had number systems which were not well suited for arithmetical calculations.
		The Egyptians were very practical in their approach to mathematics.
		To overcome the deficiencies of their system of numerals the Egyptians devised cunning ways round the fact that their numbers were unsuitable for multiplication as is shown in the Rhind papyrus which date from about 1700 BC.
	www.veling.nl /anne/templars/Babylonian_and_Egyptian.html (956 words)

	Ancient Mathematics (Site not responding. Last check: 2007-10-20)
		Many of the mathematical developments of Indian origin are often unjustly ignored, overlooked, or attributed to ancient Egyptian or Babylonian developments.
		Babylonian mathematics was taught by example, and in word problems; no general algorithms for solving problems were ever given, and the somewhat more advanced concept of symbolic mathematics had not dawned upon them (Melville).
		Though a slightly incorrect assertion by modern rigorous mathematical standards, the concept is mostly correct, and a similar concept of the infinite is a major part of modern calculus.
	jhunix.hcf.jhu.edu /~blee27/essays/ancient_mathematics.htm (2230 words)

	Civilization.ca - Egyptian civilization - Sciences - Mathematics
		lthough the Egyptians lacked the symbol for zero, they calculated numbers based on the decimal and the repetitive (numbers based on the power of 10).
		hen building the pyramids, the hypostyle hall at Karnak with its gigantic pillars and colossal statues, and the many temples and palaces throughout the land, architects and engineers used their knowledge of mathematics to design and develop the specifications.
		To calculate length, they used a cubit, which was the length of the forearm, from the elbow to the tip of the thumb (approximately 52.5 cm or 20.6 in.).
	www.civilization.ca /civil/egypt/egcs04e.html (310 words)

	Mathematics HQ : Egyptian Mathematics
		Egyptian Mathematical Papyri - Mathematicians of the African Diaspora
		Egyptian mathematical fractions, including algorithms, transcriptions of networkconversations, and links to other Egyptian mathematical resources.
		Mathematics HQ excludes all liability of any kind (including negligence) in respect of any third party information or other material made available on, or which can be accessed using, this Website.
	mathematicshq.com /egyptianmathematics/index.php (860 words)

	Egyptian Schools (Site not responding. Last check: 2007-10-20)
		The Roman Egyptian mummies did not have hieroglyphs (picture writing) on the cartonnage or wrappings, as did mummies in the earlier Egyptian periods.
		However, much of what we know about the Ancient Egyptians comes from the hieroglyphs on the walls of their tombs and in their art.
		Much is known about the Ancient Egyptian knowledge of Mathematics because of a document recorded in the second century B.C. by the scribe, Ahmes.
	www.stemnet.nf.ca /CITE/egypt_school.htm (153 words)

	[HM] Mathematics in Ancient Egypt by Beatrice Lumpkin. (Site not responding. Last check: 2007-10-20)
		This reference was based not on a mathematical papyrus, but on balance sheets in papyrus Bulaq 18, a bookkeeping record written 3700 years ago and translated to German in the 1920's.
		The translation of Lepsius, side by side with the original German, is titled Richard Lepsius, The Ancient Egyptian Cubit and Its Subdivision (1865) translated by J. Degreef and edited by Michael St.
		Usages of mathematical interest include representation of a zero remainder in a bookkeeping papyrus and using a zero reference point on construction lines.
	www.africahistory.net /lumpkin.htm (377 words)

	Mathematics - Encyclopedia Of Mathematics (Site not responding. Last check: 2007-10-20)
		classical mathematics, by the strict interpretation of the phrase `there exists' as...
		Inconsistent mathematics is the study of the mathematical theories that result
		when classical mathematical axioms are asserted within the framework of a...
	mathematics.information-about.net /encyclopediaofmathematics (140 words)

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