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Topic: Plimpton 322

	Eleanor Robson and Plimpton 322
		In proposing the use of reciprocals for generating Plimpton 322 she went contrary to Neugebauer, and she went contrary to the underlying mathematics.
		The extant first column of Plimpton 322 suggested to Robson that the OB scribes used the "squaring" of the Diagonal numbers to somehow obtain their results.
		I would suggest that Plimpton 322 originated in an intellectual milieu and culture that was conversant with Pythagoreans at a higher sophisticated level.
	www.world-destiny.org /or/plimpton322f.htm (1864 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		A famous cuneiform tablet Plimpton 322 strongly suggests that they knew a general procedure for constructing Babylonian triples: i.e., three integers that satisfy the Pythagorean theorem (Ne-40).
		Plimpton 322 was first deciphered by O. Neugebauer and A.
		But Plimpton 322 is part of the Plimpton Collection of Columbia University and one is free to go to the Plimpton 322 page of Columbia's Collections & Treasures site.
	www.physics.unlv.edu /~jeffery/astro/mesopotamia/pythagorean.html (177 words)

	[No title]
		Plimpton 322 came from Larsa and conforms as far as can be determined to the formatting features of about six other tablets that date from that region between 1822 and 1784 BC.
		Thus Robson concludes that Plimpton 322 comes from the same period and should be similarly formatted in its missing column.
		According to Robson, an interpretation of a text such as Plimpton 322 should be consistent with all our knowledge of the period in which it originated.
	www.westmont.edu /~phunter/ma155/hw2.doc (445 words)

	American Mathematical Monthly, The: Words and pictures: New light on Plimpton 322 (Site not responding. Last check: 2007-10-11)
		However, if we look at triangles drawn on ancient cuneiform tablets like Plimpton 322, we see that they all point right and are much longer than they are tall: very like a cuneiform wedge in fact.
		In the case of Plimpton 322, for instance, there are three competing interpretations, all equally valid mathematically.
		Plimpton 322 is just one of several thousand mathematical documents surviving from ancient Iraq (also called Mesopotamia).
	www.findarticles.com /p/articles/mi_qa3742/is_200202/ai_n9032871 (1254 words)

	Plimpton 322 Tablet
		The clay tablet with the catalog number 322 in the G. Plimpton Collection at Columbia University may be the most well known mathematical tablet, certainly the most photographed one, but it deserves even greater renown.
		Methods and traditions of Babylonian Mathematics I: Plimpton 322, Pythagorean triples, and the Babylonian triangle parameter equations.
		The numbers on the cuneiform tablet are written sexigesimally (in base 60) with combinations of two symbols, one for tens and one for units.
	aleph0.clarku.edu /~djoyce/mathhist/plimpnote.html (1149 words)

	MAT 300 Spring 2004 --Answers to E-mail assignments
		One way in which the Babylonians found the area of a circle was to square the circumference and then multiply the result by 1/12 = 0;05 (which is equivalent to dividing the result by 12).
		Plimpton 322 is a tablet in the Plimpton Collection at Columbia University.
		In the book's discussion of Plimpton 322, the column that does not appear on the tablet is the column on the far right, labeled y.
	www.southernct.edu /~gingrich/mat3002004/emailassignments2004answers.html (462 words)

	[No title] (Site not responding. Last check: 2007-10-11)
		An amazing example of this is the clay tablet Plimpton 322, so called because it is item number 322 in a collection of artifacts assembled by G. Plimpton in the 1930s and donated to Columbia University in New York City.
		This tablet dates to the 19th century BCE, and can be traced to the Old Babylonian civilization that flourished in Mesopotamia, the fertile valley of the Tigris and Euphrates rivers (in present-day Iraq).
		Plimpton 322 is an example of the use of cuneiform writing.
	cerebro.xu.edu /math/math147/04f/plimpton/plimptonintro.html (431 words)

	Babylonian Pythagoras references (Site not responding. Last check: 2007-10-11)
		J Friberg, Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples and the Babylonian triangle parameter equations, Historia Math.
		O Schmidt, On Plimpton 322: Pythagorean numbers in Babylonian mathematics, Centaurus 24 (1980), 4-13.
		T Viola, On the list of Pythagorean triples ("Plimpton 322") and on a possible use of it in old Babylonian mathematics (Italian), Boll.
	www.gap-system.org /~history/HistTopics/References/Babylonian_Pythagoras.html (423 words)

	Jewels in Her Crown: Treasures of Columbia University Libraries
		"Plimpton 322" is known throughout the world to those interested in the history of mathematics as a result of the interest that Otto Neugebauer, chair of Brown University's History of Mathematics Department, took in the tablet.
		Plimpton, who collected "our tools of learning" on a broad scale, would have been delighted with this interpretation, showing the work of an excellent teacher, not a lone genius a thousand years ahead of his time.
		This unpretentious little book could almost be taken as a symbol of the third component in the collection of George A. Plimpton: "reading, writing and ‘rithmetic." It intends to teach commercial arithmetic, starting from the most elementary level to explain numbers and their positions as designators of units, tens, hundreds, and so forth.
	www.columbia.edu /cu/lweb/eresources/exhibitions/treasures/html/long_topic9.html (2850 words)

	Plimpton 322
		Sometime before 300 BCE, but after Plimpton 322 was written, a special symbol was devised as a zero, but in Plimpton 322 there is potential confusion because of this problem.
		The conventional way to write floating point sexagesimal numbers is by using comma separators, so that 1,29 is 60+29 = 89 in decimal notation, and 1,1,1 is 3661.
		The Internet has a large collection of material on cuneiform and Bablyonian tablets, although not much concerned with mathematics, and no recent photographs of the tablet Plimpton 322.
	www.math.ubc.ca /~cass/courses/m446-03/pl322/pl322.html (1126 words)

	Science News: Reassessing an ancient artifact - Plimpton clay tablet - Brief Article
		The famous Mesopotamian clay tablet known as Plimpton 322 has tantalized historians of mathematics ever since its discovery more than 60 years ago.
		By comparing Plimpton 322 with other ancient tablets, Robson established that its style is consistent with temple records and documents of about 1800 B.C. in Larsa.
		Such evidence enables modern mathematicians to view Plimpton 322 "not as a freakish anomaly in the history of early mathematics but as the epitome of Mesopotamian mathematical culture at its best," Robson says.
	www.findarticles.com /p/articles/mi_m1200/is_4_159/ai_71191539 (488 words)

	Pythagorean Triples
		Plimpton 322 is one of 600 such tablets donated to Columbia University's Rare Book and Manuscript Library by George Plimpton and was item 322 in his catalogue, hence its name.
		Words and Pictures: New Light on Plimpton 322 by Eleanor Robson in American Mathematical Monthly vol 109 (2002), pages 105-120 explores three theories as to the meaning of the numbers on Plimpton 322, one of which is that it is a trigonometric table.
		There is a section on the Plimpton Tablet 322 (not 332 as he mistakenly labels his picture of it), a Babylonian list of Pythagorean triples and how it might have been used by the Babylonians.
	www.mcs.surrey.ac.uk /Personal/R.Knott/Pythag/pythag.html (6318 words)

	Babylonian Pythagoras
		Plimpton 322 is the tablet numbered 322 in the collection of G A Plimpton housed in Columbia University.
		I feel that the arguments are weak, particularly since there are numerous tablets which show that the Babylonians of this period had a good understanding of Pythagoras's theorem.
		Other authors, although accepting that Plimpton 322 is a collection of Pythagorean triples, have argued that they had, as Viola writes in [31], a practical use in giving a:-
	www-history.mcs.st-and.ac.uk /history/HistTopics/Babylonian_Pythagoras.html (1921 words)

	Babylonian Pythagoras references (Site not responding. Last check: 2007-10-11)
		J Friberg, Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples and the Babylonian triangle parameter equations, Historia Math.
		R J Gillings, Unexplained error in Babylonian cuneiform tablet, Plimpton 322, Australian J. Sci.
		O Schmidt, On Plimpton 322: Pythagorean numbers in Babylonian mathematics, Centaurus 24 (1980), 4-13.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/References/Babylonian_Pythagoras.html (423 words)

	Plimpton 322: Commentary
		Cuneiform writing is clearly recognized on our photo of Plimpton 322.
		This is extended to encompass noninteger values by employing the decimal point after the ones digit and placing additional digits to the right of the point to represent negative powers of 10.
		It was originally thought that Plimpton 322 was one of dozens of tablets that simply recorded inventories of food and merchandise.
	cerebro.xu.edu /math/math147/02f/plimpton/plimptontext.html (1514 words)

	The Babylonian Number System (Site not responding. Last check: 2007-10-11)
		It is believed to have been found at Senkereh and was purchased by George Arthur Plimpton in 1923 and brought to the U.S. but was not deciphered until 1945 by Neugebauer and Sachs.
		Designated PLIMPTON 322 in the Plimpton Collection at Columbia University, it is the oldest surviving document on number theory.
		It was made in Babylon between 1900 and 1600 B.C. Traces of modern glue can be seen on the left edge but the left fragment is now lost.
	chemistry.csudh.edu /oliver/smt310-handouts/babylon/babylon.htm (281 words)

	Pythagoras of Samos
		Plimpton 322 (1900 B.C.E. This century, archeologists have unearthed close to half a million Babylonian clay tablets.
		One such tablet, called Plimpton 322 (so called because it is item number 322 in the G.A. Plimpton collection at Columbia University) is of special interest to this essay (figure 2C).
		At first glance, when the cuneiform is translated to our numerals, (figure 2D) the table looks like another record of business transactions, stocktaking etc. Analysis however, shows that it has a deep mathematical significance in the theory of numbers.
	www.mathgym.com.au /history/pythagoras/pytheor.htm (1224 words)

	Reassessing an ancient artifact: Science News Online, Jan. 27, 2001 (Site not responding. Last check: 2007-10-11)
		The famous Mesopotamian clay tablet known as Plimpton 322 represents an ordered list of worked examples that a teacher would use to prepare a sequence of closely related questions about squares and reciprocals for student exercises.
		Neither Sherlock Holmes nor Babylon: A reassessment of Plimpton 322.
		Background information about Plimpton 322 and early interpretations of its meaning can be found at http://aleph0.clarku.edu/~djoyce/mathhist/plimpnote.html.
	www.sciencenews.org /articles/20010127/note13ref.asp (161 words)

	Primary_Source (Site not responding. Last check: 2007-10-11)
		Explore this example of an early Babylonian mathematical tablet: Bill Casselman, of the University of British Columbia, walks you through the Plimpton 322 tablet.
		T or F? The far-left column of the Plimpton 322 tablet numbers each row beginning with 1.
		T or F? Bill Casselman argues that the Plimpton 322 tablet suggests that the Babylonians knew how to generate primitive Pythagorean triples.
	homepage.mac.com /kvmagruder/hsci/02-NearEast/source.html (1199 words)

	Plimpton 322 Tablet (Site not responding. Last check: 2007-10-11)
		The Plimpton 322 Tablet is so named because it is part of the G.A. Plimpton Collection at Columbia University.
		Because of these uncertainties, there is debate about the meaning of the numbers in this table ([1]).
		One interesting pattern that has been noticed on this tablet is in the fourth column.
	www.saintjoe.edu /~lgh4071/Plimpton322.html (578 words)

	Plimpton 322: a remarkable ancient Babylonian tablet on number theory (Site not responding. Last check: 2007-10-11)
		Plimpton 322: a remarkable ancient Babylonian tablet on number theory
		Plimpton 322 is part of a baked clay tablet made in Babylon between 1900 and 1600 BC, probably found at Senkereh in the 1920's, and now in the G.A. Plimpton Collection in Columbia University Library, New York.
		It is the oldest preserved document on number theory.
	zakuski.utsa.edu /~gokhman/ecz/l_p000.html (102 words)

	Bibliography of Mesopotamian Mathematics
		Bruins, E.M. 'Pythagorean triads in Babylonian mathematics; the errors on Plimpton 322'.
		Friberg, J. 'Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples and the Babylonian triangle parameter equation', Historia Mathematica 8, 277-318.
		Viola, T. 'Sull'elenco di terne pitagoriche ("Plimpton 322") e su un suo possible uso nella matematica vetero-babilonese.' Bolletino di storia della sciennze matematiche 1, 103-132.
	it.stlawu.edu /~dmelvill/mesomath/biblio/bigbib.html (7797 words)

	AMERICAN MATHEMATICAL MONTHLY - February 2001
		Words and Pictures: New Light on Plimpton 322
		In the half-century since its publication, Plimpton 322 has become one of the most famous mathematical objects in the world.
		It is a small clay tablet from ancient Mesopotamia (modern-day Iraq) made nearly 4,000 years ago, bearing a mathematical table of Pythagorean triples and related numbers.
	www.maa.org /pubs/monthly_feb02_toc.html (697 words)

	Decoding Museum Numbers (Site not responding. Last check: 2007-10-11)
		YBC 7289 is in the Yale Babylonian Collection and is object number 7289 in their catalog, while the tablet
		Plimpton 322 is the object numbered 322 in the catalog of the George A. Plimpton Collection of the Rare Book and Manuscript Library at Columbia University.
		Below is a list of the more common museum codes and their explanation.
	it.stlawu.edu /~dmelvill/mesomath/museums.html (130 words)

	Mathematics 3573
		Plimpton 322: A Picture is a jpg file of a famous Babylonian clay tablet.
		Plimpton 322: the Old Babylonian Pythagorean Theorem from David Joyce provides a mathematical transcription of the contents of Plimpton 322.
		Plato’s Meno contains the famous discussion in which Socrates shows how to have an uneducated slave boy understand the Pythagorean Theorem.
	ace.acadiau.ca /math/M3573/oldpages/histlinks.htm (383 words)

	[No title]
		Credit: material adapted from Cuneiform Inscriptions of the University of Minnesota Libraries web site ; Reproduced by permission for 2003/2004 academic year; download site: UM 5.
		Plimpton 322 The most famous Babylonian mathematical tablet.
		The Plimpton 322 page is part of Columbia's Collections & Treasures site They do permit educational use with proper credit, but their permission is obscurely written.
	www.physics.unlv.edu /~jeffery/astro/mesopotamia/meso.html (566 words)

	Essay 1 -- Pythagorean Theorem
		Although the theorem was named after him but there is evidence that the Babylonians knew this relationship some 1000 years earlier.
		Plimpton 322, a Babylonian mathematical tablet dated back to 1900 B.C., contains a table of Pythagorean triples.
		The Chou-pei, an ancient Chinese text, also provides the evidence that the Chinese knew about the Pythagorean theorem many years before Pythagorean.
	jwilson.coe.uga.edu /EMT668/EMAT6680.2002/Rouhani/Essay1/pythagorastheorem.html (552 words)

	Topic 2 - Making a table.
		The events surrounding them reads much like a modern detective story, with the sleuth being archaeologist Otto Neugebauer.
		We begin in about 1945 with the Plimpton 322 tablet, which is now the Primpton collection at Yale University, and dates from about 1700 BCE.
		It appears to have the left section broken away.
	www.math.tamu.edu /~veselin.dobrev/math696/document2/node2.html (185 words)

	Babylonian Mathematics (YBC 7289, Plimpton 322)
		These limitations may have led the Egyptian and Babylonian mathematicians of the second millenium BC to convey their knowledge by way of telling examples.
		I dare also say that the 15 triples mentioned in the famous Babylonian clay tablet Plimpton 322 are a 'book' of mathematics in a very condensed form.
		Let me have a look at the 15 triples and invent some tasks to go with the numbers.
	www.seshat.ch /home/babylon.htm (1453 words)

	FoRK-Fork: Talent (dozens & degrees)
		Now, a while back on FoRK, we had traced 80-column lines back a century or so, but 60s go all the way back to Babylon.
		(see Plimpton 322) A "J U S T - S O" S T O R Y --------------------------- Just as we try to determine if a particular computation can be done in a polynomial number of steps, geometers in ancient times would try to construct entities with compass and straightedge.
		When fiddling about with a compass, it is difficult to avoid making hexagons: with [0] the radius set, rotate the compass around a point on the circumference, scribing an arc through the center; this will strike off two of the hexagon's sides.
	www.xent.com /pipermail/fork/2002-May/011635.html (474 words)

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