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Topic: Johann Benedict Listing

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	Listing biography
		Soon Listing was attending mathematics courses given by Gauss and he was quickly spotted by Gauss as being both a very able and a very hard working student.
		Listing was an obvious choice for an assistant to accompany him and the pair set off less than a month after Listing had obtained his doctorate.
		However, Listing did not find favour with his colleagues because of the behaviour of himself and his wife and it is certain that he received less recognition for his scientific achievements because of it.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Listing.html (1652 words)

	[No title]
		Johann Benedict Listing (1802-1882) was the first to use the word topology.
		Listing's topological ideas were due mainly to Gauss, although Gauss himself chose not to publish any work on topology.
		In 1861 Listing published a much more important paper in which he described the Möbius band (4 years before Möbius) and studied components of surfaces and connectivity.
	www.lycos.com /info/topology--studies.html (359 words)

	Listing (Site not responding. Last check: 2007-10-11)
		Although there was a time when architecture was considered as a branch of mathematics, it certainly wasn't considered such in Listing's day so the combination was a rather peculiar one dictated by a compromise between Listing's wishes and the remit of the Städel foundation.
		It was a journey on which Listing maintained his interests in many different topics and as well as the geology and physics which were the purpose of the trip, he worked in his spare time on mathematics, in particular working on the topological ideas which had first been suggested by Gauss.
		Although little changed in the research that Listing undertook, he had always gone in the direction which interested him, he did have to give up a large part of his laboratory to Weber.
	mirror.math.nankai.edu.cn /mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/Listing.html (1584 words)

	Mathematician Biography (Site not responding. Last check: 2007-10-11)
		Gauss realized how hard Listing was willing to work and invited him into his circle of friends.
		In 1839 Listing was appointed the Professor of Physics.
		Listing was one of those students who loved to learn about everything.
	academies.culver.org /alg1xs03/stampej/biograph.htm (241 words)

	listing - Search Results - MSN Encarta
		An example of an early topological problem is the Königsberg bridge problem: Is it possible to cross the seven bridges over the Pregel River,...
		Dictionary, listing of the words of a language, usually in alphabetical order but sometimes also by topic, with their meanings or their equivalents....
		Unlike most American cities, which make up only a part of a particular county, New York is made up of five separate counties, which are called...
	encarta.msn.com /listing.html (155 words)

	Topology in mathematics (Site not responding. Last check: 2007-10-11)
		Listing was not the first to examine connectivity of surfaces.
		Listing had examined connectivity in three dimensional Euclidean space but Betti extended his ideas to n dimensions.
		Jacob Bernoulli and Johann Bernoulli invented the calculus of variations where the value of an integral is thought of as a function of the functions being integrated.
	physics.rug.ac.be /Fysica/Geschiedenis/HistTopics/Topology_in_mathematics.html (1454 words)

	Listing (Site not responding. Last check: 2007-10-11)
		Listing was not the only student invited into close friendship with
		Although little changed in the research that Listing undertook, since he had always gone in the direction which interested him, he did have to give up a large part of his laboratory to
		Among the honours which Listing did receive were election to the Göttingen Academy and the Royal Society of Edinburgh.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Listing.htm (1483 words)

	Johann Benedict Listing - Wikipedia
		Johann Benedict Listing (Francoforte, Germania, 25 luglio 1808 - Göttingen, Germania, 24 dicembre 1882), matematico, fisico e geodeta tedesco.
		Nel 1858 Listing scoprì le proprietà della superficie che ora è ampiamente nota come nastro di Möbius, indipendentemente e un poco prima di questi.
		Listing si occupò ampiamente di geodesia eseguendo molte osservazioni e coordinando campagne di misurazioni; a lui si deve anche il termine geoide.
	it.wikipedia.org /wiki/Johann_Benedict_Listing (456 words)

	CITR - Technical Reports
		Johann Benedict Listing (1802-1882) introduced the term "topology" into mathematics in a paper published in 1847, and he also defined cell complexes for the first time in a paper published in 1862.
		Carl Friedrich Gauss (1777-1855) is often cited as the one who initiated these ideas, but he did not publish either on topology or on cell complexes.
		The pioneering work of Leonhard Euler (1707-1783) on graphs is also often cited as the birth of topology, and Euler's work was cited by Listing in 1862 as a stimulus for his research on cell complexes.
	www.citr.auckland.ac.nz /techreports/show.php?id=60 (346 words)

	Michael Kelly's Page of Misery: Questions: Mobius Strip
		His father, also named Johann Benedict Listing, as they were too poor to afford two names, was a maker of brushes.
		Listing was appointed to a professorship in physics 1839 despite never having published a paper.
		Listing borrowed frequently and heavily, sometimes from usurers; Pauline habitually suggested he got a proper job instead of folding bits of paper all the time.
	www.michaelkelly.fsnet.co.uk /qmobius.htm (1267 words)

	Espn2 Listing (Site not responding. Last check: 2007-10-11)
		Multiple Listing Service - Multiple Listing Service (MLS) (also Multiple Listing System or Multiple Listings Service) is a database which allows real estate brokers representing sellers under a listing contract to widely share information about properties with real estate brokers who may represent potential buyers or wish to cooperate with a seller'...
		Johann Benedict Listing - Johann Benedict Listing (born July 25, 1808, died December 24 1882) was a German mathematician, born in Frankfurt, Germany, and died in GÃ¶ttingen, Germany.
		List of Atlanta Radio Stations and Advertising Services: Wras Radio Station Request Line 33 Gilmer St Se Atlanta, GA (404)...
	tvlistings.vvvvvv3.com /espn2listing.html (661 words)

	BIBLIOGRAPHY
		Johann Benedict Listing introduced this subject, while Euler is regarded as the founder of topology.
		Listing published his Census; Bernhard Riemann studied the multiplicities of the roots of equations, while Klein and Fricke developed his ideas.
		Möbius was born on November 17, 1790 in Schulpforta, Saxony to Johann Heinrich Möbius, who died when he was only 3 years old.
	www.facstaff.bucknell.edu /udaepp/090/w3/melissal.htm (2174 words)

	Johann Benedict Listing
		GEOID was first used in unsere jetzige Kenntniss by Johann Benedict Listing (1808-1882) German (geoide) in 1872 in Ueber der Gestalt u.
		It was (Calculus and Pizza), 1858 by German mathematicians August Ferdinand Benedict Listing.
		Johann Benedict Benedict Listing Biography of Johann Listing's family were...
	johanngmpw.beexifli.info (598 words)

	History (Site not responding. Last check: 2007-10-11)
		In 1861 Listing published a much more important paper in which he described the Mobius band (4 years before Mobius) and studied components of surfaces and connectivity.
		This is not as straightforward as it might appear since even in three dimensions it is possible to have a surface that cannot be reduced to a point yet closed curves on the surface can be reduced to a point.
		This was a topic which arose from mathematical physics and astronomy, brought about because the methods of classical analysis were somewhat inadequate in tackling certain types of problems.
	differential-topology.net /hist.html (1499 words)

	References for Listing (Site not responding. Last check: 2007-10-11)
		E Breitenberger, Johann Benedict Listing, Neue Deutsche Biographie 14 (Berlin, 1952-), 700-701.
		E Breitenberger, Johann Benedict Listing, in I M James (ed.), History of Topology (Amsterdam, 1999), 909-924.
		A Tripodi, L'introduzione alla topologia di Johann Benedict Listing, Accad.
	www.gap-system.org /~history/Printref/Listing.html (90 words)

	Möbius Strip
		Take a strip of paper, give it a half-twist, then attach the ends together to form a single band, and you have a Möbius Strip.
		Co-discovered in the mid-19th century by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing, the Möbius strip has the curious property of having only one side.
		A line drawn starting from the seam down the middle will meet back at the seam but at the "other side." If continued the line will meet the starting point and will be double the length of the original strip of paper.
	www.arcadiastreet.com /cgdoodles/geometries_110.htm (190 words)

	Ivars Peterson's MathTrek -Möbius and his Band
		Nonetheless, it is the name Möbius rather than Listing that we now associate with one-sidedness.
		It's also a bit surprising that no one before Möbius and Listing seems to have noticed the existence of one-sided surfaces.
		Interestingly, the first "application" of the idea that I can find outside of mathematics is in the realm of magic.
	www.maa.org /mathland/mathtrek_7_10_00.html (1064 words)

	Origins of some arithmetic terms-2
		According to John Conway, this was the common term in use until around 1870 to 1900 when it gave way to parallelepiped; although the OED lists its use by John Playfair as early as 1812.
		It contains lists of scratch marks indicating the prime numbers and is believed to be the oldest record of prime numbers in still existing.
		I was told by Mary Dolciani herself, that the SMSG group "decided "to use y=mx+b because of the French (Descartes, I presume)-"montant"; I found it strange because the "logical word" would be "pente"(which is slope (and the standard term in Spanish is pendiente, which matches this).
	www.pballew.net /arithme3.html (8676 words)

	Coast to Coast July 3
		The Möbius band is a puzzlingly twisted strip of paper joined at the ends with, remarkably, only one side.
		It was discovered separately in 1858 by German mathematicians August Ferdinand Möbius and Johann Benedict Listing.
		As Pickover (Calculus and Pizza), a prolific science author and former Discover columnist, tells us, today Möbius's strip is everywhere: it forms the familiar recycling symbol; freestyle skiers attempt a stunt called a "Möbius flip"; and it appears in the works of artists like M.C. Escher and writers like Arthur C. Clarke.
	www.aceemploymentservices.net /coast_to_coast__july__3.htm (474 words)

	What is Topology ?- Lituraterre.org :Site de l'illettrisme européen
		The central problem in proving the conjecture in three dimensions is that, unlike the two-manifolds cases, topologists have no complete classification scheme for three-manifolds.
		There exists no list of all possible manifolds that can be checked one by one to make sure that all have different homotopy groups.
		Topology is also concerned with the ways in which one manifold may be embedded within another, such as the ways a knotted circle may be embedded in three-dimensional space.
	www.lituraterre.org /Illiteracy-what_is_topology.htm (2002 words)

	Listing Johann Benedict 1808 1882 Papers, 1827-1882. AIP International Catalog of Sources
		Listing, Johann Benedict, 1808-1882 -- Family -- Correspondence.
		Wicke and Listing on blood sugar (urinary sugar) measurement]; Items 26.
		Letters to Listing from: Aegidi [1], Airy [1], Ballot [1], Böttger [1]; Brugsch [1], Denhardt [1], Erman [1], Ettinghausen [1], Ficus [1], Ad.
	www.aip.org /history/catalog/icos/637.html (323 words)

	Metta Bracelet, sterling silver: Dharmacrafts meditation supplies
		Mobius was not the first to discover the geometrical phenomena, nor was he was the first to publish his findings.
		German mathematician Johann Benedict Listing (1808-1882) actually discovered the planal surface in July 1858 and published his discovery in 1861.
		If your order includes other items in addition to the items listed above, our regular shipping rates apply (see shipping chart).
	www.dharmacrafts.com /105xBS/2J084/Metta-Bracelet-sterling-silver.html (609 words)

	Möbius strip Summary
		The Möbius strip was named for August Ferdinand Möbius (1790-1868), a German mathematician and astronomer, who discovered it in 1858 while studying the properties of one-sided surfaces.
		At almost the same time another German mathematician, Johann B. Listing (1806-1882), discovered the surface and published the first description in his book on topological investigations.
		Most historians agree, however, that Möbius was not the first to discover the strip named after him: by coincidence, the German mathematician Johann Benedict Listing also discovered the Möbius strip in 1858, edging out Möbius by a few months.
	www.bookrags.com /M%C3%B6bius_strip (2073 words)

	Earliest Known Uses of Some of the Words of Mathematics (M)
		Johannes Tropfke in his "Geschichte der Elementar-Mathematik, vol.
		A list of matrix and linear algebra terms having entries on this web site is here.
		Micron (one millionth of a meter) was coined by Johann Benedict Listing (1808-1882), according to Breitenberger (1999).
	members.aol.com /jeff570/m.html (9381 words)

	Why is the lemniscate or mobius strip symbol used to represent infinity? (Site not responding. Last check: 2007-10-11)
		However, this explanation is improbable, since the symbol had been in use to represent infinity for over two hundred years before August Ferdinand Möbius and Johann Benedict Listing discovered the Möbius strip in 1858.
		John Wallis is usually credited with introducing infty as a symbol for infinity in 1655 in his De sectionibus conicus.
		Edit: An alternate way of writing lower case omega is omega with a line over it which looks similar to the infinity symbol.
	www.answerbag.com /q_view/39338 (908 words)

	Earliest Known Uses of Some of the Words of Mathematics (T) (Site not responding. Last check: 2007-10-11)
		was introduced in German in 1847 by Johann Benedict Listing (1808-1882) in "Vorstudien zur Topologie," Vandenhoeck und Ruprecht, Göttingen, pp.
		Topology is found in English in February 1883 in Nature: "The term Topology was introduced by Listing to distinguish what may be called qualitative geometry from the ordinary geometry in which quantitative relations chiefly are treated" (OED2).
		Listing, however, was not a major contributor to the field he named and the major contributors of the 19
	members.aol.com /jeff570/t.html (4928 words)

	local tv listing (Site not responding. Last check: 2007-10-11)
		Endangered Species Program, Listing Program (Local tv listing)
		Through the Listing Program, the Service determines whether to add a species to...
		In some instances, species listing can be avoided by the development of...
	acarballeira.com /local-tv-listing/archive_31_2006.php (79 words)

	Origins of some arithmetic terms
		Other related words are minor (smaller of two), minced (cut into small pieces), miniature (on a small scale) and menu (a small list).
		Multiply comes from the combined roots of multi, many, and pli, for folds, as in a number folded on itself many times.
		Torus is from the Latin word for bulge and was first used to describe the molding around the base of a column.
	www.pballew.net /arithmet.html (4349 words)

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