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Topic: Hugo Steinhaus

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	Steinhaus
		Hugo Steinhaus was born in Galicia into a family of Jewish intellectuals.
		However, by the time Steinhaus was born in Jaslo, Austria had named the region the Kingdom of Galicia and Lodomeria and given it a large degree of administrative autonomy.
		To Steinhaus mathematics was a mirror of reality and life much in the same way as poetry is a mirror, and he liked to "play" with numbers, sets, and curves, the way a poet plays with words, phrases, and sounds.
	www.educ.fc.ul.pt /icm/icm2003/icm14/Steinhaus.htm (1519 words)

	Hugo Dyonizy Steinhaus (Site not responding. Last check: 2007-10-19)
		Steinhaus studied for a year in Lvov, spent a term in Munich but then spent 5 years studying mathematics at the University of Göttingen.
		Steinhaus was the main figure in the Lvov School until 1941.
		Steinhaus spent the war years hiding from the Nazis, suffering great hardships, going hungry most of the time but always thinking about mathematics.
	www.stetson.edu /~efriedma/periodictable/html/Sn.html (676 words)

	HUGO STEINHAUS (1987 - 1972) and his contribution to the applied mathematics
		Thus Hugo Steinhaus was one of the founders and the leading member of the two mathematical schools: one in Lwów and the second in Wroclaw.
		Steinhaus clearly recognized that the definition extends to situations with a continuum of choices and takes note of the computational difficulties to be encountered in both cases.
		In Wroclaw Professor Steinhaus established two mathematical centres for teaching and research in applications: the chair of Applied Mathematics at the Wroclaw University and a similar chapter in the Mathematical Institute of the Polish Academy of Sciences.
	www.it.lut.fi /mat/EcmiNL/ecmi33/arti.html (1703 words)

	Steinhaus biography
		Steinhaus studied Lebesgue's two major books Leçons sur l'intégration et la recherche des fonctions primitives (1904) and Leçons sur les séries trigonmétriques (1906) around 1912 after completing his doctorate.
		When the prospect of war was looming in 1938, Steinhaus proposed Lebesgue for an honorary degree from Lvov.
		Steinhaus spent the war years from June 1941 hiding from the Nazis, suffering great hardships, going hungry most of the time but always thinking about mathematics [Amer.
	www-history.mcs.st-andrews.ac.uk /Biographies/Steinhaus.html (1748 words)

	Steinhaus Graphs - Description
		Steinhaus Graphs are named for Hugo Steinhaus who asked if there are Steinhaus triangles containing the same number of 0's ans 1's.
		A Steinhaus triangle is the upper triangular part of a Steinhaus matrix (excluding the the diagonal).
		All Steinhaus graphs are connected, except for the ones generated by the all zero string, but the complements c an be disconnected.
	home.wlu.edu /~dymacekw/steinhaus/descrip.html (275 words)

	Seminar Abstract (Site not responding. Last check: 2007-10-19)
		Hugo Steinhaus (1887-1972), a prominent Jewish-Polish mathematician, began the modern study of -the now widely discussed- "Fair Division" problem, some sixty years ago.
		It turns out that Steinhaus' basic idea was known already in two ancient cultures, which at the time were apparently independent.
		The solution was dormant in the European economic tradition until Steinhaus rediscovered it, but appeared explicitly in an early Homiletic-Mishnaic text, reappears in the Talmud as a standard legal ruling, and an ethical-behavioral aspect of it was raised by medieval Rabbinic commentaries.
	www.ratio.huji.ac.il /showSeminarAbstract.asp?seminarID=187 (263 words)

	University of North Texas North Texan Online Spring 2003 : Mysterious Math
		Steinhaus asks if a set of points on the plane can be created, where exactly one point in the set will match one intersection on a lattice — no matter how the lattice is moved.
		Imagine the Steinhaus set of points is a constellation of stars.
		Once they solved the Steinhaus problem, Mauldin and Jackson sought out new problems for which they could exercise skills and techniques they had developed.
	www.unt.edu /northtexan/archives/p03/mmath.htm (632 words)

	MATHEWS: Steinhaus Triangles
		It's easy to see that the minimal number of minus signs is zero (corresponding to the triangle existing entirely of +'s) and that the average number of minus signs is exactly N/2 where N=n(n+1)/2 denotes the total number of signs in the triangle.
		Steinhaus Graphs were introduced by John Molluzz in 1975 as undirected graphs where the upper triangular part of the adjacency matrix is a Steinhaus triangle.
		Steinhaus Graphs are still a research topic, for a starting point see http://www.wlu.edu.
	www.wschnei.de /number-theory/steinhaus-triangles.html (638 words)

	Dividing the Spoils
		Steinhaus, meanwhile, concentrated his thoughts on cake--cake as a symbol of all the goods we lust after.
		Perhaps Steinhaus had seen hungry families quarreling over pitifully small rations of food; perhaps he was haunted by the many partitions of Poland.
		Steinhaus did use examples involving land to illustrate the problem he was trying to solve.
	www.colorado.edu /education/DMP/dividing_spoils.html (4748 words)

	Washington and Lee University Steinhaus Research (Site not responding. Last check: 2007-10-19)
		Planar: The planar Steinhaus graphs have been classified.
		Bipartite: The generating strings for bipartite Steinhaus graphs are known.
		Disconnected Components; The generating strings for the Steinhaus graphs with disconnected complements are known.
	home.wlu.edu /~dymacekw/steinhaus/index.html (32 words)

	Steinhaus Research Publications (Site not responding. Last check: 2007-10-19)
		Wayne M. Dymacek and Tom Whaley, Steinhaus graphs as a source of bit-wise projects, Journal of Computing in Small Colleges (1992).
		J.C. Molluzzo, Steinhaus graphs, theory and Applications of Graphs (Kalamazoo, Michigan, 1976) (Yousef Alavi and Don R. Lick, eds.), Lecture Notes in Math.
		Hugo Steinhaus, One hundred problems in elementary mathematics, Dover, New York, 1979.
	math.wlu.edu /steinhau/publications.html (369 words)

	the way to CD-ROM
		After the changes of regime in 1956 Steinhaus decided that it was his time to help in the analysis of an economic problem.
		Knowing all the options, costs of the transportation of raw materials, the sources of labor force and all other data, Steinhaus came to the meeting ready to show the minister the results of his calculations and analyses.
		Steinhaus frowned: “I'm sorry to say that this is the worst possibility; the sources of raw materials are more distant in this case and the constant cost of transport will make it economically prohibitive”.
	www.andsol.org /meu/4-en.html (4062 words)

	Steinhaus–Moser notation - Wikipedia, the free encyclopedia
		Steinhaus only defined the triangle, the square, and a circle
		It has been proven that Moser's number, although extremely large, is smaller than Graham's number.
		Robert Munafo's Big Numbers, which hints Steinhaus and Moser came up with this notation jointly in the '70s.
	en.wikipedia.org /wiki/Steinhaus_polygon_notation (332 words)

	Stefan Banach Summary
		Steinhaus later wrote that he was "so struck by the words 'the Lebesgue integral'" that he heard from the two that he came closer and introduced himself to the young men.
		"I was greatly surprised," Steinhaus went on to say, "when, after a few days, Banach brought me a negative answer with a reservation which resulted from his ignorance of [a technical point about which he did not know]." Banach and Steinhaus were later to collaborate on a number of mathematical studies.
		In addition, he wrote an important popular textbook, Differential and Integral Calculus (1929-30) and was founder with Steinhaus of the journal Studia mathematica.
	www.bookrags.com /Stefan_Banach (1233 words)

	E.W.Dijkstra Archive: Another look at the problem from Hugo Steinhaus (EWD 1311)
		Let a,b,c,d be, in order, the 4 sides of a convex polygon; let a and b meet at an end point of diagonal x, and let y be the other diagonal.
		My proof seems to repeat the same argument about four times, each time with a different permutation of the letters; I have not been able to avoid that repetition by exploiting the symmetries.
		By phrasing the argument as a reductio ad absurdum, Steinhaus could postpone the introduction of nomenclature and thus reduce the repetition somewhat.
	www.cs.utexas.edu /~EWD/transcriptions/EWD13xx/EWD1311.HTML (713 words)

	February 7, 2003 UNT Inhouse publication: UNT mathematics professors find solution to 50-year-old math problem
		The problem was first posed in the 1950s by Polish mathematician Hugo Steinhaus.
		Steinhaus' problem asks if there is exactly one point in a set of points in a plane that will always intersect with a lattice or grid when that lattice is rotated or moved horizontally or vertically.
		Imagine the set of points is a constellation of stars and the lattice is a wire grid.
	www.unt.edu /inhouse/february72003/lattice.htm (358 words)

	Steinhaus, Hugo Dyonizy (1887-1972)
		During the Second World War, as a Jew he was compelled to hide from persecution by the Nazis, yet continued his mathematical work despite great hardship.
		In 1944, Steinhaus proposed the problem of dividing a cake into n pieces so that it is proportional and envy free (see cake-cutting).
		He is also well known as the author of the widely-read Mathematical Snapshots.
	www.daviddarling.info /encyclopedia/S/Steinhaus.html (223 words)

	ScienceNow
		In 1957, Polish mathematician Hugo Steinhaus challenged his colleagues to find a curious set of numbers.
		First, imagine a set of numbers arrayed in a regular grid, like intersections within an infinite piece of graph paper.
		Steinhaus asked if it were possible to make a set such that no matter how you placed the grid on the plane, the grid and the irregular set always intersect at exactly one point.
	bric.postech.ac.kr /science/97now/02_11now/021126a.html (273 words)

	Monuments on Mathematicians / Portrait of H. Steinhaus (Site not responding. Last check: 2007-10-19)
		Dieses Portrait von Hugo Steinhaus ist im Hörsaal des Mathematischen Instituts der Universität in Breslau zu finden.
		This portrait of Hugo Steinhaus can be found in the lecture-hall at the institute for mathematics of the university in Wrocław.
		The photograph was taken in August 2005 by H.-J. Caspar.
	www.w-volk.de /museum/poster01.htm (74 words)

	In Memory of Z. W. Birnbaum
		He practiced law for a year, but during that time he resumed his studies in mathematics.
		In 1926, he received a Teaching Certificate in mathematics and taught at a gymnasium in Lwów from 1925-29 while continuing his graduate studies in mathematics under Steinhaus and Banach among others.
		He received his Ph.D. in 1929, with Hugo Steinhaus as his major professor.
	www.math.washington.edu /~sheetz/Obituaries/zwbirnbaum.html (1059 words)

	Large Numbers at MROB
		These numbers were constructed by Hugo Steinhaus and Leo Moser (in the late 1970's or earlier, exact date unknown) just to show that it is easy to create a notation for extremely large numbers.
		(In a slightly different version, described in Steinhaus' 1983 book Mathematical Snapshots (pages 28-29), the pentagon is replaced by a circle, so mega is 2 inside a circle.
		Steinhaus also defines megiston as 10 inside a circle.
	home.earthlink.net /~mrob/pub/largenum-3.html (2715 words)

	Hugo Steinhaus - Wikipedia, wolna encyklopedia
		W 1929 Steinhaus wspólnie ze Stefanem Banachem założył czasopismo "Studia Mathematica" o zasięgu międzynarodowym, poświęcone wyłącznie analizie funkcjonalnej.
		Po wkroczeniu do Lwowa wojsk niemieckich (29 czerwca 1941), wobec represji hitlerowców wobec Żydów, Steinhaus wraz z rodziną kilka miesięcy ukrywał się w mieszkaniach znajomych we Lwowie, po czym w końcu listopada 1941 uciekł do Osiczyna pod Lwowem i stamtąd w lipcu 1942 do Berdechowa koło Gorlic.
		Tam pod zmienionym nazwiskiem (Grzegorz Krochmalny) uczestniczył w tajnym nauczaniu.
	pl.wikipedia.org /wiki/Hugo_Steinhaus (510 words)

	Ivars Peterson's MathTrek - Digits, Squares, and Cycles
		Beginning with 123,457 leads to the repeating set of numbers 4, 16, 37, 58, 89, 145, 42, and 20.
		Mathematician Eugene D. Nichols, now retired from Florida State University in Tallahassee, first encountered a mathematical proof establishing this cyclic digital behavior in a Polish book of problems by Hugo Steinhaus, published in 1958.
		However, Steinhaus proved the theorem only for squaring the digits.
	www.maa.org /mathland/mathtrek_2_2_98.html (769 words)

	Earliest Known Uses of Some of the Words of Mathematics (H)
		Hugo Steinhaus posed the following problem in the famous Lvov Scottish Book "Given are three sets A
		The note was by Steinhaus and others but the proof they presented was due to Banach; this is based on the Borsuk-Ulam Theorem.
		The note indicates that the problem can be formulated as follows: "Can we place a piece of ham under a meat cutter so that meat, bone and fat are cut in halves?" (Based on WA Beyer, A Zardecki "The early history of the ham sandwich theorem," American Mathematical Monthly, January 2004, pp.
	members.aol.com /jeff570/h.html (5875 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		With the adoption of Austria’s new constitution in 1867, guaranteeing equality to all citizens under the law and permitting freedom of movement as well as domicile, Jews began to move to Jaslo.
		Ignacy was a prominent lawyer and for a number of years served as a member of the Austrian parliament.
		The Steinhaus family took no interest in the Jewish life of Jaslo.
	home.earthlink.net /~jackherzig/jaslo (10861 words)

	The Mathematics Genealogy Project - Wladyslaw Hugo Steinhaus (Site not responding. Last check: 2007-10-19)
		The Mathematics Genealogy Project - Wladyslaw Hugo Steinhaus
		According to our current on-line database, Wladyslaw Hugo Steinhaus has 10 students and 1202 descendants.
		If you have additional information or corrections regarding this mathematician, please use the update form.
	www.genealogy.ams.org /html/id.phtml?id=7383 (87 words)

	Chapter 3a -The 3 x 3 x 3 Cube
		This particular version of what has now become a very common type of puzzle is unusual in that all of the pieces are flat and contain different numbers of cubes increasing in arithmetic progression.
		The next reference known to the author for the 3 x 3 x 3 cube is a version that appeared in Mathematical Snapshots, by Hugo Steinhaus published by Oxford University Press in 1950.
		Puzzle historians might well be puzzled by this half-century gap.
	www.johnrausch.com /PuzzlingWorld/chap03a.htm (1300 words)

	An algorithm to list all the permutations
		Rediscovered many times since, the procedure is due originally to the Polish mathematician Hugo Steinhaus (January 1887-February 1972), a student of David Hilbert at Göttingen, did important work on orthogonal series, probability theory, real functions and their applications.
		Theorem 4.5.1 (Steinhaus) There is a sequence of (not necessarily distinct) 2-cycles,
		In other words, each permutation can be written as a product of (not necessarily disjoint) 2-cycles
	web.usna.navy.mil /~wdj/book/node156.html (120 words)

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