81. Wallpaper Groups: History Harold Brown, Rolf Bülow, Joachim Neubüser, hans Wondratschek, and hans zassenhaus. Crystallographic Groups of FourDimensional Space. Wiley, New York, 1978. http://www.clarku.edu/~djoyce/wallpaper/history.html

History of crystallographic groups and related topics People have always been interested in patterns, both planar patterns and spacial patterns. Classification of patterns started two and a half millennia ago with the Pythagorean discovery that there are five regular solids: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. Archimedes generalized these to some nearly regular solids, now called Archimedean solids, such as the solid made out of pentagons and hexagons that is used for soccer balls and Buckyballs. Kepler found other nearly regular solids and noted the regular tessellations (tilings) of the plane. There are only three regular tessellations, one of triangles, one of squares, and one of hexagons. There are also several nearly regular tessellations analogous to the Archimedean solids. In the seventeenth century, Robert Hooke piled up "a company of bullets and some few other very simple bodies" to see the different ways that atoms could be arranged to build crystals, in particular, alum crystals. Classification in two and three dimensions In the nineteenth century the classification of planar and spacial lattices and patterns began. One of the problems was, of course, deciding when different patterns exhibited the same sort of regularity. A variety of classification methods were developed. At first, lattice structures were studied. Later, symmetries, and the way the symmetries were related, were used to make finer distinctions. The lattices were generally analyzed by means of quadratic forms using two variables in the planar case and three variables in the spacial case.

82. This Is Info File Eplain.info, Produced By Makeinfo-1.43 From The Warner, Frank W. Construction of commutative diagrams. * zassenhaus, hans Construction of commutative diagrams. * active characters Category codes. http://www.mit.edu/afs/athena/contrib/tex-contrib/info/eplain.info-3

83. This Is Info File Eplain.info, Produced By Makeinfo-1.55 From The whatsits made by index entries Indexing commands. * whitespace Obeying spaces. * zassenhaus, hans Construction of commutative diagrams. http://www.mit.edu/afs/sipb/project/tex-new/info/eplain.info-4

84. Blacker Hovse, House Members, Alpha List By Last Name, 10 Of 10 Zakhor, Avideh, 1980, 1983. Zame, William Robin, 1961, 1965. zassenhaus, hans Peter, 1966, 1970. Zats, Harold R. 1986, 1990. Zeidman, Kenneth, 1951, 1955. http://www.gdbg.org/alphaL_10.html

Blacker Hovse, House Members Alpha list by Last Name Page 10 of 10 Previous Year Main Page Official Blacker Hovse page ... Acronyms and Notes Name Frosh Grad Todd, George Judson Todorovich, Mark Milenko Tollefson, Jeremy J. DNG Tomlinson, Ernest S. DNG Tompkins, Peter Lewis Toomey, Jonathan Edward Torkelson, John Mark DNG Townsend, Michael Jellison Trabert, Steven Gregory Tran-Nhut, Thanh-Van Tran, Thanh M. DNG Trapnell, Jr, Frederick MacKay Trauerman, Jr, Joeseph Klee Ex Traynor, Raymond William Tressel, Patricia Ellen Trott, Delano Brookings DNG Tryon, Robert Christian Tsao, Doris Y. Tserliangos, Platon Themistocles Tuan, Jian-Jin Tucker, John Douglas DNG Tuinenga, Paul William BS:1977 MS:1978 Tung, Ka-Kit BS: 1972 MS:1972 Turk, Benjamin Edward Turner, Marc Louis Turtledove, Harry DNG Twining, David S. Tyler, Douglas Blaine Tyler, Mattew L. Tyler, William King Tyrrill, Alfred Ramsey Tytell, David Edward Uehara, Dean Tsutomu Uhl, Joathan Thomas Upchurch, Paul Robert Upchurch, Sean Alan Updike, Jared Fisher

85. M. Armstrong Groups And Symmetry. Springer 1988. 180p. 3-540 Translate this page H. Brown/R. Buelow/J. Neubueser/H. Wondratschek/hans zassenhaus Crystallographic groups of four-dimensional space. hans zassenhaus What is an angle? Am. http://felix.unife.it/Root/d-Mathematics/d-Groups-and-semigroups/b-Group-theory-

M. Armstrong: Groups and symmetry. Springer 1988. 180p. 3-540-96675-7. DM 72. 569 Martin Belger/Lothar Ehrenberg: Theorie und Anwendungen der Symmetriegruppen. Deutsch 1981. [Teubner 1988, 120p. 3-322-00464-3. DM 14.] H. Bigalke: Heinrich Heesch. Kristallgeometrie, Parkettierungen, Vierfarbenforschung. Birkhaeuser 1988, 320p. DM 78. 2332 Klaus Bongartz/Walter Borho/Detlef Mertens/Andreas Steins: Farbige Parkette. Birkhaeuser 1988. H. Brown/R. Buelow/J. Neubueser/H. Wondratschek/Hans Zassenhaus: Crystallographic groups of four-dimensional space. Wiley 1978. 2637 Johann Jakob Burckhardt: Die Symmetrie der Kristalle. Birkhaeuser 1988. Michael Field/Martin Golubitsky: Chaotische Symmetrien. Birkhaeuser 1993. [= Symmetry and chaos. Oxford UP.] 14271 Istvan Hargittai/Magdolna Hargittai: Symmetrie. Rowohlt 1998, 290p. DM 27. 4930 Michael Klemm: Symmetrien von Ornamenten und Kristallen. Springer 1982. 6231 J. Lomont: Applications of finite groups. Dover 1993, 350p. 0-486-67376-6. $10. 8578 Erhard Quaisser: Die Symmetriestruktur von Figuren. In 8567 Beutelspacher/, 147-161. 2604 Marjorie Senechal/Jean Taylor: Quasicrystals: The view from Les Houches. Math. Intell. 12/2 (1990), 54-64. 5730 Ian Stewart: Alle Jahre wieder bricht das Chaos aus. Spektrum 1993/12, 12-15. Wirklich schoene Bilder durch das Zusammenspiel von Symmetrie und Chaos. Ian Stewart/Martin Golubitsky: Denkt Gott symmetrisch? Birkhaeuser 1993. Hans Zassenhaus: What is an angle? Am. Math. Monthly 61 (1954), 369-378.

86. Some Personal Reminiscences Of Olga Taussky Hans Schneider The There was a session of the Mathematical Association of America in memory of Emil Artin whose speakers were hans zassenhaus and Helmut Hasse. http://www.math.wisc.edu/~hans/olga

87. Citations: A New Algorithm For Factoring Polynomials Over Finite Fields - Cantor D. G. Cantor and H. zassenhaus. A new algorithm for factoring polynomials over finite fields. Math. Comput. 26 (1981), 587592. http://citeseer.nj.nec.com/context/220145/0

39 citations found. Retrieving documents... D. G. Cantor and H. Zassenhaus " A new algorithm for factoring polynomials over finite fields ", Math. Comp. 36 (1981), no. 154, 587592. Home/Search Document Not in Database Summary Related Articles Check This paper is cited in the following contexts: Modular Rational Sparse Multivariate Polynomial Interpolation - Erich Kaltofen Lakshman (1990) (2 citations) (Correct) large if each m i is less than p : Choosing p m i implies that the roots of (z) modulo p are the the m i : Thus the modular image of (z) is sufficient for recovering the m i : Finding the integer roots of (z) in Step 4 is accomplished using a randomized Cantor Zassenhaus algorithm (see [Cantor and Zassenhaus, 1981] ) to factor (z) modulo a prime p: Then the true roots are reconstructed from their modular images by Hensel lifting. Furthermore, we only need a modular image of (z) The transposed Vandermonde system in step 5 can be solved using the method of Zippel (1990) We now state the modular version of .... David G. Cantor and Hans Zassenhaus. "

88. Zassenhaus http://www.metaspinner-media.de/datenbank/page/zassenhaus.shtml

Hilfe  Smart Options: Metafilter Quicktipps Favoriten Suchmaschinentipp Suche [international] Suche [deutsch] Bilder-Suche Finanzen Geschichte Internationale News Job-Suche Kids ´n Family Medizin [metamed] MP3-Suche PC-Magazine Software Religion Online-Auktionen Wissen megameta-Suche alle Wörter eines der Wörter genauer Text Auktionen Finanzen Autos Preisvergleich ... Metakiosk Schriftgrösse ändern Katalog Gesundheit Lifestyle Reisen Versicherung Onlinespiele Drei neue Spiele am Start: Snake, F1 Challenge und Curve Scratch - nehmen Sie die neue Heraus- forderung an? Hier gehts los Spartipps Telefon Werktags Wochenende Strom ... Gebrauchtwagen Surftipp Stimmungsvolle E-Cards bequem übers Internet verschicken ... Intern Über uns Pressestimmen 10 Gründe Suchspion ... Suchstatistik metaspinner Datenbank Home - Datenbankabfrage: zassenhaus Halt Wacht im Dunkel EUR 0,00 Ein Baum bl?im November. Bericht aus den Jahren des Zweiten Weltkriegs. EUR 12,27 Ein Baum bl?im November EUR 6,60 The Theory of groups EUR 0,00 Ein Baum bl?im November. (6829 996). EUR 2,97 Halt Wacht im Dunkel EUR 0,00 ?er die ?uivalenz ganzzahliger Darstellungen EUR 0,00

89. AIP Niels Bohr Library MARC Display. Briefe an David Hilbert / Hermann Minkowski ; mit Beitr. u. hrsg. von L. Rüdenberg uH zassenhaus. by Minkowski, H. (Hermann), 18641909. http://libserv.aip.org:81/ipac20/ipac.jsp?uri=full=3100001~!17268~!0&profile=aip

90. Untitled 1974 Aull, Charles E. Brown, Ezra Dierker, Paul F. Exoo, Geoffrey Gardner, Ben HANSON, DENIS Hare, Donovan R. Katchalski, Meir Liu, Andy C. KLEITMAN, DANIEL J. Klimmek, Regina Li, Anping Mielke http://personalwebs.oakland.edu/~grossman/Erdos1

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