
	Where results make sense

Topic: Klein quartic

Related Topics

Felix Klein

Klein bottle

Erlangen programme

Topology

Riemannian geometry

Timeline of mathematics

Bernhard Riemann

Nikolai Ivanovich Lobachevsky

Basque people

1733

East Coast of the United States

In the News (Thu 10 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Klein quartic - Wikipedia, the free encyclopedia
		The order 168 of G is the maximum allowed for this genus 3; and this curve is uniquely determined by requiring that the symmetry is as large as this.
		The Klein quartic can be given a metric of constant negative curvature and then tiled with 24 regular heptagons.
		Klein's quartic occurs all over mathematics, in contexts including representation theory, homology theory, octonion multiplication, Fermat's last theorem, and Stark's theorem on imaginary quadratic number fields of class number 1.
	en.wikipedia.org /wiki/Klein_quartic (168 words)

	Encyclopedia: Klein
		The Klein quartic x3y + y3z + z3x = 0, named after Felix Klein, is a Riemann surface, and a curve of genus 3 over the complex numbers C. The Klein quartic has automorphism group isomorphic to the projective special linear group G = PSL(2,7).
		Bruce J. Klein is the Chairman of the Immortality Institute and a graduate of finance from the University of Georgia.
		The Honourable Ralph Phillip Klein (born November 1, 1942), leader of the Alberta Progressive Conservatives, is current premier of the Canadian province of Alberta.
	www.nationmaster.com /encyclopedia/Klein (854 words)

	Pure and Applied Geometry - Polyhedral Models of Klein's Quartic (Site not responding. Last check: 2007-10-21)
		Felix Klein's quartic, also called Klein's curve, Klein's regular map or Klein's group PSL (2,7) is one of the most famous mathematical objects, or, as A.M. Macbeath formulated ([L], p.
		Felix Klein discovered this finite group of order 168 in 1879 [K], and since then its properties were investigated, generalized, applied and discussed in hundreds of papers.
		Klein's quartic is the algebraic curve with equation
	www.math.uni-siegen.de /wills/klein (1589 words)

	Read This: The Eightfold Way
		The Klein Quartic is the plane curve of lowest degree that attains this upper bound.
		The proof that Klein's quartic is a plane curve of genus 3 uses Euler's formula for a triangulation and is arguably simpler than using Hurwitz's formula for branched coverings.
		Klein showed that the ring of invariants is generated by four invariants, and gave geometric explanations of the algberaic zero loci of these invariants.
	www.maa.org /reviews/eightfold.html (1298 words)

	Klein, Montana - Encyclopedia Glossary Meaning Explanation Klein, Montana (Site not responding. Last check: 2007-10-21)
		Klein is a census-designated place located in Musselshell County, Montana.
		Klein is located at 46°24'10" North, 108°32'54" West (46.402844, -108.548378).
		Out of the total population, 50.0% of those under the age of 18 and 0.0% of those 65 and older are living below the poverty line.
	www.encyclopedia-glossary.com /en/Klein-Montana.html (428 words)

	Klein's Quartic Curve
		Part of the distortion is caused by embedding the Klein quartic in ordinary 3d Euclidean space.
		If we gave the Klein quartic the metric it inherits from the hyperbolic plane, the edges of the cube would be geodesics.
		The Klein quartic is tiled by 56 triangles.
	math.ucr.edu /home/baez/klein.html (3607 words)

	Search Results for Klein (Site not responding. Last check: 2007-10-21)
		Klein's synthesis of geometry as the study of the properties of a space that are invariant under a given group of transformations, known as the Erlanger Programm (1872), profoundly influenced mathematical development.
		Klein assumed the fifth dimension to be periodic with a period l = planck c(2k)1/2/e where e was the charge of the electron and k was Einstein's constant of gravitation.
		Klein's new view on modular functions, uniting geometrical aspects such as the fundamental domain with group theory tools such as the congruence subgroups and with topological notions such as the genus of the Riemann surface, was fully exploited by Hurwitz.
	www-history.mcs.st-and.ac.uk /Search/historysearch.cgi?SUGGESTION=Klein&CONTEXT=1 (10446 words)

	psl(2,7) (Site not responding. Last check: 2007-10-21)
		The projective special linear group G = PSL(2,7) is a finite group in mathematics that has important applications in algebra, geometry, and number theory.
		It is the automorphism group of the Klein quartic, and it is the second-smallest nonabelian simple group, next to the alternating group A
		Klein's quartic pops up all over the place in mathematics, not least of which includes representation theory, homology theory, octonion multiplication, Fermat's Last Theorem, and Stark's theorem on imaginary quadratic number fields of class number 1!
	www.yourencyclopedia.net /PSL(2,7).html (545 words)

	Klein Quartic Physics
		I am happy that Klein Quartic Physics as I have described it seems to me to be not only consistent with, but also equivalent to, my D4D5E6E7E8 VoDou Physics model.
		The Klein surface is the Riemann surface of the algebraic curve with equation...
		The Riemann surface of...[ the Klein Quartic ]...
	www.valdostamuseum.org /hamsmith/KQphys.html (5084 words)

	Ck Calvin Klein (Site not responding. Last check: 2007-10-21)
		1) " Ck" -- In the context of Ck Calvin Klein
		2) " Calvin" -- In the context of Ck Calvin Klein
		3) " Klein" -- In the context of Ck Calvin Klein
	www.lottery-news.net /dust31838-ck_calvin_klein.html (303 words)

	Felix Klein - Wikipedia, the free encyclopedia
		Felix Christian Klein (April 25, 1849 – June 22, 1925) was a German mathematician.
		His enunciation of the Erlangen programme classifying geometries by their underlying group of symmetries was hugely influential: a synthesis of much of the mathematics of its time.
		This article about a mathematician is a stub.
	en.wikipedia.org /wiki/Felix_Klein (120 words)

	week215
		This means that the Klein quartic has 24 symmetries forming a group isomorphic to the rotation/reflection symmetry group of a tetrahedron.
		This is an excellent example of Klein's Erlangen program for reducing geometry to group theory, which I discussed in "week213".
		Klein's Quartic Curve Fano plane --------------------- ---------- 28 pairs of opposite 28 choices of a point triangular faces and a non-incident line, {p,l}.
	math.ucr.edu /home/baez/week215.html (4051 words)

	quartic products at MSN Shopping (Site not responding. Last check: 2007-10-21)
		Many of these questions are touched on in this classic volume: such as the classification of quartic surfaces, the description of moduli spaces for abelian surfaces, and the automorphism group of a Kummer surface.
		First printed in 1905 after the untimely death of the author, this work has stood for most of this century as one of the classic reference works in geometry.
		More that the surface that we now call the Klein quartic has many remarkable properties, including an incredible 336-fold symmetry, the maximum possible degree of symmetry for any surface of its type.
	shopping.msn.com /results/shp?bcatid=4,ptnrid=8,text=quartic,ptnrdata=1 (434 words)

	Klein quartic -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		Klein quartic -- Facts, Info, and Encyclopedia article
		The Klein quartic has (Click link for more info and facts about automorphism group) automorphism group isomorphic to the (Click link for more info and facts about projective special linear group) projective special linear group G = (Click link for more info and facts about PSL(2,7)) PSL(2,7).
		The order 168 of G is the (The largest possible quantity) maximum allowed for this genus 3; and this curve is uniquely determined by requiring that the symmetry is as large as this.
	www.absoluteastronomy.com /encyclopedia/K/Kl/Klein_quartic.htm (112 words)

	Calvin Klein Sleepwear (Site not responding. Last check: 2007-10-21)
		1) " Calvin" -- In the context of Calvin Klein Sleepwear
		2) " Klein" -- In the context of Calvin Klein Sleepwear
		3) " Sleepwear" -- In the context of Calvin Klein Sleepwear
	www.cabaret-54.com /dust38918-calvin%20klein%20sleepwear.html (273 words)

	Calvin Klein Obsession (Site not responding. Last check: 2007-10-21)
		1) " Calvin" -- In the context of Calvin Klein Obsession
		2) " Klein" -- In the context of Calvin Klein Obsession
		3) " Obsession" -- In the context of Calvin Klein Obsession
	www.lottery-news.net /dust5332-calvin_klein_obsession.html (397 words)

	Klein Quartic Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-21)
		Looking For klein quartic - Find klein quartic and more at Lycos Search.
		Find klein quartic - Your relevant result is a click away!
		Look for klein quartic - Find klein quartic at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Klein_quartic (336 words)

	Geometry
		In the newsgroup sci.physics.research, we were discussing a heptagonal tiling of a genus 3 object, that we call "Klein's Quartic".
		A somewhat prettier figure is the tiling of "Fermats quartic", with 12 octagons.
		Klein suggest that his figure should have octagonal symmetry, and that the 6 vertices of the octagon are of at infinity.
	www.xs4all.nl /~westy31/Geometry/Geometry.html (971 words)

	Edge (Site not responding. Last check: 2007-10-21)
		Bring's curve was first studied in Klein's 1884 book in connection with the transformation to reduce the general
		Edge was not someone uninterested in modern techniques, however, and it may come as a surprise to some that in a 1991 paper he included computer-drawn pictures.
		Other topics Edge worked on, all of which exhibit his mastery of the subject, include nets of quadric surfaces, the geometry of the Veronese surface, Klein's quartic, Maschke's quartic surfaces, Kummer's quartic, the Kummer surface, Weddle surfaces, Fricke's octavic curve, the geometry of certain groups, finite planes and
	www-history.mcs.st-and.ac.uk /history/Mathematicians/Edge.html (1182 words)

	Calvin Klein Perfumes (Site not responding. Last check: 2007-10-21)
		1) " Calvin" -- In the context of Calvin Klein Perfumes
		2) " Klein" -- In the context of Calvin Klein Perfumes
		This is a list of people with the surname Klein:
	www.lottery-news.net /dust2303-calvin_klein_perfumes.html (384 words)

	The Eightfold Way - Cambridge University Press
		MSRI and the Klein quartic William P. Thurston; 2.
		The geometry of Klein’s Riemann surface Hermann Karcher and Matthias Weber; 3.
		The Klein quartic in number theory Noam Elkies; 4.
	www.cambridge.org /catalogue/print.asp?isbn=0521660661&print=y (307 words)

	Encyclopedia: Klein quartic
		Updated 257 days 22 hours 54 minutes ago.
		The Eightfold Way: The Beauty of Klein's Quartic Curve (http://www.msri.org/publications/books/Book35/contents.html)
		Click for other authoritative sources for this topic (summarised at Factbites.com).
	www.nationmaster.com /encyclopedia/Klein-quartic (160 words)

	[No title]
		He showed this surface could be described by an incredibly symmetrical quartic equation in 3 complex variables:u^3 v + v^3 w + w^3 u = 0where we count two solutions as the same if they differ by an overall factor.
		This is an example of a "congruence subgroup"; these serveto relate complex analysis to number theory in lots of cool ways.In particular, Klein's quartic curve is justH/Gamma(7)Since Gamma(7) is a normal subgroup of PSL(2,Z), the quotientgroup PSL(2,Z)/Gamma(7) = PSL(2,Z/7) acts as symmetries of Klein's quartic curve.
		Alsoavailable as math.SG/0312252.I've got to read these sometime.Having the number 56 on my brain, I can't resist nothing that ifyou take Klein's quartic curve tiled by heptagons, and you count the vertices, you get 24 x 7 / 3 = 56since each vertex is shared by 3 heptagons.
	www.altelco.net /~lovekgc/HSdocumentsandlinks/MagicNumber168.doc (1894 words)

	Mathematics 536 (Spring 2003) Information
		This curve is a smooth plane quartic, so it has genus 3.
		It is a theorem of Harnack that at most g+1 ovals are possible in the real locus of a plane curve.
		history of the geometry of a genus 3 curve, the Klein quartic.
	www.math.rutgers.edu /courses/536/536-s03/math536.html (367 words)

	Abbeys Bookshop - Eightfold Way: The Beauty of Kleins Quartic Curve (Site not responding. Last check: 2007-10-21)
		The German mathematician Felix Klein discovered in 1879 that the surface that we now call the Klein quartic has many remarkable properties, including an incredible 336-fold symmetry, the maximum possible degree of symmetry for any surface of its type.
		MSRI and the Klein quartic William P. Thurston
		The geometry of Klein's Riemann surface Hermann Karcher and Matthias Weber
	www.abbeys.com.au /items/07/02/66 (286 words)

	MAT 539 -- Algebraic Topology -- Spring 2003
		VRML models: a Möbius band, a Klein bottle and a Trefoil Knot.
		For instance here is "Klein's modular quartic" which is on the patio of MSRI Berkeley.
		Torus and Klein Bottle Games: a collection of Java applets/games played on the surface of a torus or a Klein bottle (chess, tic-tac-toe, crossword puzzles, and more).
	www.math.sunysb.edu /~sorin/539 (708 words)

	Felix Klein Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-21)
		Looking For felix klein - Find felix klein and more at Lycos Search.
		Find felix klein - Your relevant result is a click away!
		Look for felix klein - Find felix klein at one of the best sites the Internet has to offer!
	www.karr.net /search/encyclopedia/Felix_Klein (288 words)

	Felix Klein
		German mathematician who created the Klein bottle (1849-1925).
		Indra's Pearls: The Vision of Felix Klein (reference)
		Source: compiled by the editor from various references; see credits.
	www.websters-online-dictionary.org /definition/english/Fe/Felix+Klein.html (288 words)

Try your search on: Qwika (all wikis)