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Encyclopedia > Klein quartic

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). 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.


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.


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  Results from FactBites:
 
Klein quartic - Wikipedia, the free encyclopedia (168 words)
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.
Encyclopedia: Klein (854 words)
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.
  More results at FactBites »


 
 

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