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. Since then, mathematicians have discovered that the same object comes up in different guises in many areas of mathematics, from complex analysis and geometry to number theory. This volume explores the rich tangle of properties and theories surrounding this multiform object. It includes expository and research articles by renowned mathematicians in different fields. It also includes a beautifully illustrated essay by the mathematical sculptor Helaman Ferguson, who distilled some of the beauty and remarkable properties of this surface into a sculpture entitled "The Eightfold Way." The book closes with the first English translation of Klein's seminal article on this surface.
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The German mathematician Felix Klein discovered in 1879 that the surface that we now call the Klein quartic has many remarkable properties. Since then, mathematicians have discovered that the same object comes up in different guises in many areas of mathematics, from complex analysis and geometry to number theory.This volume explores the rich tangle of properties and theories surrounding this multiform object. It includes expository and research articles by renowned mathematicians in different fields and a beautifully illustrated essay by the mathematical sculptor Helaman Ferguson. The book closes with the first English translation of Klein's seminal article on this surface.
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This introduction to The Eightfold Way and the Klein quartic was written for the sculpture's inauguration. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inflection triangle, klein curve, second degree character, heptagon edges, platonic tessellation, hyperbolic honeycomb, step geodesics, quotient tori, invariant line bundles, linear holonomy, quartic invariant, cone metrics, parametrizes elliptic curves, bicycle operations, perspective axes, polar conics, graded bicycle, pants decomposition, quotient surface, plane quartic curve, inflection tangents, modular curves, triangle tessellation, nonconstant map, quotient sphere Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Bicycle Conjecture, London Math, Main Figure, Felix Klein, Bill Thurston, Geometry Center, Johnson Reprint, Gesammelte Mathematische Abhandlungen, Publications Volume, Helaman Ferguson, Graduate Texts, Silvio Levy, Abelschen Functionen, Academic Press, Elliptische Funktionen, Gesammelte Werke, Acta Math, Cambridge University Press, Glasgow Math, Identification of the Curve, Medici Chapel, Robert Fricke, Gauss the Cat, John Horton Conway New!
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This introduction to The Eightfold Way and the Klein quartic was written for the sculpture's inauguration. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inflection triangle, klein curve, second degree character, heptagon edges, platonic tessellation, hyperbolic honeycomb, step geodesics, quotient tori, invariant line bundles, linear holonomy, quartic invariant, cone metrics, parametrizes elliptic curves, bicycle operations, perspective axes, polar conics, graded bicycle, pants decomposition, quotient surface, plane quartic curve, inflection tangents, modular curves, triangle tessellation, nonconstant map, quotient sphere Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Bicycle Conjecture, London Math, Main Figure, Felix Klein, Bill Thurston, Geometry Center, Johnson Reprint, Gesammelte Mathematische Abhandlungen, Publications Volume, Helaman Ferguson, Graduate Texts, Silvio Levy, Abelschen Functionen, Academic Press, Elliptische Funktionen, Gesammelte Werke, Acta Math, Cambridge University Press, Glasgow Math, Identification of the Curve, Medici Chapel, Robert Fricke, Gauss the Cat, John Horton Conway New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 37
books:
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- Linear Groups with an Exposition of the Galois Field Theory by Leonard Eugene Dickson on page 112, and page 129
- Ludwig Otto Hesse's Gesammelte Werke (AMS Chelsea Publishing) (German Edition) by Ludwig Otto Hesse on page 129, and page 329
- Michelangelo: The Medici Chapel by James Beck on page 167
- Current Topics in Complex Algebraic Geometry (Mathematical Sciences Research Institute Publications) by Herbert Clemens in Front Matter
- Comparison Geometry (Mathematical Sciences Research Institute Publications) by Karsten Grove in Front Matter
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