The Eightfold Way: The Beauty of Klein's Quartic Curve

Mathematical Sciences Research Institute

doi:10.1017/9781009701730

The Eightfold Way

The Beauty of Klein's Quartic Curve

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Berkolaiko, Gregory and Liu, Wen 2018. Eigenspaces of symmetric graphs are not typically irreducible. Letters in Mathematical Physics, Vol. 108, Issue. 8, p. 1825.

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Edited by Silvio Levy
Mathematical Sciences Research Institute

Publisher:: Cambridge University Press
Online publication date:: June 2025
Print publication year:: 1999
Online ISBN:: 9781009701730
DOI:: https://doi.org/10.1017/9781009701730

Subjects:: Mathematics, Real and Complex Analysis, Geometry and Topology, Algebra
Series:: Mathematical Sciences Research Institute Publications

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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, 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 Eightfold Way

The Beauty of Klein's Quartic Curve

This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface: MSRI and the Klein Quartic
pp ix-x

The Eightfold Way: A Mathematical Sculpture by Helaman Ferguson
pp 1-8

The Geometry of Klein's Riemann Surface
pp 9-50

The Klein Quartic in Number Theory
pp 51-102

Hurwitz Groups and Surfaces
pp 103-114

From the History of a Simple Group
pp 115-132

Eightfold Way: The Sculpture
pp 133-174

Invariants of SL2(𝔽q) . Aut(𝔽q) Acting on ℂn for q = 2n ± 1
pp 175-220

Hirzebruch's Curves Fl , F2 , F4 , Fl4 , F28 for Q(V7)
pp 221-286

On the Order-Seven Transformation of Elliptic Functions
pp 287-332

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The Eightfold Way

The Beauty of Klein's Quartic Curve

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