#35: The Eightfold Way: The Beauty of Klein's Quartic Curve
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# MSRI Publications -- Volume 35

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

### Edited by
Silvio Levy

### Contents

Table of Contents

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Preface: MSRI and the Klein Quartic

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The Eightfold Way:
A Mathematical Sculpture by Helaman Ferguson,
by **William P. Thurston**, 1-7

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The Geometry of Klein's Riemann Surface,
by **Hermann Karcher** and **Matthias Weber**, 9-49

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The Klein Quartic in Number Theory, by **Noam Elkies**, 51-101

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Hurwitz Groups and Surfaces, by
**A. Murray Macbeath**, 103-113

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From the History of a Simple Group, by
**Jeremy Gray**, 115-131 (reprinted from *The Mathematical
Intelligencer*)

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Eightfold Way: The Sculpture, by
**Helaman** and **Claire Ferguson**, 132-173 plus 4 color pages

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Invariants of SL_{2}(**F**_{q})
Aut(**F**_{q}) Acting on
**C**^{n} for
*q* = 2*n* ± 1, by
**Allan Adler**, 175-219

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Hirzebruch's Curves
*F*_{1},
*F*_{2},
*F*_{4},
*F*_{14},
*F*_{28}
for **Q**(7^{1/2}), by
**Allan Adler**, 221-285

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On the Order-Seven Transformation of Elliptic Functions, by
**Felix Klein** (translated by Silvio Levy),
287-331

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