How Does One Cut a Triangle?

by Soifer, Alexander; Engel, Philip L.; Erdos, Paul; Grunbaum, Branko; Johnson, Peter D., Jr.

• ISBN13: 9780387746500
• ISBN10: 0387746501
• Edition: 2nd
• Format: Paperback
• Copyright: 2009-08-05
• Publisher: Springer Verlag

Summary

Including dozens of proofs and counterexamples, this second edition of Soifer 's inspirational book uses geometry, algebra, trigonometry, linear algebra, and rings to show how different areas of mathematics can be juxtaposed in the solution of a given problem.

Table of Contents

Forewords for the Second Edition
Foreword	p. ix
Foreword	p. x
Forewords for the First Edition
Foreword	p. xiii
Foreword	p. xiv
Foreword	p. xv
Foreword	p. xvi
Preface to the Second Edition	p. xxi
Preface to the First Edition	p. xxvii
The Original Book
A Pool Table, Irrational Numbers, and Integral Independence	p. 3
A Pool Table Problem	p. 3
Numbers Rational and Irrational	p. 7
Integral Independence	p. 8
How Does One Cut a Triangle? I	p. 15
Excursions in Algebra	p. 25
A Good Try	p. 25
Excursion in Linear Algebra	p. 27
Excursion in Algebraic Equations	p. 34
How Does One Cut a Triangle? II	p. 37
Excursion in Trigonometry	p. 41
Is There Anything Beyond the Solution?	p. 47
Pursuit of the Best Result	p. 51
Birth of a Problem	p. 51
The Optimal Result	p. 55
Second Solution to the Five-Point Problem	p. 60
Convex Figures and the Function S(F)	p. 65
Creating a Function	p. 65
Study of Convex Figures: The Upper Bound of S(F)	p. 70
Study of Convex Figures: A Lower Bound of S(F)	p. 77
A Very Brief Introduction to Affine Geometry	p. 79
Study of Convex Figures: The Best Lower Bound of S(F)	p. 86
A One-Hundred-Dollar Problem	p. 96
Triangle in Ellipse	p. 99
Paul Erdos: Our Joint Problems	p. 107
PGOM Erdos	p. 107
Problems	p. 109
Solutions	p. 110
Convex Figures and Erdos' Function Sa (F)	p. 121
Developments of the Subsequent 20 Years
An Alternative Proof of Grand Problem II	p. 127
Miklos Laczkovich on Cutting Triangles	p. 129
Matthew Kahle on the Five-Point Problem	p. 137
Soifer's One-Hundred-Dollar Problem and Mitya Karabash	p. 143
Coffee Hour and the Conway-Soifer Cover-Up	p. 147
Farewell to the Reader	p. 157
Cutting a Triangle into Congruent Triangles	p. 161
The Five-Point Problem	p. 163
References	p. 167
Notation	p. 171
Index	p. 173
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