Geometry Geometry Revisited by Coxeter

micromass

Author: H. S. M. Coxeter, Samuel L. Greitzer
Title: Geometry Revisited
Amazon Link: http://www.amazon.com/Geometry-Revis.../dp/0883856190
Prerequisities: High-School mathematics
Level: Undergrad

Table of Contents:

Code:

 Preface
 Points and Lines Connected with a Triangle The extended Law of Sines
 Ceva's theorem
 Points of interest
 The incircle and excircles
 The Steiner-Lehmus theorem
 The orthic triangle
 The medial triangle and Euler line
 The nine-point circle
 Pedal triangles

 Some Properties of Circles The power of a point with respect to a circle
 The radical axis of two circles
 Coaxal circles
 More on the altitudes and orthocenter of a triangle
 Simson lines
 Ptolemy's theorem and its extension
 More on Simson lines
 The Butterfly
 Morley's theorem

 Collinearity and Concurrence Quadrangles; Varignon's theorem
 Cyclic quadrangles; Brahmagupta's formula
 Napoleon triangles
 Menelaus's theorem
 Pappus's theorem
 Perspective triangles; Desargues's theorem
 Hexagons
 Pascal's theorem
 Brianchon's theorem

 Transformations Translation
 Rotation
 Half-turn
 Reflection
 Fagnano's problem
 The three jug problem
 Dilatation
 Spiral similarity
 A genealogy of transformations

 An Introduction to Inversive Geometry Separation
 Cross ratio
 Inversion
 The inversive plane
 Orthogonality
 Feuerbach's theorem
 Coaxal circles
 Inversive distance
 Hyperbolic functions

 An Introduction to Projective Geometry Reciprocation
 The polar circle of a triangle
 Conics
 Focus and directrix
 The projective plane
 Central conics
 Stereographic and gnomonic projection

 Hints and Answers to Exercises
 References
 Glossary
 Index

BloodyFrozen

Good for high school math competitions. Almost all the topics are not covered in a standard high school math course.

Snow-Leopard

The Book is used for AMC VIII to AMC XII.The best book ever written for Mathematics Olympiad Geometry.

Vargo

It seems that the best thing people can say about this book is that it helps you to win high school math competitions.

I read this book after finishing my undergraduate degree in mathematics. I found it enjoyable, but I preferred Coxeter's Introduction to Geometry because it had more depth and breadth.

mathwonk

I agree. I am not nuts about this book. Winning contests involves using facts that you may not understand fully how to prove. This book is like that. E.g. the discussion of the "power of the point" claims correctly that this theorem of Euclid is an easy corollary of the principle of similarity. True enough.

However what they do not mention is that the theory of similarity is quite deep, and was not available to Euclid when he proved this theorem, so he gave a different proof using Pythagoras. Indeed if one uses Euclid's proof, then one can use this result to deduce the important principle of similarity without going to as much difficulty as is usually done.

If like me you are interested in the logical connections between different results, then you believe in doing them in logical order, not assuming the most difficult and deep ones first without justification, and then using them to make other results appear easy.

If however you want to solve contest problems quickly, then you want to use all the big guns available on the littlest peanut problems, in order to dispatch them in enough time to finish the test with the highest possible score. There is no harm in this, and I was myself so motivated in high school, but not so much any more.

fourier jr

the only thing I remember about this book is it's the place where I found out how to solve the 3 jugs problem using barycentric coordinates:
http://www.cut-the-knot.org/triangle/glasses.shtml

View Poll Results: For those who have used this book
Strongly Recommend	3	60.00%
Lightly Recommend	2	40.00%
Lightly don't Recommend	0	0%
Strongly don't Recommend	0	0%
Voters: 5. You may not vote on this poll

Similar discussions for: Geometry Revisited by Coxeter
Thread	Forum	Replies
the FCT revisited	Differential Geometry	0
LaTeX: Drawing Coxeter/Dynkin graph	Linear & Abstract Algebra	2
Oil Revisited	General Physics	2
Oil Revisited	General Physics	2
x^y=y^x REVISITED	General Math	3

BloodyFrozen Recognitions: Gold Member	Good for high school math competitions. Almost all the topics are not covered in a standard high school math course.

Snow-Leopard	The Book is used for AMC VIII to AMC XII.The best book ever written for Mathematics Olympiad Geometry.

Vargo	Geometry Revisited by Coxeter It seems that the best thing people can say about this book is that it helps you to win high school math competitions. I read this book after finishing my undergraduate degree in mathematics. I found it enjoyable, but I preferred Coxeter's Introduction to Geometry because it had more depth and breadth.

fourier jr	the only thing I remember about this book is it's the place where I found out how to solve the 3 jugs problem using barycentric coordinates: http://www.cut-the-knot.org/triangle/glasses.shtml