Geometry Revisited (New Mathematical Library): H. S. M. Coxeter, Samuel L. Greitzer: 9780883856192: Amazon.com: Books

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H. S. M. Coxeter

Geometry Revisited (New Mathematical Library) Paperback – September 5, 1996

by H. S. M. Coxeter (Author), Samuel L. Greitzer (Author)

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Among the many beautiful and nontrivial theorems in geometry found in Geometry Revisited are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed.

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Print length

193 pages
Language

English
Publisher

American Mathematical Society
Publication date

September 5, 1996
Dimensions

5.9 x 0.6 x 8.9 inches
ISBN-10

0883856190
ISBN-13

978-0883856192
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Editorial Reviews

Review

'The book is rich in remarkable facts and thereby is very effective in promoting the significance and the value of geometry in mathematical teaching, a promotion which is very necessary.' Mathematical Reviews

Book Description

A fascinating collection of geometric proofs and properties.

Product details

Publisher ‏ : ‎ American Mathematical Society (September 5, 1996)
Language ‏ : ‎ English
Paperback ‏ : ‎ 193 pages
ISBN-10 ‏ : ‎ 0883856190
ISBN-13 ‏ : ‎ 978-0883856192
Item Weight ‏ : ‎ 1.16 pounds
Dimensions ‏ : ‎ 5.9 x 0.6 x 8.9 inches

Best Sellers Rank: #815,720 in Books (See Top 100 in Books)
- #131 in Topology (Books)
- #2,428 in Applied Mathematics (Books)

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H. S. M. Coxeter

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Terrific review

Reviewed in the United States on September 14, 2015

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The word "revisited" is important. This is not suitable as an introduction, but is excellent as a review. The exercises should be done, I think, but be careful. I found a mistake on page 3. Exercise 4 there asks you to prove a false statement: "Let p and q be the radii of two circles through A, touching B and C, respectively. Then pq equals R squared [where R is the radius of the circle circumscribing triangle ABC]." However, with A, B, C fixed, R is also fixed, but p and q can be as large as you like. This was surely a mistake; the authors do not indicate that the reader will be given possibly false statements to prove in the exercises.

3 people found this helpful

Charles Saunders

Reviewed in the United States on October 29, 2007

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This is a wonderful book if you want to gain a real understanding of what geometry can be (if you like this book you should buy the biography of Coxeter: "King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry" - it is one of the best biographies of a mathematician on the market and shows that Coxeter was a genius and a hoot). However, if you know a significant amount of geometry, then try "Introduction to Geometry, 2nd Edition" as that is the more complete (and (very) much more rigorous) text. Also, if you like this book, then buy "Visual Complex Analysis".

PS. My son is using this book in his high school geometry course (at my insistence) rather than the 'text' he was issued. He is now assisting the teacher with the proofs and problems.

15 people found this helpful

A great geometry book to prepare for high school competition

Reviewed in the United States on February 18, 2013

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This is an excellent book for those high school students preparing for proof oriented math competitions (such as USAJMO and USAMO). It contains many advanced theorems (Ceva, Menelaus, Pappus, etc) and techniques (geometry transformation including spiral similarity) that are wildly used by those people making creative geometry contest problems.
However, this book is not written as a typical textbook and you need to have some basic geometry foundation first. For a typical America high school students I would recommend you read Kiselev's Geometry book first (available at [...] before reading this book.

Also for a more structured treatment of similar topics, I recommend "college geometry" by Nathan Altshiller-Court.

7 people found this helpful

Great Information and Great Delivery

Reviewed in the United States on December 26, 2018

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The book provides an in-depth explanation of some geometrical concepts that passed over my head in Geometry class, and the exercises in the book provide a fun activity to practice what has been learned. This, coupled with a wonderfully speedy delivery, made the product a wise purchase in my opinion.

3 people found this helpful

The best text on Elementary Geometry in English

Reviewed in the United States on March 22, 2009

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This is one of my three favorite texts in Elementary Geometry, and the only one written in English. It's a multipurpose text. You will probably won't cover these material at school, but if you are interested on math contests, or more serious geometry study, this is also a good text to follow to learn, or if you, like me, learned most of this material over a decade ago, but need a good text as a reference, this text is a great to do so. Dearly recommended.

12 people found this helpful

The Best Book in Geometry

Reviewed in the United States on February 5, 2011

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This book is the best book I can find in Geometry. It is compact (less than 200 pages), but it covers a lot of advanced topics in Geometry. The book is extremely well-written and easy to follow. Each section focuses on one concept, with a couple of excellent exercises. It helped my child (and I) to discover and appreciate the beauty of Geometry. We enjoyed the book immensely. Highly recommended for talented students with Honors Geometry background.

4 people found this helpful

I am half way through it. Can't put it down.

Reviewed in the United States on January 26, 2020

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I only wish they could have expanded on some of the topics. I was left wanting more.
Very well written.

Want to know what has happened in geometry in the last 400 years?

Reviewed in the United States on September 9, 2014

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A first-class introduction to pure geometry after the Greeks, covering developments from the 17th century to the middle 20th century. The material presented is well chosen. The proofs are very clear and easy to follow. The exercises are interesting because they usefully develop the material presented in the text and are neither too easy nor too hard.

3 people found this helpful

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George C

Great book

Reviewed in the United Kingdom on January 23, 2021

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Absolute classic. A must read for anyone who is interested in geometry. One of my favorite books on the subject.

Carlo

Geometria

Reviewed in Italy on January 14, 2019

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Ottimo testo d'approfondimento geometrico nel piano. Bella la selezione degli esercizi. Dallo studio del triangolo mediale, ortico e podale alla circonferenza dei nove punti e la retta di Simson. Per proseguire con lo studio delle trasformazioni del piano, i teoremi di allineamento e concorrenza come Pappo, Desargues, Menelao e Ceva, fino all'introduzione della geometria proiettiva. Minime le conoscenze di base necessarie alla lettura.

One person found this helpful

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PC

and book was in excellent condition. Book contains many theorems and properties beyond ...

Reviewed in Canada on April 16, 2016

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Arrive right on time, and book was in excellent condition.
Book contains many theorems and properties beyond high-school geometry. It is well illustrated with figures and topic-related exercises with hints to solution. Excellent casual reading for those interested in the subject, and a must for those working on geometry.

Kindle-Kunde

Moderne Einführung in die Geometrie mit Übungen

Reviewed in Germany on January 13, 2013

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H.S.M. Coxeter ist einer der bekanntesten Geometer des 20. Jahrhunderts; S.L. Greitzer ist Mitarbeiter bei der IMO, die die internationale Wettbewerbe für Mathematik ausrichtet. Dieses Buch, zuerst publiziert in der anspruchsvollen Reihe des MAA (Mathematical Association of America) enthält 6 Kapitel (Dreieckslehre, Kreislehre, Kollinearität, Transformationen, Kreisinversionen und projektive Geometrie) und liefert eine perfekte, moderne Darstellung der "Euklidische Geometrie" im 20. Jahrhundert für Vorlesungen. Das Buch ist unentbehrlich für alle die Geometrie unterrichten; es erfordert fundierte Mathematik- und Englisch-Kenntnisse. Das Buch enthält zahlreiche Übungsaufgaben verschiedenen Schwierigkeitsgrades. Hinweise zu den nichttrivialen Aufgaben werden gegeben. Diese Übungsaufgaben zu allen Kapiteln führen teilweise den Text fort und sind als Herausforderung des Lesers gedacht. Zitat aus dem Buch: "The problems throughout the book contain extensions of the text as well as challenges to the reader."

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kawayosi

興味深い初等幾何の本

Reviewed in Japan on November 25, 2014

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すでに一度日本語で読み、よさを実感していますので、原語で読むのが楽しみです。

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