Geometry Revisited New Mathematical Library Pdf

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Dec 12, 2018 Circul Wyrd rated it it was amazing

This is a special book for me: Late in life it helped me to rediscover math. Technically speaking, I haven't actually completed it (the number of math books I have ever actually 'completed', whatever that means, being approximately 0), however I did make a point of working *all* of the exercises from chapters 1-4, occasionally with help, and for the remaining 5th chapter, I have only scanned, thus far. This is not because I expect it to be less reachable than the other chapters, but I wanted to This is a special book for me: Late in life it helped me to rediscover math. Technically speaking, I haven't actually completed it (the number of math books I have ever actually 'completed', whatever that means, being approximately 0), however I did make a point of working *all* of the exercises from chapters 1-4, occasionally with help, and for the remaining 5th chapter, I have only scanned, thus far. This is not because I expect it to be less reachable than the other chapters, but I wanted to postpone projective geometry until I had pursued some other paths for awhile. The writing is beautiful, and from the beginning I felt as if I was in a séance, but the real genius of the book is in the exercises. Some of them are far from easy. But in the hints you are given just enough information to put it together yourself, usually. As a note however, for some of the more difficult ones I had assistance from PhD students who found them interesting, and for some of those questions, certain aspects raised issues that I never found anyone who could give a definitive answer. Coxeter is, in my opinion, in a special category of mathematician. He was foremost in his time, and he was also genuinely vested in finding a way to communicate to as large an audience as possible. From every thing I know about him, this book, written later in his own career, was not written for personal advancement, but for love of the subject and desire to communicate, but without pulling even one single punch (there is no royal road to geometry). I wrote the following inscription in my copy: To whomever discovers and reads this book ... After a 30+ year absence from this type of math and a presence of mostly tedious bean-counting math this book came my way (from where I don't recall, unless Euclid?) and began a new interest in math. May it do the same for another. Enjoy. ...more

Jan 21, 2019 Beau rated it it was amazing

This book literally made me laugh out loud with sheer awe and delight at the theorems proved; there are so many beautiful, striking, and elegant results in this dense volume. Basic topics from Euclidean geometry covered include Ceva's theorem, the Euler line, the nine-point circle, coaxal circles, Simson lines, Ptolemy's theorem, the butterfly theorem, Morley's theorem, Napoleon triangles, Varignon's theorem, theorems of Menelaus, Pappus, and Desargues. Other chapters include using transformatio This book literally made me laugh out loud with sheer awe and delight at the theorems proved; there are so many beautiful, striking, and elegant results in this dense volume. Basic topics from Euclidean geometry covered include Ceva's theorem, the Euler line, the nine-point circle, coaxal circles, Simson lines, Ptolemy's theorem, the butterfly theorem, Morley's theorem, Napoleon triangles, Varignon's theorem, theorems of Menelaus, Pappus, and Desargues. Other chapters include using transformations of the plane (translation, rotation, reflection, spiral symmetry) to prove theorems; an introduction to inversive geometry—containing some of the most enjoyable material in the book including a wonderful proof that the nine-point circle is tangent to the incircle and three excircles of a given triangle; and an introduction to projective geometry.

The book is extremely well-written with an economy of language and notation and very readable, concise, and beautiful proofs. There are also bits of historical information and interesting quotations throughout. There are many excellent exercises ranging from trivial to extremely difficult; and there are outlines of solutions to all of them.

To be able to read this book you need to remember your high school geometry pretty well (as most of it is assumed), as well as some analytic geometry and trigonometry. This book would be an excellent resource for students preparing for difficult high school mathematical competitions, like olympiads and their precursors. Some of the exercises are probably of olympiad caliber.

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