Episodes in Nineteenth and Twentieth Century Euclidean Geometry (New Mathematical Library)
By Ross Honsberger
* Publisher: The Mathematical Association of America
* Number Of Pages: 188
* Publication Date: 1996-09-05
* ISBN-10 / ASIN: 0883856395
* ISBN-13 / EAN: 9780883856390
* Binding: Paperback
Book Description:
Professor Honsberger has succeeded in 'finding' and 'extricating' unexpected and little known properties of such fundamental figures as triangles, results that deserve to be better known. He has laid the foundations for his proofs with almost entirely synthetic methods easily accessible to students of Euclidean geometry early on. While in most of his other books Honsberger presents each of his gems, morsels, and plums, as self contained tidbits, in this volume he connects chapters with some deductive treads. He includes exercises and gives their solutions at the end of the book. In addition to appealing to lovers of synthetic geometry, this book will stimulate also those who, in this era of revitalizing geometry, will want to try their hands at deriving the results by analytic methods. Many of the incidence properties call to mind the duality principle; other results tempt the reader to prove them by vector methods, or by projective transformations, or complex numbers.
Summary: A honeypot of sweet problems in geometry
Rating: 5
Geometry is such a sweet science and this book is a honeypot. Ross Honsberger is one of the best in creating crafty, delightful problems. In reading this book, you will be amazed at how hard the problems appear when stated and how simple and elegant the proofs are.
Some topics are relatively obscure. I am sure that Honsberger is quite correct in stating that few modern mathematicians have heard of the symmedian point of a triangle. I certainly had not. However, the level of the material is such that even teachers of high school geometry will be able to find some suitable exercises. College instructors will find it essential. Problems are given at the end of each chapter and detailed solutions are included in an appendix.
It is hard to read this book and not understand why the Greeks were so captivated by geometry. Properly presented, as is done here, it is addictive.
Published in Smarandache Notions Journal, reprinted with permission.
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