Episodes in Nineteenth and Twentieth Century Euclidean Geometry (Anneli Lax New Mathematical Library, Series Number 37)

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. "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. 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."--Jacket Today's personal computer gives its owner tremendous power which can be used for experimental investigations and simulations of unprecedented scope, leading to mini-research. This book is a first step into this exciting field. This is a mathematics book, not a programming book, although it explains Pascal to beginners. It is aimed at high school students and undergraduates with a strong interest in mathematics and teachers looking for fresh ideas. It is full of diverse mathematical ideas requiring little background. It includes a large number of challenging problems that illustrate how computing leads to conjectures, many of which can then be proved by mathematical reasoning. - Back cover Euclidean geometry was worked out by Euclid and his predecessors more than 2300 years ago and is studied today mostly as a background to other branches of mathematics. In fact, however, as Professor Honsberger masterfully demonstrates, geometry in the style of Euclid is still alive and well. Mathematicians have again been studying the properties of geometric figures from a synthetic point of view and have discovered many new and unexpected results which Euclid himself never found. And since all of us have studied Euclidean geometry, at least the ancient version, this book is easily accessible. Exercises with their solutions are included in the book Presents topology as a unifying force for larger areas of mathematics through its application in existence theorems.