Episodes in nineteenth and twentieth century Euclidean geometry / by Ross Honsberger.

By: Honsberger, Ross, 1929-.

Contributor(s): Mathematical Association of America.

Material type: materialTypeLabel

BookSeries: New mathematical library ; 37.Publisher: Washington : Mathematical Association of America, c1995Description: x, 174 p. : ill. ; 23 cm. + pbk.ISBN: 0883856395.Subject(s): Geometry, Projective

DDC classification: 516.2

Contents:

Cleavers and splitters -- The orthocenter -- On triangles -- On quadrilaterals -- A property of triangles -- The Fuhrmann circle -- The symmedian point -- The Miquel theorem -- The Tucker circles -- The brocard points -- The orthopole -- On cevians -- The theorem of Menelaus.

Holdings
Item type	Current library	Call number	Copy number	Status	Date due	Barcode	Item holds
General Lending	MTU Bishopstown Library Lending	516.2 (Browse shelf(Opens below))	1	Available		00010588

Total holds: 0

Enhanced descriptions from Syndetics:

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.

Includes bibliographical references (page 155) and index.

Table of contents provided by Syndetics

Preface
Introduction
1 Cleavers and splitters
2 The orthocenter
3 On triangles
4 On quadrilaterals
5 A property of triangles
6 The Fuhrmann circle
7 The symmedian point
8 The Miquel theorem
9 The Tucker circle
10 The Brocard points
11 The orthopole
12 On cevians
13 The theorem of Menelaus; Suggested reading; Solutions to the exercises
Index.

Reviews provided by Syndetics

CHOICE Review

Even if it is hardly a fashionable area of research now, geometry in the spirit of Euclid lives on, and Honsberger shows that it was a lively subject too, as least through the first quarter of this century. The algebraization of geometry renders the proof of any theorem of Euclidean geometry routine (though tedious), at least in principle, but the discovery of a new theorem with the aesthetic appeal of, say, the classic nine-point circle would still require considerable insight. Here is a selection of really beautiful theorems. Few will be familiar even to the professional mathematician, but all are accessible to undergraduates, or even to the lay reader with a firm grounding in Euclid. Prepare to encounter such exotica as cleavers, Fuhrmann circles, symmedian points, Tucker circles, Brocard points, and Simpson lines. For good reasons, Euclidean geometry, not, for example, basic set theory, was the traditional ground for initiating students to the habit of reason. Highly recommended. D. V. Feldman; University of New Hampshire