Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37

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Cambridge University Press, 1995 - 174 páginas
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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.
 

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Conteúdo

Cleavers and Splitters
1
The Orthocenter
17
On Triangles
27
On Quadrilaterals
35
A Property of Triangles
43
The Fuhrmann Circle
49
The Symmedian Point
53
The Miquel Theorem
79
The Brocard Points
99
The Orthopole
125
On Cevians
137
The Theorem of Menelaus
147
Suggested Reading
155
Solutions to the Exercises
157
Index
173
Direitos autorais

The Tucker Circles
87

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