EPISODES IN NINETEENTH AND TWENTIETH CENTURY EUCLIDEAN GEOMETRY

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.

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.