Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37Cambridge University Press, 1995 - 174 páginas 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. |
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 |
| 173 | |
The Tucker Circles | 87 |
Outras edições - Ver todos
Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37 Ross Honsberger Visualização parcial - 1995 |
Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37 Ross Honsberger Prévia não disponível - 1995 |
Episodes in Nineteenth and Twentieth Century Euclidean Geometry, Volume 37 Ross Honsberger Prévia não disponível - 1995 |
Termos e frases comuns
AABC Figure ADEF altitude angle bisector anticenter APQR bisects Brocard circle Brocard point Brocard triangle center of gravity centroid G Ceva's theorem cevian triangle chord circle with center circumcenter circumcircle of AABC cleaver collinear concurrent congruent cyclic quadrilateral dilatation equal angles Euler line excircle exterior angle follows Fuhrmann circle G trisects Geometry give given triangle ABC Hence implying incenter incircle isogonal conjugates isosceles John Rigby Lemoine circle masses Mathematical medial triangle Miquel Nagel point nine-point circle opposite angles opposite side orthic triangle orthocenter H orthopole P₁ parallel to BC parallelogram perpendicular bisector perpendicular to BC point of intersection proof Prove ratio result right angles right triangle segment sides of AABC similar triangles Similarly Simson line Spieker circle subtends symmedian point tangent triangle of AABC Tucker circle Tucker hexagon vertex vertices
Referências a este livro
Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study Carmelo Mammana,V. Villani Prévia não disponível - 1998 |
Perspectives on the Teaching of Geometry for the 21st Century: An ICMI Study Carmelo Mammana,V. Villani Prévia não disponível - 1998 |