Geometry revisited / / by H.S.M. Coxeter and S.L. Greitzer [[electronic resource]]
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| Autore: |
oxeter H. S. M (Harold Scott Macdonald), <1907-2003, >
|
| Titolo: |
Geometry revisited / / by H.S.M. Coxeter and S.L. Greitzer [[electronic resource]]
|
| Pubblicazione: | Washington : , : Mathematical Association of America, , 1967 |
| Descrizione fisica: | 1 online resource (xiv, 193 pages) : digital, PDF file(s) |
| Disciplina: | 516.04 |
| Soggetto topico: | Geometry, Modern |
| Persona (resp. second.): | GreitzerSamuel L. |
| Note generali: | Title from publisher's bibliographic system (viewed on 31 May 2016). |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | ""Front Cover""; ""Geometry Revisited""; ""Copyright Page""; ""Contents""; ""Preface""; ""Chapter 1. Points and Lines Connected with a Triangle""; ""1.1 The extended Law of Sines""; ""1.2 Ceva�s theorem""; ""1.3 Points of interest""; ""1.4 The incircle and excircles""; ""1.5 The Steiner-Lehmus theorem""; ""1.6 The orthic triangle""; ""1.7 The medial triangle and Euler line""; ""1.8 The nine-point Circle""; ""1.9 Pedal triangles""; ""Chapter 2. Some Properties of Circles""; ""2.1 The power of a point with respect to a circle""; ""2.2 The radical axis of two circles""; ""2.3 Coaxal circles"" |
| ""2.4 More on the altitudes and orthocenter of a triangle""""2.5 Simson lines""; ""2.6 Ptolemy�s theorem and its extension""; ""2.7 More on Simson lines""; ""2.8 The Butterfly""; ""2.9 Morley�s theorem""; ""Chapter 3. Collinearity and Concurrence""; ""3.1 Quadrangles; Varignon�s theorem""; ""3.2 Cyclic quadrangles; Brahmagupta�s formula""; ""3.3 Napoleon triangles""; ""3.4 Menelaus�s theorem""; ""3.5 Pappus�s theorem""; ""3.6 Perspective triangles; Desargues�s theorem""; ""3.7 Hexagons""; ""3.8 Pascal�s theorem""; ""3.9 Brianchon�s theorem"" | |
| ""Chapter 4. Transformations""""4.1 Translation""; ""4.2 Rotation""; ""4.3 Half-turn""; ""4.4 Reflection""; ""4.5 Fagnano�s problem""; ""4.6 The three jug problem""; ""4.7 Dilatation""; ""4.8 Spiral similarity""; ""4.9 A genealogy of transformations""; ""Chapter 5. An Introduction to Inversive Geometry""; ""5.1 Separation""; ""5.2 Cross ratio""; ""5.3 Inversion""; ""5.4 The inversive plane""; ""5.5 Orthogonality""; ""5.6 Feuerbach�s theorem""; ""5.7 Coaxal circles""; ""5.8 Inversive distance""; ""5.9 Hyperbolic functions""; ""Chapter 6. An Introduction to Projective Geometry"" | |
| ""6.1 Reciprocation""""6.2 The polar circle of a triangle""; ""6.3 Conics""; ""6.4 Focus and directrix""; ""6.5 The projective plane""; ""6.6 Central conics""; ""6.7 Stereographic and gnomonic projection""; ""Hints and Answers to Exercises""; ""References""; ""Glossary""; ""Index""; ""Back Cover"" | |
| Sommario/riassunto: | Among the many beautiful and nontrivial theorems in geometry found here are the theorems of Ceva, Menelaus, Pappus, Desargues, Pascal, and Brianchon. A nice proof is given of Morley's remarkable theorem on angle trisectors. The transformational point of view is emphasized: reflections, rotations, translations, similarities, inversions, and affine and projective transformations. Many fascinating properties of circles, triangles, quadrilaterals, and conics are developed. |
| Titolo autorizzato: | Geometry revisited |
| ISBN: | 0-88385-934-3 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910817763703321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
New mathematical library ; ; 19.