Geometry revisited [[electronic resource] /] / by H.S.M. Coxeter and S.L. Greitzer

• Record Nr.: UNINA9910461901003321
• Autore: Coxeter H. S. M (Harold Scott Macdonald), <1907-2003.>
• Pubbl/distr/stampa: Washington, DC, : Mathematical Association of America, 1967
• ISBN: 0-88385-934-3
• Descrizione fisica: 1 online resource (208 p.)
• Collana: Anneli Lax New Mathematical Library ; ; 19
• Altri autori (Persone): GreitzerSamuel L
• Disciplina: 516
• Soggetti: Geometry; Mathematics; Electronic books.
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• 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 Cevaâ€?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 Ptolemyâ€?s theorem and its extension""; ""2.7 More on Simson lines""; ""2.8 The Butterfly""; ""2.9 Morleyâ€?s theorem""; ""Chapter 3. Collinearity and Concurrence""; ""3.1 Quadrangles; Varignonâ€?s theorem""; ""3.2 Cyclic quadrangles; Brahmaguptaâ€?s formula""; ""3.3 Napoleon triangles""; ""3.4 Menelausâ€?s theorem""; ""3.5 Pappusâ€?s theorem""; ""3.6 Perspective triangles; Desarguesâ€?s theorem""; ""3.7 Hexagons""; ""3.8 Pascalâ€?s theorem""; ""3.9 Brianchonâ€?s theorem""; ""Chapter 4. Transformations""""4.1 Translation""; ""4.2 Rotation""; ""4.3 Half-turn""; ""4.4 Reflection""; ""4.5 Fagnanoâ€?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 Feuerbachâ€?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.