Linear Fractional Transformations. An Illustrated Introduction
Book information
Description
978-3-031-25002-6 1 Preface Acknowledgements Contents 978-3-031-25002-6_1 1 Euclidean Isometries and Similarities 1.1 The Complex Plane and Affine Maps 1.2 Isometries 1.3 Similarities 1.4 Classifying Similarities 1.5 Applications 1.6 A Little Bit of Group Theory Problems 1.1 COMPUTATIONAL EXERCISES 1.2 PROOFS 1.3 PROOFS (Calculus) 1.4 PROOFS (Group Theory) 978-3-031-25002-6_2 2 Inversive Geometry 2.1 The Extended Euclidean Plane 2.2 A Little Bit More Group Theory 2.3 Circle Inversions 2.4 Generalized Circles 2.5 Oriented Circles 2.6 Angles, Revisited 2.7 The Cross-Ratio 2.8 The Group of Möbius Transformations Problems 2.1 COMPUTATIONAL EXERCISES 2.2 PROOFS 2.3 PROOFS (Calculus) 2.4 PROOFS (Group Theory) 978-3-031-25002-6_3 3 Applications of Inversive Geometry 3.1 Steiner's Porism 3.2 Apollonian Gaskets 3.3 Inversive Coordinates 3.4 The Special Linear Group 3.5 Inversive Distance 3.6 Steiner's Porism Revisited 3.7 Apollonian Gaskets Revisited 3.8 Descartes' Theorem Problems 3.1 COMPUTATIONAL EXERCISES 3.2 PROOFS 3.3 PROOFS (Group Theory) 978-3-031-25002-6_4 4 Construction of Hyperbolic Geometry 4.1 Metric Geometry 4.2 The Real Special Linear Group 4.3 The Poincaré Half-Plane 4.4 Circles and Lines 4.5 Isometries and Geometric Notions 4.6 The Poincaré Disk Model 4.7 Quaternions 4.8 Hyperbolic 3-Space 4.9 Hyperbolic Spheres, Planes, and Isometries Problems 4.1 COMPUTATIONAL EXERCISES 4.2 PROOFS 4.3 PROOFS (Calculus) 4.4 PROOFS (Linear Algebra) 4.5 PROOFS (Metric Geometry) 978-3-031-25002-6_5 5 Properties of Hyperbolic Geometry 5.1 Peculiarities of Hyperbolic Geometry 5.2 Decomposing via the Trace 5.3 Elliptic Elements 5.4 Hyperbolic Elements 5.5 Parabolic Elements 5.6 Loxodromic Elements 5.7 Other Decomposition Theorems Problems 5.1 COMPUTATIONAL EXERCISES 5.2 PROOFS 5.3 PROOFS (Calculus) 5.4 PROOFS (Group Theory) 1 (1) Appendix A Set Theory A.1 Basic Constructions A.2 Some Common Sets A.3 Ordered Pairs and Relations A.4 Injections, Surjections, and Bijections References Index
Similar books
Linear Fractional Transformations: An Illustrated Introduction (Undergraduate Texts in Mathematics)
2023 · PDF
Linear Fractional Transformations: An Illustrated Introduction
2023 · EPUB
Linear Fractional Transformations: An Illustrated Introduction
2023 · PDF
MySQL® Notes for Professionals book
2018 · PDF
MrExcel 2022: Boosting Excel
2022 · PDF
MrExcel 2022: Boosting Excel
2022 · PDF
Session C11: Ancient Cultural Landscapes in South Europe – their Ecological Setting and Evolution, Session C22: Gardeners from South America, Session S04: Agro-Pastoralism and Early Metallurgy Sessions, Session WS29: The Idea of Enclosure in Recent Iberian Prehistory, Session C88: Rhytmes et causalites des dynamiques de l'anthropisation en Europe entre 6500 ET 500 BC: Hypotheses socio-culturelles et/ou climatiques: Proceedings of the XV UISPP World Congress (Lisbon 4-9 September 2006) / Actes du XV Congrès Mondial (Lisbonne 4-9 Septembre 2006) Vol.36
2010 · PDF
THE BRITISH ARMY IN INDIA: ITS PRESERVATION BY AN APPROPRIATE CLOTHING, HOUSING, LOCATING, RECREATIVE EMPLOYMENT, AND HOPEFUL ENCOURAGEMENT OF THE TROOPS. with AN APPENDIX ON INDIA : THE CLIMATE OP ITS HILLS ; THE DEVELOPMENT OF ITS RESODRCBS, INDUSTRY, AND ARTS ; THE ADMINISTRATION OF JUSTICE ; THE BLACK ACT ; THE PROGRESS OF CHRISTIANITY ; THE TRAFFIC IN OPIUM ; THE VALUE OF INDIA ; PERMANENT CAUSES OF DISAFFECTION, AND OF THE RECENT REBELLION ; THE TRADITIONARY POLICY; MISGOVERNMENT BY NATIVE RULERS ; ANNEXATIONS OF THEIR TERRITORY, ETC.
1858 · PDF