Euclidean And Non Euclidean Geometry International Student Edition
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📒Euclidean And Non Euclidean Geometry International Student Edition ✍ Patrick J. Ryan
✏Euclidean and Non Euclidean Geometry International Student Edition Book Summary : This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
✏Foundation of Euclidean and Non Euclidean Geometries according to F Klein Book Summary : Foundation of Euclidean and Non-Euclidean Geometries according to F. Klein aims to remedy the deficiency in geometry so that the ideas of F. Klein obtain the place they merit in the literature of mathematics. This book discusses the axioms of betweenness, lattice of linear subspaces, generalization of the notion of space, and coplanar Desargues configurations. The central collineations of the plane, fundamental theorem of projective geometry, and lines perpendicular to a proper plane are also elaborated. This text likewise covers the axioms of motion, basic projective configurations, properties of triangles, and theorem of duality in projective space. Other topics include the point-coordinates in an affine space and consistency of the three geometries. This publication is beneficial to mathematicians and students learning geometry.
📒Introductory Non Euclidean Geometry ✍ Henry Parker Manning
✏Introductory Non Euclidean Geometry Book Summary : This fine and versatile introduction begins with the theorems common to Euclidean and non-Euclidean geometry, and then it addresses the specific differences that constitute elliptic and hyperbolic geometry. 1901 edition.
📒Euclidean Geometry In Mathematical Olympiads ✍ Evan Chen
✏Euclidean Geometry in Mathematical Olympiads Book Summary : This is a challenging problem-solving book in Euclidean geometry, assuming nothing of the reader other than a good deal of courage. Topics covered included cyclic quadrilaterals, power of a point, homothety, triangle centers; along the way the reader will meet such classical gems as the nine-point circle, the Simson line, the symmedian and the mixtilinear incircle, as well as the theorems of Euler, Ceva, Menelaus, and Pascal. Another part is dedicated to the use of complex numbers and barycentric coordinates, granting the reader both a traditional and computational viewpoint of the material. The final part consists of some more advanced topics, such as inversion in the plane, the cross ratio and projective transformations, and the theory of the complete quadrilateral. The exposition is friendly and relaxed, and accompanied by over 300 beautifully drawn figures. The emphasis of this book is placed squarely on the problems. Each chapter contains carefully chosen worked examples, which explain not only the solutions to the problems but also describe in close detail how one would invent the solution to begin with. The text contains as selection of 300 practice problems of varying difficulty from contests around the world, with extensive hints and selected solutions. This book is especially suitable for students preparing for national or international mathematical olympiads, or for teachers looking for a text for an honor class.
📒Euclidean Geometry And Its Subgeometries ✍ Edward John Specht
✏Euclidean Geometry and its Subgeometries Book Summary : In this monograph, the authors present a modern development of Euclidean geometry from independent axioms, using up-to-date language and providing detailed proofs. The axioms for incidence, betweenness, and plane separation are close to those of Hilbert. This is the only axiomatic treatment of Euclidean geometry that uses axioms not involving metric notions and that explores congruence and isometries by means of reflection mappings. The authors present thirteen axioms in sequence, proving as many theorems as possible at each stage and, in the process, building up subgeometries, most notably the Pasch and neutral geometries. Standard topics such as the congruence theorems for triangles, embedding the real numbers in a line, and coordinatization of the plane are included, as well as theorems of Pythagoras, Desargues, Pappas, Menelaus, and Ceva. The final chapter covers consistency and independence of axioms, as well as independence of definition properties. There are over 300 exercises; solutions to many of these, including all that are needed for this development, are available online at the homepage for the book at www.springer.com. Supplementary material is available online covering construction of complex numbers, arc length, the circular functions, angle measure, and the polygonal form of the Jordan Curve theorem. Euclidean Geometry and Its Subgeometries is intended for advanced students and mature mathematicians, but the proofs are thoroughly worked out to make it accessible to undergraduate students as well. It can be regarded as a completion, updating, and expansion of Hilbert's work, filling a gap in the existing literature.
📒Non Euclidean Geometry ✍ H. S. M. Coxeter
✏Non Euclidean Geometry Book Summary : A reissue of Professor Coxeter's classic text on non-Euclidean geometry. It surveys real projective geometry, and elliptic geometry. After this the Euclidean and hyperbolic geometries are built up axiomatically as special cases. This is essential reading for anybody with an interest in geometry.
📒The Power Of International Theory ✍ Fred Chernoff
✏The Power of International Theory Book Summary : This new study challenges how we think about international relations, presenting an analysis of current trends and insights into new directions. It shows how the discipline of international relations was created with a purpose of helping policy-makers to build a more peaceful and just world. However, many of the current trends, post-positivism, constructivism, reflectivism, and post-modernism share a conception of international theory that is inherently incapable of offering significant guidance to policy-makers. The Power of International Theory critically examines these approaches and offers a novel conventional-causal alternative that allows the reforging of a link between IR theory and policy-making. While recognizing the criticisms of earlier forms of positivism and behaviouralism, the book defends holistic testing of empirical principles, methodological pluralism, criteria for choosing the best theory, a notion of 'causality,' and a limited form of prediction, all of which are needed to guide policy-makers. This is an essential book for all students and scholars of international relations.
📒The Foundations Of Geometry And The Non Euclidean Plane ✍ G.E. Martin
✏The Foundations of Geometry and the Non Euclidean Plane Book Summary : This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
📒Euclidean Geometry And Transformations ✍ Clayton W. Dodge
✏Euclidean Geometry and Transformations Book Summary : This introduction to Euclidean geometry emphasizes transformations, particularly isometries and similarities. Suitable for undergraduate courses, it includes numerous examples, many with detailed answers. 1972 edition.
📒Elementary Euclidean Geometry ✍ C. G. Gibson
✏Elementary Euclidean Geometry Book Summary : This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.