Read The Elements of Non-Euclidean Geometry (Dover Books on Mathematics)

[Get.pO8H] The Elements of Non-Euclidean Geometry (Dover Books on Mathematics)

[Get.pO8H] The Elements of Non-Euclidean Geometry (Dover Books on Mathematics)

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This volume became the standard text in the field almost immediately upon its original publication. Renowned for its lucid yet meticulous exposition, it can be appreciated by anyone familiar with high school algebra and geometry. Its arrangement follows the traditional pattern of plane and solid geometry, in which theorems are deduced from axioms and postulates. In this manner, students can follow the development of non-Euclidean geometry in strictly logical order, from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.Topics include elementary hyperbolic geometry; elliptic geometry; analytic non-Euclidean geometry; representations of non-Euclidean geometry in Euclidean space; and space curvature and the philosophical implications of non-Euclidean geometry. Additional subjects encompass the theory of the radical axes, homothetic centers, and systems of circles; inversion, equations of transformation, and groups of motions; and the classification of conics.Although geared toward undergraduate students, this text treats such important and difficult topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, Gauss proof of the defect-area theorem, geodesic representation, and other advanced subjects. In addition, its 136 problems offer practice in using the forms and methods developed in the text. Philosophical Dictionary: Leibniz-Logos Recommended Reading: Vladimir Lenin Essential Works of Lenin: 'What Is to Be Done?' and Other Writings ed by Henry M Christman (Dover 1987); Robert Service Parallel Postulate -- from Wolfram MathWorld Parallel Postulate Given any straight line and a point not on it there "exists one and only one straight line which passes" through that point and never intersects Books in the Mathematical Sciences This site is intended as a resource for university students in the mathematical sciences Books are recommended on the basis of readability and other pedagogical value Euclid Ancient History Encyclopedia Euclid of Alexandria (lived c 300 BCE) systematized ancient Greek and Near Eastern mathematics and geometry He wrote The Elements the most widely used mathematics Non-Euclidean Geometry -- from Wolfram MathWorld Non-Euclidean Geometry In three dimensions there are three classes of constant curvature geometries All are based on the first four of Euclid's postulates but Geometry - Wikipedia The earliest recorded beginnings of geometry can be traced to ancient Mesopotamia and Egypt in the 2nd millennium BC Early geometry was a collection of empirically What Is Circle? - Interactive Mathematics Miscellany and Circle is the locus of points equidistant from a given point the center of the circle The common distance from the center of the circle to its points is called radius Plane geometry Introduction to Euclid's Elements What plane geometry is about I N T R O D U C T I O N Geometry: The Study of Figures Plane geometry Magnitudes Maths Heroes Maths Week 2012 Maths Heroes links to the past An appreciation of the history of mathematics can motivate some students as it gives an insight into how great mathematicians of Euclid - Wikipedia Proclus later retells a story that when Ptolemy I asked if there was a shorter path to learning geometry than Euclid's Elements "Euclid replied there is no royal
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