Geometry Euclid And Beyond
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📒Geometry Euclid And Beyond ✍ Robin Hartshorne
✏Geometry Euclid and Beyond Book Summary : This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.
📒Geometry ✍ Robin Hartshorne
✏Geometry Book Summary :
📒Beyond Geometry ✍ John Tabak
✏Beyond Geometry Book Summary : Discusses the history, progress, and applications of topology, and its usefulness to science and society, along with a timeline of notable events.
📒Geometrical Researches On The Theory Of Parallels ✍ Nicholas Lobachevsky
✏Geometrical Researches on the Theory of Parallels Book Summary : "Lobachevsky believed that another form of geometry existed, a non-Euclidean geometry, and this 1840 treatise is his argument on its behalf. Line by line in this classic work he carefully presents a new and revolutionary theory of parallels, one that allows for all of Euclids axioms, except for the last. This 1891 translation includes a bibliography and translator George B. Halsteds essay on elliptic geometry. Russian mathematician NICHOLAS LOBACHEVSKY (17921856) is best remembered as the founder (along with Janos Bolyai) of non-Euclidean geometry. He is also the author of New Foundations of Geometry (18351838) and Pangeometry (1855)."
📒College Geometry ✍ Howard Whitley Eves
✏College Geometry Book Summary : College Geometry is divided into two parts. Part I is a sequel to basic high school geometry and introduces the reader to some of the important modern extensions of elementary geometry- extension that have largely entered into the mainstream of mathematics. Part II treats notions of geometric structure that arose with the non-Euclidean revolution in the first half of the nineteenth century.
📒Worlds Out Of Nothing ✍ Jeremy Gray
✏Worlds Out of Nothing Book Summary : Based on the latest historical research, Worlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
📒On Beyond Euclid ✍ Ben Jacobs
✏On Beyond Euclid Book Summary : This curious little book is basically a hitchhiker's guide to Book I of Euclid's Elements. We travel through each of the forty-eight Propositions--more or less in order--and see how each one generalizes--or does not generalize--to hyperbolic and other non-Euclidean spaces. Few people seem to realize that Einstein's special theory of relativity is a model of hyperbolic geometry. The connection between Minkowski geometry and special relativity is well-known, while the connection between hyperbolic geometry and special relativity is, rather, known of. But this book makes the hyperbolic connection explicit; PoincareA' disks rather than the traditional Minkowski diagrams are used to illustrate concepts of special relativity. As we progress through Euclid's propositions, it becomes increasingly clear that every theorem in neutral and hyperbolic geometry can be translated into a true statement in special relativity.
✏Euclid s Book on Divisions of Figures with a Restoration Based on Woepcke s Text and on the Practica Geometriae of Leonardo Pisano Book Summary :
📒The Four Pillars Of Geometry ✍ John Stillwell
✏The Four Pillars of Geometry Book Summary : This book is unique in that it looks at geometry from 4 different viewpoints - Euclid-style axioms, linear algebra, projective geometry, and groups and their invariants Approach makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic Abundantly supplemented with figures and exercises
📒Computing The Continuous Discretely ✍ Matthias Beck
✏Computing the Continuous Discretely Book Summary : This textbook illuminates the field of discrete mathematics with examples, theory, and applications of the discrete volume of a polytope. The authors have weaved a unifying thread through basic yet deep ideas in discrete geometry, combinatorics, and number theory. We encounter here a friendly invitation to the field of "counting integer points in polytopes", and its various connections to elementary finite Fourier analysis, generating functions, the Frobenius coin-exchange problem, solid angles, magic squares, Dedekind sums, computational geometry, and more. With 250 exercises and open problems, the reader feels like an active participant.