Download or read book Tentamen juventutem studiosam in elementa matheseos purae elementaris ac sublimioris methodo intuitiva evidentia que huic propria introducendi written by Farkas Bolyai and published by . This book was released on 1832 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Elements of Non Euclidean Plane Geometry and Trigonometry written by Horatio Scott Carslaw and published by . This book was released on 1916 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Non Euclidean Geometry written by Harold E. Wolfe and published by Courier Corporation. This book was released on 2013-09-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: College-level text for elementary courses covers the fifth postulate, hyperbolic plane geometry and trigonometry, and elliptic plane geometry and trigonometry. Appendixes offer background on Euclidean geometry. Numerous exercises. 1945 edition.
Download or read book Non Euclidean Geometry written by H.S.M. Coxeter and published by University of Toronto Press. This book was released on 1965-12-15 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism. Such a system was developed independently by Bolyai in Hungary and Lobatschewsky in Russia, about 120 years ago. Another system, differing more radically from Euclid's, was suggested later by Riemann in Germany and Cayley in England. The subject was unified in 1871 by Klein, who gave the names of parabolic, hyperbolic, and elliptic to the respective systems of Euclid-Bolyai-Lobatschewsky, and Riemann-Cayley. Since then, a vast literature has accumulated. The Fifth edition adds a new chapter, which includes a description of the two families of 'mid-lines' between two given lines, an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, a computation of the Gaussian curvature of the elliptic and hyperbolic planes, and a proof of Schlafli's remarkable formula for the differential of the volume of a tetrahedron.
Download or read book Tentamen juventutem studiosam in elementa matheseos purae elementaris ac sublimioris methodo intuitiva evidentiaque huic propria introducendi Editio 2a written by Farkas Bólyai De Bolya and published by . This book was released on 1897 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Reverse Mathematics written by John Stillwell and published by Princeton University Press. This book was released on 2019-09-24 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Download or read book Experiment and Metaphysics written by Edgar Wind and published by Routledge. This book was released on 2017-12-02 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Edgar Wind was one of the most distinguished art historians and philosophers of the twentieth century. He made crucial contributions to debates on aesthetics and on the interdisciplinary nature of cultural history involving such other leading figures as Ernst Cassirer and Erwin Panofsky. It is not always realised, however, that his early thinking was moulded by a concern with the German philosophical tradition, culminating in the analysis of the meaning and function of scientific experimentation and proof. This first edition in English of Edgar Wind's important work Das Experiment und die Metaphysik: Zur Auflosung der kosmologischen Antinomien (1934) also carries a new introduction by Matthew Rampley, placing Wind's philosophical thinking in context. The work is being published to coincide with the opening in 2000 of the Sackler Library at Oxford, which will include a Wind Reading Room."
Download or read book A History of Non Euclidean Geometry written by Boris A. Rosenfeld and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility, to the arithmetics and algebras of many groups and fields in addition to the arith metic and algebra of real and complex numbers, and, finally, to new mathe matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe matics.
Download or read book The Story of Proof written by John Stillwell and published by Princeton University Press. This book was released on 2022-11-15 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: How the concept of proof has enabled the creation of mathematical knowledge The Story of Proof investigates the evolution of the concept of proof—one of the most significant and defining features of mathematical thought—through critical episodes in its history. From the Pythagorean theorem to modern times, and across all major mathematical disciplines, John Stillwell demonstrates that proof is a mathematically vital concept, inspiring innovation and playing a critical role in generating knowledge. Stillwell begins with Euclid and his influence on the development of geometry and its methods of proof, followed by algebra, which began as a self-contained discipline but later came to rival geometry in its mathematical impact. In particular, the infinite processes of calculus were at first viewed as “infinitesimal algebra,” and calculus became an arena for algebraic, computational proofs rather than axiomatic proofs in the style of Euclid. Stillwell proceeds to the areas of number theory, non-Euclidean geometry, topology, and logic, and peers into the deep chasm between natural number arithmetic and the real numbers. In its depths, Cantor, Gödel, Turing, and others found that the concept of proof is ultimately part of arithmetic. This startling fact imposes fundamental limits on what theorems can be proved and what problems can be solved. Shedding light on the workings of mathematics at its most fundamental levels, The Story of Proof offers a compelling new perspective on the field’s power and progress.
Download or read book Polyhedra written by Peter R. Cromwell and published by Cambridge University Press. This book was released on 1997 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics an d group theory. This book comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra, and presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics, as well as those more interested in the mathematics itself, will find this unique book fascinating.
Download or read book Pangeometry written by Nikolaĭ Ivanovich Lobachevskiĭ and published by European Mathematical Society. This book was released on 2010 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a resume of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.
Download or read book Topology Calculus and Approximation written by Vilmos Komornik and published by Springer. This book was released on 2017-04-04 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.
Download or read book Geometries and Transformations written by Norman W. Johnson and published by Cambridge University Press. This book was released on 2018-06-07 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Euclidean and other geometries are distinguished by the transformations that preserve their essential properties. Using linear algebra and transformation groups, this book provides a readable exposition of how these classical geometries are both differentiated and connected. Following Cayley and Klein, the book builds on projective and inversive geometry to construct 'linear' and 'circular' geometries, including classical real metric spaces like Euclidean, hyperbolic, elliptic, and spherical, as well as their unitary counterparts. The first part of the book deals with the foundations and general properties of the various kinds of geometries. The latter part studies discrete-geometric structures and their symmetries in various spaces. Written for graduate students, the book includes numerous exercises and covers both classical results and new research in the field. An understanding of analytic geometry, linear algebra, and elementary group theory is assumed.
Download or read book Non Euclidean Geometry Sixth Edition written by H. S. M. Coxeter and published by American Mathematical Soc.. This book was released on 1998-12-31 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A reissue of Professor Coxeter's classic text on non-euclidean geometry.
Download or read book Tentamen juventutem studiosam in elementa matheseos purae elementaris ac sublimioris methodo intuitiva evidentiaque huic propria introducendi cum appendice triplici Editio IIa written by Farkas Bǒlyai de Bolya and published by . This book was released on 1897 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Research Problems in Discrete Geometry written by Peter Brass and published by Springer Science & Business Media. This book was released on 2006-06-19 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the result of a 25-year-old project and comprises a collection of more than 500 attractive open problems in the field. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research.
Download or read book God Created The Integers written by Stephen Hawking and published by Running Press Adult. This book was released on 2007-10-09 with total page 1376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Looks at landmark mathematical discoveries over the past 2,500 years by such mathematicians as Euclid, Isaac Newton, Pierre Simon de Laplace, Georg Cantor, Alan Turing, and others, offering profiles of twenty-one important mathematical masters, facsimiles of their key works, and commentary on their contributions to the history of mathematics.
