Download or read book Advanced Euclidean Geometry written by Roger A. Johnson and published by Courier Corporation. This book was released on 2013-01-08 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text explores the geometry of the triangle and the circle, concentrating on extensions of Euclidean theory, and examining in detail many relatively recent theorems. 1929 edition.
Download or read book Problems and Solutions in Euclidean Geometry written by M. N. Aref and published by Courier Corporation. This book was released on 2010-01-01 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on classical principles, this book is intended for a second course in Euclidean geometry and can be used as a refresher. Each chapter covers a different aspect of Euclidean geometry, lists relevant theorems and corollaries, and states and proves many propositions. Includes more than 200 problems, hints, and solutions. 1968 edition.
Download or read book Modern Geometry with Applications written by George A. Jennings and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to modern geometry differs from other books in the field due to its emphasis on applications and its discussion of special relativity as a major example of a non-Euclidean geometry. Additionally, it covers the two important areas of non-Euclidean geometry, spherical geometry and projective geometry, as well as emphasising transformations, and conics and planetary orbits. Much emphasis is placed on applications throughout the book, which motivate the topics, and many additional applications are given in the exercises. It makes an excellent introduction for those who need to know how geometry is used in addition to its formal theory.
Download or read book Newton s Principia for the Common Reader written by Subrahmanyan Chandrasekhar and published by Oxford University Press. This book was released on 2003 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: Newton's Philosophiae Naturalis Principia Mathematica provides a coherent and deductive presentation of his discovery of the universal law of gravitation. It is very much more than a demonstration that 'to us it is enough that gravity really does exist and act according to the laws which wehave explained and abundantly serves to account for all the motions of the celestial bodies and the sea'. It is important to us as a model of all mathematical physics.Representing a decade's work from a distinguished physicist, this is the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Professor Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law ofgravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty,clarity, and breath-taking economy of Newton's methods.Subrahmanyan Chandrasekhar is one of the most reknowned scientists of the twentieth century, whose career spanned over 60 years. Born in India, educated at the University of Cambridge in England, he served as Emeritus Morton D. Hull Distinguished Service Professor of Theoretical Astrophysics at theUniversity of Chicago, where he has was based from 1937 until his death in 1996. His early research into the evolution of stars is now a cornerstone of modern astrophysics, and earned him the Nobel Prize for Physics in 1983. Later work into gravitational interactions between stars, the properties offluids, magnetic fields, equilibrium ellipsoids, and black holes has earned him awards throughout the world, including the Gold Medal from the Royal Astronomical Society in London (1953), the National Medal of Science in the United States (1966), and the Copley Medal from the Royal Society (1984).His many publications include Radiative transfer (1950), Hydrodynamic and hydromagnetic stability (1961), and The mathematical theory of black holes (1983), each being praised for its breadth and clarity. Newton's Principia for the common reader is the result of Professor Chandrasekhar's profoundadmiration for a scientist whose work he believed is unsurpassed, and unsurpassable.
Download or read book Geometry Euclid and Beyond written by Robin Hartshorne and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 535 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Euclid s Elements with Exercises Instructor s Copy written by Kathryn Goulding and published by . This book was released on 2017-09-15 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The instructor's edition of Euclid's Elements With Exercises is intended as a guide for anyone teaching Euclid for the first time. Although it could be used by anyone, it was assembled and written with small schools or homeschooling groups in mind. In addition to containing the first six books in exactly the format of the student edition (also available on Amazon), the instructor's edition provides a concise overview of the course, including suggestions for conducting the class, a discussion of the organization of the material, brief comments on supplemental and memory work, and other details about which a new instructor might have questions. It also has notes for the teacher on each of the six books of the Elements, notes on selected exercises, and an appendix explaining the basics of formal reasoning, including an explanation of the converse and contrapositive of a statement and the concept of an indirect proof, which occurs early in Book I. The primary difference between this work and Euclid's Elements as it is usually presented (aside from the fact that there are some exercises), is that, while all of Books I - VI are included in the book, some propositions are omitted in the main body of the text (all omitted propositions are in Appendix A). This was done in order to be able to finish in two semesters all the plane geometry that would normally be covered in a modern geometry class. It should be noted, of course, that the flow of logic of the propositions is never interrupted. This book was not designed for the purist. Although it is pure Euclid and contains all of the first six books, it may offend the sensibilities of some who love Euclid (as the assembler/author does) to fail to place Book II in the expected flow of the main body of the text. For anyone not under a time constraint, or anyone moving quickly through the text, the author strongly recommends the inclusion of Book II in the course flow.
Download or read book Final Report of the National Committee of Fifteen on Geometry Syllabus written by National Education Association of the United States. National Committee of Fifteen on Geometry Syllabus and published by . This book was released on 1912 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Axiomatic Geometry written by John M. Lee and published by American Mathematical Soc.. This book was released on 2013-04-10 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The story of geometry is the story of mathematics itself: Euclidean geometry was the first branch of mathematics to be systematically studied and placed on a firm logical foundation, and it is the prototype for the axiomatic method that lies at the foundation of modern mathematics. It has been taught to students for more than two millennia as a mode of logical thought. This book tells the story of how the axiomatic method has progressed from Euclid's time to ours, as a way of understanding what mathematics is, how we read and evaluate mathematical arguments, and why mathematics has achieved the level of certainty it has. It is designed primarily for advanced undergraduates who plan to teach secondary school geometry, but it should also provide something of interest to anyone who wishes to understand geometry and the axiomatic method better. It introduces a modern, rigorous, axiomatic treatment of Euclidean and (to a lesser extent) non-Euclidean geometries, offering students ample opportunities to practice reading and writing proofs while at the same time developing most of the concrete geometric relationships that secondary teachers will need to know in the classroom. -- P. [4] of cover.
Download or read book Euclidean Geometry and its Subgeometries written by Edward John Specht and published by Birkhäuser. This book was released on 2015-12-31 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Four Pillars of Geometry written by John Stillwell and published by Springer Science & Business Media. This book was released on 2005-08-09 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Art of the Infinite written by Robert Kaplan and published by Bloomsbury Publishing USA. This book was released on 2014-02-04 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traces the development of mathematical thinking and describes the characteristics of the "republic of numbers" in terms of humankind's fascination with, and growing knowledge of, infinity.
Download or read book Exercises on Euclid and in Modern Geometry written by J. MacDowell and published by . This book was released on 1881 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Geometry from a Differentiable Viewpoint written by John McCleary and published by Cambridge University Press. This book was released on 2013 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised second edition of a textbook for a first course in differential/modern geometry that introduces methods within a historical context.
Download or read book Euclidean and Non Euclidean Geometry International Student Edition written by Patrick J. Ryan and published by Cambridge University Press. This book was released on 2009-09-04 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of the fundamentals of plane geometry: Euclidean, spherical, elliptical and hyperbolic.
Download or read book Euclid s Elements written by Euclid and published by . This book was released on 2002 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book includes introductions, terminology and biographical notes, bibliography, and an index and glossary" --from book jacket.
Download or read book Euclid s Elements of Geometry written by Euclid and published by . This book was released on 2008 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: EUCLID'S ELEMENTS OF GEOMETRY, in Greek and English. The Greek text of J.L. Heiberg (1883-1885), edited, and provided with a modern English translation, by Richard Fitzpatrick.[Description from Wikipedia: ] The Elements (Ancient Greek: Στοιχεῖον Stoikheîon) is a mathematical treatise consisting of 13 books (all included in this volume) attributed to the ancient Greek mathematician Euclid in Alexandria, Ptolemaic Egypt c. 300 BC. It is a collection of definitions, postulates, propositions (theorems and constructions), and mathematical proofs of the propositions. The books cover plane and solid Euclidean geometry, elementary number theory, and incommensurable lines. Elements is the oldest extant large-scale deductive treatment of mathematics. It has proven instrumental in the development of logic and modern science, and its logical rigor was not surpassed until the 19th century.
Download or read book Elementary Euclidean Geometry written by C. G. Gibson and published by Cambridge University Press. This book was released on 2003 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.
