Plane Geometry

Author : Mark E. Saul
Publisher : American Mathematical Soc.
ISBN 13 : 0821843680
Total Pages : 362 pages
Book Rating : 4.80/5 ( download)

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Download or read book Hadamard's Plane Geometry written by Mark E. Saul and published by American Mathematical Soc.. This book was released on 2010-02-10 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Jacques Hadamard, among the greatest mathematicians of the twentieth century, made signal contributions to a number of fields. But his mind could not be confined to the upper reaches of mathematical thought. He also produced a massive two-volume work, on plane and solid geometry, for pre-college teachers in the French school system. In those books, Hadamard's style invites participation. His exposition is minimal, providing only the results necessary to support the solution of the many elegant problems he poses afterwards. That is, the problems interpret the text in the way that harmony interprets melody in a well-composed piece of music. The present volume offers solutions to the problems in the first part of Hadamard's work (Lessons in Geometry. I. Plane Geometry, Jacques Hadamard, Amer. Math. Soc. (2008)), and can be viewed as a reader's companion to that book. It requires of the reader only the background of high school plane geometry, which Lessons in Geometry provides. The solutions strive to connect the general methods given in the text with intuitions that are natural to the subject, giving as much motivation as possible as well as rigorous and formal solutions. Ideas for further exploration are often suggested, as well as hints for classroom use. This book will be of interest to high school teachers, gifted high school students, college students, and those mathematics majors interested in geometry.

Author : Amol Sasane
Publisher : World Scientific Publishing Company
ISBN 13 : 9789814740432
Total Pages : 269 pages
Book Rating : 4.38/5 ( download)

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Download or read book Plain Plane Geometry written by Amol Sasane and published by World Scientific Publishing Company. This book was released on 2015-12-07 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book constitutes an elementary course on Plane Euclidean Geometry, pitched at pre-university or at advanced high school level. It is a concise book treating the subject axiomatically, but since it is meant to be a first introduction to the subject, excessive rigour is avoided, making it appealing to a younger audience as well. The aim is to cover the basics of the subject, while keeping the subject lively by means of challenging and interesting exercises. This makes it relevant also for students participating in mathematics circles and in mathematics olympiads. Each section contains several problems, which are not purely drill exercises, but are intended to introduce a sense of "play" in mathematics, and inculcate appreciation of the elegance and beauty of geometric results. There is an abundance of colour pictures illustrating results and their proofs. A section on hints and a further section on detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.

Author : Harvey I. Blau
Publisher :
ISBN 13 : 9780130479549
Total Pages : 0 pages
Book Rating : 4.43/5 ( download)

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Download or read book Foundations of Plane Geometry written by Harvey I. Blau and published by . This book was released on 2003 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for users who may have little previous experience with abstraction and proof, this book provides a rigorous and unified--yet straightforward and accessible --exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme--the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes--with a leisurely development that allows ample time for mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular. Focus on one main topic--The axiomatic development of the absolute plane--which is pursued through a classification into Euclidean, hyperbolic, and spherical planes. Presents specific models such as the sphere, the Klein-Betrami hyperbolic model, and the "gap" plane. Gradually presents axioms for absolute plane geometry.

Author : C. Zwikker
Publisher : Courier Corporation
ISBN 13 : 0486153436
Total Pages : 316 pages
Book Rating : 4.38/5 ( download)

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Download or read book The Advanced Geometry of Plane Curves and Their Applications written by C. Zwikker and published by Courier Corporation. This book was released on 2011-11-30 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Of chief interest to mathematicians, but physicists and others will be fascinated ... and intrigued by the fruitful use of non-Cartesian methods. Students ... should find the book stimulating." — British Journal of Applied Physics This study of many important curves, their geometrical properties, and their applications features material not customarily treated in texts on synthetic or analytic Euclidean geometry. Its wide coverage, which includes both algebraic and transcendental curves, extends to unusual properties of familiar curves along with the nature of lesser known curves. Informative discussions of the line, circle, parabola, ellipse, and hyperbola presuppose only the most elementary facts. The less common curves — cissoid, strophoid, spirals, the leminscate, cycloid, epicycloid, cardioid, and many others — receive introductions that explain both their basic and advanced properties. Derived curves-the involute, evolute, pedal curve, envelope, and orthogonal trajectories-are also examined, with definitions of their important applications. These range through the fields of optics, electric circuit design, hydraulics, hydrodynamics, classical mechanics, electromagnetism, crystallography, gear design, road engineering, orbits of subatomic particles, and similar areas in physics and engineering. The author represents the points of the curves by complex numbers, rather than the real Cartesian coordinates, an approach that permits simple, direct, and elegant proofs.

Author : Jacques Hadamard
Publisher : American Mathematical Soc.
ISBN 13 : 0821897306
Total Pages : 346 pages
Book Rating : 4.00/5 ( download)

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Download or read book Lessons in Geometry: Plane geometry written by Jacques Hadamard and published by American Mathematical Soc.. This book was released on 2008-12-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: We are just fortunate that one of the greatest mathematical minds of recent times has made this effort to show to readers some of the opportunities that the intellectual tradition of Euclidean geometry has to offer."--BOOK JACKET.

Author : Victor Klee
Publisher : American Mathematical Soc.
ISBN 13 : 1470454610
Total Pages : 333 pages
Book Rating : 4.16/5 ( download)

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Download or read book Old and New Unsolved Problems in Plane Geometry and Number Theory written by Victor Klee and published by American Mathematical Soc.. This book was released on 2020-07-31 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: Victor Klee and Stan Wagon discuss some of the unsolved problems in number theory and geometry, many of which can be understood by readers with a very modest mathematical background. The presentation is organized around 24 central problems, many of which are accompanied by other, related problems. The authors place each problem in its historical and mathematical context, and the discussion is at the level of undergraduate mathematics. Each problem section is presented in two parts. The first gives an elementary overview discussing the history and both the solved and unsolved variants of the problem. The second part contains more details, including a few proofs of related results, a wider and deeper survey of what is known about the problem and its relatives, and a large collection of references. Both parts contain exercises, with solutions. The book is aimed at both teachers and students of mathematics who want to know more about famous unsolved problems.

Author : Matthew Harvey
Publisher : The Mathematical Association of America
ISBN 13 : 1939512115
Total Pages : 561 pages
Book Rating : 4.16/5 ( download)

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Download or read book Geometry Illuminated written by Matthew Harvey and published by The Mathematical Association of America. This book was released on 2015-09-25 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry Illuminated is an introduction to geometry in the plane, both Euclidean and hyperbolic. It is designed to be used in an undergraduate course on geometry, and as such, its target audience is undergraduate math majors. However, much of it should be readable by anyone who is comfortable with the language of mathematical proof. Throughout, the goal is to develop the material patiently. One of the more appealing aspects of geometry is that it is a very "visual" subject. This book hopes to takes full advantage of that, with an extensive use of illustrations as guides. Geometry Illuminated is divided into four principal parts. Part 1 develops neutral geometry in the style of Hilbert, including a discussion of the construction of measure in that system, ultimately building up to the Saccheri-Legendre Theorem. Part 2 provides a glimpse of classical Euclidean geometry, with an emphasis on concurrence results, such as the nine-point circle. Part 3 studies transformations of the Euclidean plane, beginning with isometries and ending with inversion, with applications and a discussion of area in between. Part 4 is dedicated to the development of the Poincaré disk model, and the study of geometry within that model. While this material is traditional, Geometry Illuminated does bring together topics that are generally not found in a book at this level. Most notably, it explicitly computes parametric equations for the pseudosphere and its geodesics. It focuses less on the nature of axiomatic systems for geometry, but emphasizes rather the logical development of geometry within such a system. It also includes sections dealing with trilinear and barycentric coordinates, theorems that can be proved using inversion, and Euclidean and hyperbolic tilings.

Author : George Albert Wentworth
Publisher :
ISBN 13 :
Total Pages : 360 pages
Book Rating : 4.78/5 ( download)

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Download or read book Plane and Spherical Trigonometry written by George Albert Wentworth and published by . This book was released on 1889 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Henry Frederick Baker
Publisher : Chelsea Publishing Company, Incorporated
ISBN 13 :
Total Pages : 400 pages
Book Rating : 4.65/5 ( download)

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Download or read book An Introduction to Plane Geometry written by Henry Frederick Baker and published by Chelsea Publishing Company, Incorporated. This book was released on 1971 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : George Albert Wentworth
Publisher :
ISBN 13 :
Total Pages : 278 pages
Book Rating : 4.30/5 ( download)

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Download or read book Plane Geometry written by George Albert Wentworth and published by . This book was released on 1899 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: