[PDF] The Geometry Of The Circle And Mathematics As Applied To Geometry By Mathematicians eBook

Author : James Smith
Publisher : Forgotten Books
Page : 457 pages
File Size : 25,57 MB
Release : 2015-06-16
Category : Mathematics
ISBN : 9781330111888

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Excerpt from The Geometry of the Circle and Mathematics as Applied to Geometry by Mathematicians, Shewn to Be a Mockery, Delusion, and a Snare: Letter to G. G. Stokes I assume that you are a Geometer. If so, you may have mastered every proposition of Euclid, without having acquired even so much knowledge of Arithmetic, as to be master of the Multiplication Table. But, if you are a Mathematician, you will know that, we cannot apply Mathematics to pure Geometry, without the aid of "that indispensable instrument of science, Arithmetic," upon which all Mathematics are founded. In the geometrical figure in the margin, A B C D is a square on the radius of the circle; and, A C E F is a square on A C, a diagonal of the square A B C D, by construction. It is not only axiomatic, but self-evident, that A C E F is an inscribed square, and G B H K circumscribing square to the circle. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Author : Alexander Shen
Publisher : American Mathematical Soc.
Page : 229 pages
File Size : 16,89 MB
Release : 2016
Category : Juvenile Nonfiction
ISBN : 1470419211

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Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving. The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for self-study (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost self-contained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions. The book can be used by motivated high-school students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession. What a joy! Shen's ``Geometry in Problems'' is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroom-relevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time. This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problem-solving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book. --James Tanton, Mathematician-at-Large, Mathematical Association of America We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience. --Mark Saul, Director of Competitions, Mathematical Association of America

Author : Maureen T. Carroll
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 18,39 MB
Release : 2018-12-20
Category : Geometry
ISBN : 1470448432

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Geometry: The Line and the Circle is an undergraduate text with a strong narrative that is written at the appropriate level of rigor for an upper-level survey or axiomatic course in geometry. Starting with Euclid's Elements, the book connects topics in Euclidean and non-Euclidean geometry in an intentional and meaningful way, with historical context. The line and the circle are the principal characters driving the narrative. In every geometry considered—which include spherical, hyperbolic, and taxicab, as well as finite affine and projective geometries—these two objects are analyzed and highlighted. Along the way, the reader contemplates fundamental questions such as: What is a straight line? What does parallel mean? What is distance? What is area? There is a strong focus on axiomatic structures throughout the text. While Euclid is a constant inspiration and the Elements is repeatedly revisited with substantial coverage of Books I, II, III, IV, and VI, non-Euclidean geometries are introduced very early to give the reader perspective on questions of axiomatics. Rounding out the thorough coverage of axiomatics are concluding chapters on transformations and constructibility. The book is compulsively readable with great attention paid to the historical narrative and hundreds of attractive problems.

Author : James Smith
Publisher : Palala Press
Page : 462 pages
File Size : 27,22 MB
Release : 2016-05-19
Category :
ISBN : 9781357399443

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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : Dan Pedoe
Publisher : American Mathematical Soc.
Page : 102 pages
File Size : 39,69 MB
Release : 2020-08-03
Category : Mathematics
ISBN : 1470457326

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This revised edition of a mathematical classic originally published in 1957 will bring to a new generation of students the enjoyment of investigating that simplest of mathematical figures, the circle. The author has supplemented this new edition with a special chapter designed to introduce readers to the vocabulary of circle concepts with which the readers of two generations ago were familiar. Readers of Circles need only be armed with paper, pencil, compass, and straight edge to find great pleasure in following the constructions and theorems. Those who think that geometry using Euclidean tools died out with the ancient Greeks will be pleasantly surprised to learn many interesting results which were only discovered in modern times. Novices and experts alike will find much to enlighten them in chapters dealing with the representation of a circle by a point in three-space, a model for non-Euclidean geometry, and the isoperimetric property of the circle.

Author : Alfred S. Posamentier
Publisher : Prometheus Books
Page : 352 pages
File Size : 27,31 MB
Release : 2016-08-23
Category : Mathematics
ISBN : 1633881687

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The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson’s terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometry—leading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves – many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle’s place on the sphere bring "full circle" this presentation of a key element of geometry.

Author : Joel David Hamkins
Publisher : MIT Press
Page : 350 pages
File Size : 34,45 MB
Release : 2021-03-09
Category : Mathematics
ISBN : 0262542234

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An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.