Geometry Through The Circle

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Geometry: The Line and the Circle

Author : Maureen T. Carroll
Publisher : American Mathematical Soc.
ISBN 13 : 1470448432
Total Pages : 480 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometry: The Line and the Circle by : Maureen T. Carroll

Download or read book Geometry: The Line and the Circle written by Maureen T. Carroll and published by American Mathematical Soc.. This book was released on 2018-12-20 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Squaring the Circle

Author : Paul A. Calter
Publisher : John Wiley & Sons
ISBN 13 : 9780470648599
Total Pages : 0 pages
Book Rating : 4.6/5 (485 download)

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Book Synopsis Squaring the Circle by : Paul A. Calter

Download or read book Squaring the Circle written by Paul A. Calter and published by John Wiley & Sons. This book was released on 2010-02-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry is a dynamic branch of mathematics that also serves as a creative tool for engineers, artists, and architects. Squaring the Circle: Geometry in Art and Architecture includes all the topics necessary for a solid foundation in geometry and explores the timeless influence of geometry on art and architecture. The text offers wide-ranging exercise sets and related projects that allow students to practice and master the mathematics presented. Each chapter introduces mathematical concepts geometrically and illustrates their nontraditional applications in art and architecture throughout the centuries. Appropriate for both basic mathematics courses and cross-discipline courses in mathematics and art, Squaring the Circle requires no previous mathematics.

Lectures on the Philosophy of Mathematics

Author : Joel David Hamkins
Publisher : MIT Press
ISBN 13 : 0262542234
Total Pages : 350 pages
Book Rating : 4.2/5 (625 download)

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Book Synopsis Lectures on the Philosophy of Mathematics by : Joel David Hamkins

Download or read book Lectures on the Philosophy of Mathematics written by Joel David Hamkins and published by MIT Press. This book was released on 2021-03-09 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Wonder Book of Geometry

Author : David Acheson
Publisher : Oxford University Press
ISBN 13 : 0192585371
Total Pages : 240 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis The Wonder Book of Geometry by : David Acheson

Download or read book The Wonder Book of Geometry written by David Acheson and published by Oxford University Press. This book was released on 2020-10-22 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: How can we be sure that Pythagoras's theorem is really true? Why is the 'angle in a semicircle' always 90 degrees? And how can tangents help determine the speed of a bullet? David Acheson takes the reader on a highly illustrated tour through the history of geometry, from ancient Greece to the present day. He emphasizes throughout elegant deduction and practical applications, and argues that geometry can offer the quickest route to the whole spirit of mathematics at its best. Along the way, we encounter the quirky and the unexpected, meet the great personalities involved, and uncover some of the loveliest surprises in mathematics.

Geometry in Problems

Author : Alexander Shen
Publisher : American Mathematical Soc.
ISBN 13 : 1470419211
Total Pages : 229 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Geometry in Problems by : Alexander Shen

Download or read book Geometry in Problems written by Alexander Shen and published by American Mathematical Soc.. This book was released on 2016 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

College Geometry

Author : Nathan Altshiller-Court
Publisher : Dover Publications
ISBN 13 : 9780486788470
Total Pages : 336 pages
Book Rating : 4.7/5 (884 download)

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Book Synopsis College Geometry by : Nathan Altshiller-Court

Download or read book College Geometry written by Nathan Altshiller-Court and published by Dover Publications. This book was released on 2013-12-30 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard university-level text for decades, this volume offers exercises in construction problems, harmonic division, circle and triangle geometry, and other areas. 1952 edition, revised and enlarged by the author.

Advanced Euclidean Geometry

Author : Roger A. Johnson
Publisher : Courier Corporation
ISBN 13 : 048615498X
Total Pages : 338 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Advanced Euclidean Geometry by : Roger A. Johnson

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.

Geometry of Complex Numbers

Author : Hans Schwerdtfeger
Publisher : Courier Corporation
ISBN 13 : 0486135861
Total Pages : 228 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Geometry of Complex Numbers by : Hans Schwerdtfeger

Download or read book Geometry of Complex Numbers written by Hans Schwerdtfeger and published by Courier Corporation. This book was released on 2012-05-23 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

First Steps for Math Olympians

Author : J. Douglas Faires
Publisher : MAA
ISBN 13 : 9780883858240
Total Pages : 344 pages
Book Rating : 4.8/5 (582 download)

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Book Synopsis First Steps for Math Olympians by : J. Douglas Faires

Download or read book First Steps for Math Olympians written by J. Douglas Faires and published by MAA. This book was released on 2006-12-21 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: A major aspect of mathematical training and its benefit to society is the ability to use logic to solve problems. The American Mathematics Competitions have been given for more than fifty years to millions of students. This book considers the basic ideas behind the solutions to the majority of these problems, and presents examples and exercises from past exams to illustrate the concepts. Anyone preparing for the Mathematical Olympiads will find many useful ideas here, but people generally interested in logical problem solving should also find the problems and their solutions stimulating. The book can be used either for self-study or as topic-oriented material and samples of problems for practice exams. Useful reading for anyone who enjoys solving mathematical problems, and equally valuable for educators or parents who have children with mathematical interest and ability.

Circles: A Mathematical View

Author : Dan Pedoe
Publisher : American Mathematical Soc.
ISBN 13 : 1470457326
Total Pages : 102 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Circles: A Mathematical View by : Dan Pedoe

Download or read book Circles: A Mathematical View written by Dan Pedoe and published by American Mathematical Soc.. This book was released on 2020-08-03 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geometry Through the Circle

Author : James Richard King
Publisher :
ISBN 13 : 9781559530477
Total Pages : 208 pages
Book Rating : 4.5/5 (34 download)

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Book Synopsis Geometry Through the Circle by : James Richard King

Download or read book Geometry Through the Circle written by James Richard King and published by . This book was released on 1996 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Shadows of the Circle

Author : Vagn Lundsgaard Hansen
Publisher : World Scientific
ISBN 13 : 9789810234188
Total Pages : 128 pages
Book Rating : 4.2/5 (341 download)

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Book Synopsis Shadows of the Circle by : Vagn Lundsgaard Hansen

Download or read book Shadows of the Circle written by Vagn Lundsgaard Hansen and published by World Scientific. This book was released on 1998 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to throw light on various facets of geometry through development of four geometrical themes. The first theme is about the ellipse, the shape of the shadow east by a circle. The next, a natural continuation of the first, is a study of all three types of conic sections, the ellipse, the parabola and the hyperbola. The third theme is about certain properties of geometrical figures related to the problem of finding the largest area that can be enclosed by a curve of given length. This problem is called the isoperimetric problem. In itself, this topic contains motivation for major parts of the curriculum in mathematics at college level and sets the stage for more advanced mathematical subjects such as functions of several variables and the calculus of variations. Here, three types of conic section are discussed briefly. The emergence of non-Euclidean geometries in the beginning of the nineteenth century represents one of the dramatic episodes in the history of mathematics. In the last theme the non-Euclidean geometry in the Poincare disc model of the hyperbolic plane is developed.

The Geometry of the Circle and Mathematics as Applied to Geometry by Mathematicians

Author : James Smith
Publisher :
ISBN 13 :
Total Pages : 459 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis The Geometry of the Circle and Mathematics as Applied to Geometry by Mathematicians by : James Smith

Download or read book The Geometry of the Circle and Mathematics as Applied to Geometry by Mathematicians written by James Smith and published by . This book was released on 1869 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Circle

Author : Alfred S. Posamentier
Publisher : Prometheus Books
ISBN 13 : 1633881679
Total Pages : 352 pages
Book Rating : 4.6/5 (338 download)

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Book Synopsis The Circle by : Alfred S. Posamentier

Download or read book The Circle written by Alfred S. Posamentier and published by Prometheus Books. This book was released on 2016 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Euclidean Geometry

Author : David M. Clark
Publisher : American Mathematical Soc.
ISBN 13 : 0821889850
Total Pages : 157 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Euclidean Geometry by : David M. Clark

Download or read book Euclidean Geometry written by David M. Clark and published by American Mathematical Soc.. This book was released on 2012-06-26 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometry has been an essential element in the study of mathematics since antiquity. Traditionally, we have also learned formal reasoning by studying Euclidean geometry. In this book, David Clark develops a modern axiomatic approach to this ancient subject, both in content and presentation. Mathematically, Clark has chosen a new set of axioms that draw on a modern understanding of set theory and logic, the real number continuum and measure theory, none of which were available in Euclid's time. The result is a development of the standard content of Euclidean geometry with the mathematical precision of Hilbert's foundations of geometry. In particular, the book covers all the topics listed in the Common Core State Standards for high school synthetic geometry. The presentation uses a guided inquiry, active learning pedagogy. Students benefit from the axiomatic development because they themselves solve the problems and prove the theorems with the instructor serving as a guide and mentor. Students are thereby empowered with the knowledge that they can solve problems on their own without reference to authority. This book, written for an undergraduate axiomatic geometry course, is particularly well suited for future secondary school teachers. 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.

Modern Geometry

Author : Clement Vavasor Durell
Publisher :
ISBN 13 :
Total Pages : 168 pages
Book Rating : 4.:/5 (5 download)

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Book Synopsis Modern Geometry by : Clement Vavasor Durell

Download or read book Modern Geometry written by Clement Vavasor Durell and published by . This book was released on 1920 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Four Pillars of Geometry

Author : John Stillwell
Publisher : Springer Science & Business Media
ISBN 13 : 0387255303
Total Pages : 240 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Four Pillars of Geometry by : John Stillwell

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