Lines And Circles In Taxicab Geometry
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Lines And Circles In Taxicab Geometry
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Author : Guanghui Chen
language : en
Publisher:
Release Date : 1992
Lines And Circles In Taxicab Geometry written by Guanghui Chen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Geometry, Non-Euclidean categories.
Taxicab Geometry
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Author : Eugene F. Krause
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1975
Taxicab Geometry written by Eugene F. Krause and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Juvenile Nonfiction categories.
Develops a simple non-Euclidean geometry and explores some of its practical applications through graphs, research problems, and exercises. Includes selected answers.
Taxicab Geometry
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Author : Eugene F. Krause
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
Taxicab Geometry written by Eugene F. Krause and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Fascinating, accessible introduction to unusual mathematical system in which distance is not measured by straight lines. Illustrated topics include applications to urban geography and comparisons to Euclidean geometry. Selected answers to problems.
Geometry The Line And The Circle
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Author : Maureen T. Carroll
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-12-20
Geometry The Line And The Circle written by Maureen T. Carroll and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-20 with Geometry categories.
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.
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Author : Ivan Moscovich
language : en
Publisher: Sterling Publishing Company, Inc.
Release Date : 2004
written by Ivan Moscovich and has been published by Sterling Publishing Company, Inc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Presents a collection of puzzles that focus on mathematical concepts.
The Foundations Of Geometry And The Non Euclidean Plane
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Author : G.E. Martin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Foundations Of Geometry And The Non Euclidean Plane written by G.E. Martin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref erence if necessary.
Circles In Chinese Checker Geometry And Intersection Of Taxicab Circles
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Author : David Bayne
language : en
Publisher:
Release Date : 2001
Circles In Chinese Checker Geometry And Intersection Of Taxicab Circles written by David Bayne and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Geometry, Non-Euclidean categories.
The Quadrature Of The Circle
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Author : John A. Parker
language : en
Publisher:
Release Date : 1851
The Quadrature Of The Circle written by John A. Parker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1851 with Circle-squaring categories.
College Geometry
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Author : David C. Kay
language : en
Publisher: CRC Press
Release Date : 2011-06-24
College Geometry written by David C. Kay and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
Designed for mathematics majors and other students who intend to teach mathematics at the secondary school level, College Geometry: A Unified Development unifies the three classical geometries within an axiomatic framework. The author develops the axioms to include Euclidean, elliptic, and hyperbolic geometry, showing how geometry has real and far-reaching implications. He approaches every topic as a fresh, new concept and carefully defines and explains geometric principles. The book begins with elementary ideas about points, lines, and distance, gradually introducing more advanced concepts such as congruent triangles and geometric inequalities. At the core of the text, the author simultaneously develops the classical formulas for spherical and hyperbolic geometry within the axiomatic framework. He explains how the trigonometry of the right triangle, including the Pythagorean theorem, is developed for classical non-Euclidean geometries. Previously accessible only to advanced or graduate students, this material is presented at an elementary level. The book also explores other important concepts of modern geometry, including affine transformations and circular inversion. Through clear explanations and numerous examples and problems, this text shows step-by-step how fundamental geometric ideas are connected to advanced geometry. It represents the first step toward future study of Riemannian geometry, Einstein’s relativity, and theories of cosmology.
Squigonometry The Study Of Imperfect Circles
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Author : Robert D. Poodiack
language : en
Publisher: Springer Nature
Release Date : 2022-12-15
Squigonometry The Study Of Imperfect Circles written by Robert D. Poodiack and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-15 with Mathematics categories.
This textbook introduces generalized trigonometric functions through the exploration of imperfect circles: curves defined by |x|p + |y|p = 1 where p ≥ 1. Grounded in visualization and computations, this accessible, modern perspective encompasses new and old results, casting a fresh light on duality, special functions, geometric curves, and differential equations. Projects and opportunities for research abound, as we explore how similar (or different) the trigonometric and squigonometric worlds might be. Comprised of many short chapters, the book begins with core definitions and techniques. Successive chapters cover inverse squigonometric functions, the many possible re-interpretations of π, two deeper dives into parameterizing the squigonometric functions, and integration. Applications include a celebration of Piet Hein’s work in design. From here, more technical pathways offer further exploration. Topics include infinite series; hyperbolic, exponential, and logarithmic functions; metrics and norms; and lemniscatic and elliptic functions. Illuminating illustrations accompany the text throughout, along with historical anecdotes, engaging exercises, and wry humor. Squigonometry: The Study of Imperfect Circles invites readers to extend familiar notions from trigonometry into a new setting. Ideal for an undergraduate reading course in mathematics or a senior capstone, this book offers scaffolding for active discovery. Knowledge of the trigonometric functions, single-variable calculus, and initial-value problems is assumed, while familiarity with multivariable calculus and linear algebra will allow additional insights into certain later material.
