Taxicab Geometry

An Adventure in Non-Euclidean Geometry

Author: Eugene F. Krause

Publisher: Courier Corporation

ISBN: 048613606X

Category: Mathematics

Page: 96

View: 2836

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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.

The Last Recreations

Hydras, Eggs, and Other Mathematical Mystifications

Author: Martin Gardner

Publisher: Springer Science & Business Media

ISBN: 0387258272

Category: Mathematics

Page: 392

View: 8894

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Of all of Martin Gardners writings, none gained him a wider audience or was more central to his reputation than his Mathematical Recreations column in Scientific American - which virtually defined the genre of popular mathematics writing for a generation. Flatland, Hydras and Eggs: Mathematical Mystifications is the final collection of these columns, covering the period roughly from 1979 to Gardners retirement in 1986. As always in his published collections, Gardner includes letters commenting on the ideas presented in his articles. These columns show him at the top of his form and should not be missed by anyone with an interest in mathematics.

The Foundations of Geometry and the Non-Euclidean Plane

Author: G.E. Martin

Publisher: Springer Science & Business Media

ISBN: 1461257255

Category: Mathematics

Page: 512

View: 2450

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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.

Author: Ivan Moscovich

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402716683

Category:

Page: 128

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Presents a collection of puzzles that focus on mathematical concepts.

Geometry from Euclid to Knots

Author: Saul Stahl

Publisher: Courier Corporation

ISBN: 0486134989

Category: Mathematics

Page: 480

View: 6914

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This text provides a historical perspective on plane geometry and covers non-neutral Euclidean geometry, circles and regular polygons, projective geometry, symmetries, inversions, informal topology, and more. Includes 1,000 practice problems. Solutions available. 2003 edition.

Geometry Connections

Author: John K. Beem

Publisher: Prentice Hall

ISBN: N.A

Category: Education

Page: 297

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Presents a review of college-level geometry to help middle school mathematics teachers in teaching the NCTM Standards-based curricula.

Making Geometry Come Alive

Student Activities and Teacher Notes

Author: Alfred S. Posamentier

Publisher: Corwin Press

ISBN: 9780761975991

Category: Education

Page: 163

View: 2823

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All the basics of geometry in a motivating new format, from Ptolemy to Napoleon, from the Arbelos to the billiard table!

Learning mathematics through inquiry

Author: Raffaella Borasi

Publisher: Heinemann Educational Publishers

ISBN: N.A

Category: Education

Page: 234

View: 8319

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Raffaella Borasi worked closely with two high school girls who did not like math and who rarely had achieved any degree of success in the subject. Over the course of ten lessons, the students and Raffaella engaged in a personal inquiry into the nature of mathematical definitions.