Geometry: The Line and the Circle

Geometry: The Line and the Circle

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
Publisher American Mathematical Soc.
Release Date
ISBN 1470448432
Pages 480 pages
Rating 4/5 (31 users)

More Books:

Geometry: The Line and the Circle
Language: en
Pages: 480
Authors: Maureen T. Carroll
Categories: Geometry
Type: BOOK - Published: 2018-12-20 - Publisher: American Mathematical Soc.

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 o
Circle Line
Language: en
Pages: 320
Authors: Steffan Meyric Hughes
Categories: Sports & Recreation
Type: BOOK - Published: 2012-07-02 - Publisher: Summersdale Publishers LTD - ROW

"Magic, to a sailor, is harnessing the wind – getting something for nothing – the surprise of a gust, the boon of a side-wind and the trial of a headwind an
Around Manhattan Island and Other Maritime Tales of New York
Language: en
Pages: 269
Authors: Brian J. Cudahy
Categories: History
Type: BOOK - Published: 1997 - Publisher: Fordham Univ Press

Cudahy begins with a history of the Circle Line and its forerunners and erstwhile competitors in the around-Manhattan sightseeing business. Next, he gives us th
Circle Circle Line Dot
Language: en
Pages: 195
Authors: Alan Goldsamt
Categories: Fiction
Type: BOOK - Published: 2012-12-01 - Publisher: Simon and Schuster

Each of the intriguing and suggestive short stories will give the reader the opportunity to decide which of the overt and concealed messages are reasonable and
The Encyclopædia Britannica
Language: en
Pages:
Authors:
Categories: Encyclopedias and dictionaries
Type: BOOK - Published: 1895 - Publisher:

Mathematics Today-8 (ICSE)
Language: en
Pages:
Authors: S.K. Gupta & Anubhuti Gangal
Categories: Mathematics
Type: BOOK - Published: - Publisher: S. Chand Publishing

All mathematical concepts have been presented in a very simple and lucid form. Unit summary of key facts at the end, Mental Maths Exercises, Unit Review Exercis
The Encyclopaedia Britannica
Language: en
Pages:
Authors:
Categories: Encyclopedias and dictionaries
Type: BOOK - Published: 1890 - Publisher:

Geometric Constructions
Language: en
Pages: 206
Authors: George E. Martin
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all
The English Duden : picture vocabularies in English with English and German indices
Language: en
Pages: 666
Authors: Horst Klien
Categories: English language
Type: BOOK - Published: 1937 - Publisher:

A collection of problems in illustration of the principles of elementary mechanics
Language: en
Pages:
Authors:
Categories:
Type: BOOK - Published: 1858 - Publisher: