Journey into Geometries (Spectrum) [Paperback]

Marta Sved (Author), H. S. M. Coxeter (Author), John Stillwell (Author)

Book Description

ISBN-10: 0883855003 | ISBN-13: 978-0883855003 | Publication Date: July 1997

This unique book gives an informal introduction into the non-Euclidean geometries through a series of dialogues between a somewhat grown-up Alice (of Looking Glass fame), her uncle Lewis Carroll, and a visitor from the twentieth century, Dr Whatif. In the story, Lewis Carroll's geometrical beliefs are cast into the Euclidean mould, Dr Whatif asks the penetrating and controversial questions, and Alice acts as a mediator and interested participant. The book is intentionally more mathematical than Lewis Carroll's books, but for those of us who enjoyed Alice's earlier adventures there are many interesting flashbacks to those inimitable characters: the Red Queen, Tweedle-Dum and his twin brother, the Mad Hatter ... The text is filled with humour, wit, and verses of poetry. Part 1 contains the story in six chapters, each of which concludes with a problem set; Part 2 is more mathematical, and looks at the axiom systems, and gives solutions to the problems. The presentation, with its old-time borders, script headings, and cartoon drawings evokes the spirit of the original Alice.

Editorial Reviews

Review

All prospective teachers of secondary mathematics should be required to study this book both in content and style. -- Choice

Book Description

This unique book gives an informal introduction into the non-Euclidean geometries through a series of dialogues between a somewhat grown-up Alice (of Looking Glass fame), her uncle Lewis Carroll, and a visitor from the twentieth century, Dr Whatif.

See all Editorial Reviews

Product Details

• Paperback: 182 pages
• Publisher: The Mathematical Association of America (July 1997)
• Language: English
• ISBN-10: 0883855003
• ISBN-13: 978-0883855003
• Product Dimensions: 8.9 x 6.3 x 0.5 inches
• Shipping Weight: 10.4 ounces (View shipping rates and policies)
• Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #373,621 in Books (See Top 100 in Books)

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Customer Reviews

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4 of 4 people found the following review helpful:

5.0 out of 5 stars Another magical journey through the wonderland of geometry, March 25, 2000

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Journey into Geometries (Spectrum) (Paperback)

One cannot say that Lewis Carroll would be pleased, since he helps with the narration of this account of some additional travels of his darling Alice. Many of the other original Wonderland characters also help Dr. What If and him explain and illustrate a wide variety of geometric problems.
Although the author does an excellent job in presenting difficult concepts, this is not a textbook, Think of it as an excursion into the wonderland of advanced geometry. Experts will frolic, amateurs with grin and eventually understand and beginners will smile right up to the point (pun intended), where they get lost.
Problems are given at the end of each chapter and detailed solutions appear in the back of the book. A partial list of the topics covered includes inversions, reflections, a hyperbolic T-party, hyperbolic geometry, and projections. Verse with a decidedly Carrollean flavor appears throughout the text.
A joy to read and even better the second time through, it is a fitting sequel to the original adventures.

Published in Journal of Recreational Mathematics, reprinted with permission.