Enhanced descriptions from Syndetics:

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.

Table of contents provided by Syndetics

• Part I
• 1 Going round in circles
• 2 Reflections on inversion
• 3 Dr. Whatif+s Euclidean geometry
• 4 A hyperbolic T-party
• 5 Circle-land revisited
• 6 Into the shadows
• Part II
• 7 Axiom systems
• 8 Solutions to the problems
• 9 On books to follow up the journey

Reviews provided by Syndetics

CHOICE Review

Books occasionally surface that are much more than they appear or claim to be. This is one such book. Designed as an informal excursion in non-Euclidean geometry for high school students, their teachers, and the interested general reader, it has a greater potential. On the one hand, it uses dialogues to introduce and explore extensions of high school geometry into the realm of both non-Euclidean and inversion geometries. Yet, its strength lies in its appeal to the reader's imagination in the gradual development and analysis of geometrical systems from the perspective of both a product and a process. Anyone who is interested in mathematics can benefit from Sved's book, in that one is forced to reflect on prior conceptions of mathematics in general and how it is presented to students. More authors should consider this approach. The problem sets are neither trivial nor ancillary but are important factors in both the textual development and the reader's understanding. Also, rather than attempting to be comprehensive or complete, the text does its small task well (i.e., to provide tastes of alternative geometries and geometric thinking). All prospective teachers of secondary mathematics should be required to study this book both content and style. A weakness is its minimal reference list, which should be expanded to support the reader motivated to do further reading. J. Johnson; Western Washington University