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.
目錄:
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