Journey into Geometries（ISBN=9780883855003） 下载 pdf 百度网盘 epub 免费 2025 电子版 mobi 在线

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, * headings, and

cartoon drawings evokes the spirit of the original Alice.

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

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书籍介绍

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.