Journey into Geometries (Spectrum) by Marta Sved (PDF)

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. 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.

User’s Reviews

Editorial Reviews: Review All prospective teachers of secondary mathematics should be required to study this book both in content and style. — Choice Book Description Informal introduction into the non-Euclidean geometries through a series of dialogues involving Alice in Wonderland. 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. About the Author Marta Sved obtained her PhD from the University of Adelaide and also taught there until she retired. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐The book is styled after a frequently-used device: “Alice in X”, where X can be any kind of space which you wish to explain to the gentle reader. In this instance, Alice, along with Lewis Carroll and a Doctor WhatIf, gets to explore X=hyperbolic geometries. Poincare’s disk is explained in great detail, along with lots of examples and exercises. Characters from “Wonderland” and “Looking Glass” make appearances at various places. Not a book you can read as a novel but fiction is fused completely with the mathematics (except for chapter-end problems). And the author does not waste much time diving into deep geometry so it is not an easy read. Uses a lot of puns, as is to be expected, some good and some groan-worthy. She’s thrown in a few poems / limericks / doggerels as well along the way.The foreword to the book compares it directly to Synge’s “Kandelman’s Krim”. The book is an enormous amount of fun if you like geometry. Heartily recommend it to anyone who loves mathematical toys in the abstract (though nothing abstract about geometry on a sphere or on a horse’s back…).

⭐.

⭐A wonderfully written adventure full of ideas and humor. Not, however, for those who do not enjoy an indirect exposition.

⭐The only reason why I bought this book was because it was required for my Geometry class. I thought it would be an interesting book, but ohhh my godd was I wrong. The writing was very dry and I honestly understood nothing from it! My professor also sucked at explaining the content, so I was confused the entire semester! It was a waste of my money!!!

⭐I love the idea of the book, to explain math functions in a mix narrative/ theoretical fabric. I would not say the narrative is superficial, but rather, the explanation of “hierarchies” are determined by social relations to class and gender, not influence by the advent of informatics and computer science. The variables, and punchline jokes are not contemporary, quite jarring at female intelligence and acceptance in technical occupations. Certain areas of academia did not exist when this book was writen. I would not recommend this book as assigned reading, because it is very hard to distinguish what you need to believe in order to understand the mathematics, mixed with the social injustice accusations of how the world ‘is’ that certainly ride the tolerance of my attention. I would, perhaps, read this out loud to young students, after practice and editing of the material.

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