Mathematics and the Imagination (Dover Books on Mathematics) by Edward Kasner (PDF)

Description

You don’t have to love math to enjoy a hand of cards, a night at the casino, or a puzzle. But your pleasure and prowess at games, gambling, and other numerically related pursuits can be heightened with this entertaining volume, in which the authors offer a fascinating view of some of the lesser-known and more imaginative aspects of mathematics.A brief and breezy explanation of the new language of mathematics precedes a smorgasbord of such thought-provoking subjects as the googolplex (the largest definite number anyone has yet bothered to conceive of); assorted geometries — plane and fancy; famous puzzles that made mathematical history; and tantalizing paradoxes. Gamblers receive fair warning on the laws of chance; a look at rubber-sheet geometry twists circles into loops without sacrificing certain important properties; and an exploration of the mathematics of change and growth shows how calculus, among its other uses, helps trace the path of falling bombs.Written with wit and clarity for the intelligent reader who has taken high school and perhaps college math, this volume deftly progresses from simple arithmetic to calculus and non-Euclidean geometry. It “lives up to its title in every way [and] might well have been merely terrifying, whereas it proves to be both charming and exciting.” — Saturday Review of Literature.

User’s Reviews

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

⭐We are in 1940, Kasner and Newman are compiling strange things you can see using mathematics (i.e. using a mathescope). If “imagination” triggered your curiosity, this book is far better than its title. Let us define “far” as one googleplex, which is enormous but finite. One googleplex of what? Up to you. Say fish steaks or kangaroos. It is just a matter of scale, you got infinity within 0 and 1. As you can see, this book may drive you mad…. A hell of a lot of wit and ingenuity within.

⭐About 50 years ago, my plane geometry teacher recognized I might have some math ability, if properly nurtured, and gave me a copy of this book. She asked I meet with her weekly to discuss assignments in the book. The hook was that if I did so, I would be given an A+, my first math grade above a C-. I did so, and my life was transformed. Suddenly, I found the works of the greats of math explained to me in a way that changed math from a rote memory process to a thought process and I was hooked! Math had been an important part of my life ever since. The current book is still full of the same insight-provoking things that made the earlier editions so great. It is to be a gift for my grandson, in an attempt to point him down the road toward a love of math. I can’t recommend this book highly enough!

⭐I first read this book in 1956 and was amazed at its clarity. When my granddaughter had trouble understanding the concept that a series with an infinite number of terms could nevertheless have a finite sum, I thought immediately of this book. It is a classic and required reading for anyone seeking to gain an understanding of the differences between infinity and very large numbers amongst other things. Having completed the first course in algebra will be a help to understanding this book but it not a requirement.

⭐The author gives his account of the names of the two numbers and some motivation behind coining those neologisms. Some of the expectations that he raises concerning tests or experiments are inaccurate or deceptive. Since the publication of this book and its successor(s), I have provided new insights into the physical significance of a googolplex. So I respect the historical foundation of this book and hope to add to the understanding of its concepts later in mathematical writing and history and mathematics.

⭐Soy topógrafo de minas, y cultivo las ciencias exactas y el libro “Mathematics and the Imagination”para mí es interesante por la Historia de las Matemáticas descrita muy brevemente.Bye, Bye,Raúl Choque

⭐I read this for the first time in 1971, when I was in high school. It was a good layman’s introduction to many of the fields of mathematics then, and it still is. It doesn’t have anything about some of the newer developments, such as fractals, but it’s still informative and entertaining.

⭐I gained quite a few good concepts relating to the philosophies behind mathematics along with good mathematic examples that anyone with basic algebra skills would yield some benefit from.It’s a fun book with it’s twists and turns of subject matter.

⭐this book is more than 50 years old, but it still provides valuable insight for any math-oriented high school student and especially so for those students who plan for careers in mathematics or any of the sciences.

⭐I bought this book wanting to learn about the more abstract? Varieties of mathematics that seem to figure increasingly in philosophy and analysis in recent years. The book has certainly enabled me some useful insight into this area, and I liked the engaging style of the author. However I found I got completely stuck after a while. Finding some of the explanations resulting in for me a perception ambivalence which I could not move past. Probably my earlier background in engineering (where success came from structured logic and sticking to the formula).. was working against me here. I realise that others do understand these concepts though. I am now looking for a book which can hopefully get me past the bits I was stuck on.Overall I feel that for what I paid, this book does represent good value, and has certainly stimulated my interest to explore further.

⭐What this book is good at is stimulating the flavour of the mathematical adventure in its readers. It treats nothing with any depth being mainly verbal but the topics raised are not trivial and the reader is led into the story of each topic in an adult fashion without the stress of “sums”. Might suit a young person with a curious mind to win their fondness for the process of the mathematical experience as opposed to intimidating and boring them by being too hard and unimaginative. Might suit an older person with a young mind.

⭐An excellent work, worthy of many stars. But the Kindle version contains so many transcription errors that I had to refer back to the paper version every couple of pages in order to make sense of it. If and when the Kindle people correct the errors I would recommend anyone with any interest in maths at any level to read it. Otherwise it’s not much use unless you have a paper copy to resort to like I have.

⭐I had already read its paper edition, long ago… Even so, it was a very interesting book, specially the chapter about pi, e and i. It could have been better, for example giving more details about continued fractions, and other such topics.

⭐Es un excelente libro, fue el mismo que leyó Jorge Luis Borges antes de escribir el Aleph y demas cuentos, para los no matematicos , que hayamos acabado la secundaria es muy accesible

⭐

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