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The Pea and the Sun: A Mathematical Paradox

3.83  ·  Rating details ·  118 ratings  ·  7 reviews
Take an apple and cut it into five pieces. Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, autho ...more
Hardcover, 232 pages
Published April 29th 2005 by A K PETERS (first published April 2005)
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Ahmad Ashkaibi
Apr 29, 2017 rated it liked it
The Banach-Tarski Theorem, is not a easy subject even to mathematicians, yet this book gives a very clear and simplified explanation and proof of this theorem.

The general idea of Banach-Tarski Theorem is that you can make an infinite number of infinities out of just one infinity. So you can split the "mother" infinity in to several infinities of the same size as the mother infinity. Or, in other words, you can rearrange the points of a small object (as small as a pea) to get a bigger object (as
...more
Dan
Mar 30, 2008 rated it really liked it
Recommends it for: People with an undergrad degree in mathematics
This book is about the Banach-Tarski Theorem. This was a Mathematical result from the twenties that said there is a way to take apart a solid ball in a finite number of pieces and then twist and turn around the pieces, and then reassemble them into two balls of the same mass and volume. This is all mathematically speaking, of course, so it doesn't mean you can do it in real life.

The proof is presented well, and it provides a lot of background. It is not rigorous, but I definitely now how to do t
...more
Peter (Pete) Mcloughlin
I had my first experience of the continuum at about the age of seven. Lying in my bed trying to go sleep I was looking out into room illuminated with a small night light at the door I started to think and perceive the concept of size. The door across from my bed seemed immensely large one moment then infinitesimally small the next moment. I thought about the world being infinitely large and being infinitely small at the same time and how everything was made of an infinity of pieces. Anyway, Cant ...more
Joe
Nov 06, 2007 rated it liked it  ·  review of another edition
3.5 stars. fascinating subject, a lot of fun to read, and educational for me at the time, but sloppily written, fully of errors, and not brilliant.
Dio Mavroyannis
Sep 28, 2020 rated it it was amazing
Shelves: wtr-gen-math, wtr-lit
It's math in words and numbers! This is a very fun book, it goes through some deep mathematical ideas without getting too stuck up with the jargon. Additionally, he is full of graphs to create intuition. I loved the philosophy bites in the beginning, about what it takes to be a platonist. Anyway, great book all around! It's mostly structured to get you to the Banach Tarski Paradox, so all the chapters teach intuitively the pre-requisites to understanding it. I would buy this for a smart teenager ...more
Neal Alexander
Apr 18, 2020 rated it liked it
The Banach-Tarski theorem states that a ball (i.e. a solid sphere) can be split into countably many pieces and re-assembled into another ball of different radius. Like the author, as a maths student I was unsettled by this result, as were many others: according to an obituary of Tarski, an Illinois citizen once demanded that the state legislature outlaw its teaching.

The paradoxical nature of the theorem lies in our wanting to infer from mathematics to the physical world. While this is valid for
...more
Steve Gross
Jul 06, 2014 rated it really liked it
The clearest exposition of the Banach-Tarski I've ever seen. Come to think of it, the only exposition of the Banach-Tarski paradox I've ever seen. Not so hard mathematics that prove you can disassemble a pea into 5 or more pieces and reassemble them into a sphere the size of the sun.
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