Product Description
This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is included in our special Legacy Reprint Series. In the interest of creating a more extensive selection of rare historical book reprints, we have chosen to reproduce this title even though it may possibly have occasional imperfections such as missing and blurred pages, missing text, poor pictures, markings, dark backgrounds and other reproduction issues beyond our control. Because this work is culturally important, we have made it available as a part of our commitment to protecting, preserving and promoting the world's literature. ... Read more

Customer Reviews (1)

An interesting "unpretending little book"
The back cover claims that this book is "widely regarded as a classic of modern mathematics", but I think one should rather listen to Klein himself: in his preface, Klein calls it an "unpretending little book", apparently based on a few (unpretending?) little lectures, typed up into a book by some (unpretending?) little student.

Circumventing Galois Theory, Klein proves the impossibility of doubling a cube and trisecting an angle in the first ten pages. We then look at the solvable cases of circle division, especially the constructability of the regular 17-gon. Gauss proved algebraically that p-division of the circle is possible for Fermat primes p=2^2^k+1. We work through Gauss's proof in the special case p=17. Giving up on a fully geometric proof, "there remains, then, only the geometric translation of the individual algebraic steps". In the second part of the book, to prove that it is impossible to square the circle we prove the transcendence of pi, and in the process we must also show the transcendence of e (and then go through Euler's formula e^i*pi=-1). These proofs use only elementary mathematics but unfortunately they are still rather technical. Perhaps the history of these proofs--they are the results of successive reworkings of much more advanced analytic proofs--vouches for their artificiality. ... Read more

Product Description
It is impossible to trisect angles with straightedge and compass alone, but many people try and think they have succeeded. This book is about angle trisections and the people who attempt them. Its purposes are to collect many trisections in one place, inform about trisectors, to amuse the reader, and, perhaps most importantly, to reduce the number of trisectors. This book includes detailed information about the personalities of trisectors and their constructions. It can be read by anyone who has taken a high school geometry course. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This Book Is In French. Due to the very old age and scarcity of this book, many of the pages may be hard to read due to the blurring of the original text. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
This is a reproduction of a book published before 1923.This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process.We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide.We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book. ... Read more

Product Description
High Quality Content by WIKIPEDIA articles! The problem of trisecting the angle is a classic problem of compass and straightedge constructions of ancient Greek mathematics. Two tools are allowedAn un-marked straightedge, and a compass.Problem: construct an angle one-third a given arbitrary angle.With such tools, it is generally impossible, as shown by Pierre Wantzel (1837). This requires taking a cube root, impossible with the given tools. The fact that there is no way to trisect an angle in general with just a compass and a straightedge does not mean that it is impossible to trisect all angles so. Also, it is possible to trisect any angle analytically. ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more