Abstract Algebra And Famous Impossibilities

The famous problems of squaring the circle, doubling the cube, and trisecting the angle have captured the imagination of both professional and amateur mathematician for over two thousand years. These problems, however, have not yielded to purely geometrical methods. It was only the development of abstract algebra in the nineteenth century which enabled mathematicians to arrive at the surprising conclusion that these constructions are not possible. This text aims to develop the abstract algebra.

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Develops the abstract algebra necessary to prove the impossibility of constructions to square the circle, double the cube, trisect the angle by geometrical means. Assumes linear algebra. Annotation c. Book News, Inc., Portland, OR (booknews.com)