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OverviewIn this presentation of the Galois correspondence, modern theories of groups and fields are used to study problems, some of which date back to the ancient Greeks. The techniques used to solve these problems, rather than the solutions themselves, are of primary importance. The ancient Greeks were concerned with constructibility problems. For example, they tried to determine if it was possible, using straightedge and compass alone, to perform any of the following tasks? (1) Double an arbitrary cube; in particular, construct a cube with volume twice that of the unit cube. (2) Trisect an arbitrary angle. (3) Square an arbitrary circle; in particular, construct a square with area 1r. (4) Construct a regular polygon with n sides for n > 2. If we define a real number c to be constructible if, and only if, the point (c, 0) can be constructed starting with the points (0,0) and (1,0), then we may show that the set of constructible numbers is a subfield of the field R of real numbers containing the field Q of rational numbers. Such a subfield is called an intermediate field of Rover Q. We may thus gain insight into the constructibility problems by studying intermediate fields of Rover Q. In chapter 4 we will show that (1) through (3) are not possible and we will determine necessary and sufficient conditions that the integer n must satisfy in order that a regular polygon with n sides be constructible. Full Product DetailsAuthor: Maureen H. FenrickPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 2nd ed. 1998 Dimensions: Width: 15.50cm , Height: 1.30cm , Length: 23.50cm Weight: 0.403kg ISBN: 9781461272854ISBN 10: 1461272858 Pages: 244 Publication Date: 05 November 2012 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of ContentsReviewsIt is the clearest this reviewer has ever seen... Particularly remarkable is the author's avoidance of all temptations to give pretty proofs of neatly arranged theorems at the cost of clarity... Highly recommended . --Gian-Carlo Rota It is the clearest this reviewer has ever seen... Particularly remarkable is the author's avoidance of all temptations to give pretty proofs of neatly arranged theorems at the cost of clarity... Highly recommended . --Gian-Carlo Rota It is the clearest this reviewer has ever seen... Particularly remarkable is the author's avoidance of all temptations to give pretty proofs of neatly arranged theorems at the cost of clarity... Highly recommended . --Gian-Carlo Rota Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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