Ruler and the Round

Classic Problems in Geometric Constructions

Nonfiction, Science & Nature, Mathematics, Graphic Methods, Geometry
Cover of the book Ruler and the Round by Nicholas D. Kazarinoff, Dover Publications
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Author: Nicholas D. Kazarinoff ISBN: 9780486143613
Publisher: Dover Publications Publication: September 11, 2012
Imprint: Dover Publications Language: English
Author: Nicholas D. Kazarinoff
ISBN: 9780486143613
Publisher: Dover Publications
Publication: September 11, 2012
Imprint: Dover Publications
Language: English
Although easy to comprehend and fun to do, many geometric constructions defy completion with just a ruler and a compass. This book takes an intriguing look at the most famous of these "impossible" constructions.
In exploring ground rules, history, and angle trisection, the first part considers angle trisection and bird migration, constructed points, analytic geometry, algebraic classification of constructible numbers, fields of real numbers, cubic equations, and marked ruler, quadratix, and hyperbola (among other subjects). The second part treats nonconstructible regular polygons and the algebra associated with them; specifically, irreducibility and factorization, unique factorization of quadratic integers, finite dimensional vector spaces, algebraic fields, and nonconstructible regular polygons.
High school and college students as well as amateur mathematicians will appreciate this stimulating and provocative book, and its glimpses into the crucial role geometry plays in a wide range of mathematical applications.
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Although easy to comprehend and fun to do, many geometric constructions defy completion with just a ruler and a compass. This book takes an intriguing look at the most famous of these "impossible" constructions.
In exploring ground rules, history, and angle trisection, the first part considers angle trisection and bird migration, constructed points, analytic geometry, algebraic classification of constructible numbers, fields of real numbers, cubic equations, and marked ruler, quadratix, and hyperbola (among other subjects). The second part treats nonconstructible regular polygons and the algebra associated with them; specifically, irreducibility and factorization, unique factorization of quadratic integers, finite dimensional vector spaces, algebraic fields, and nonconstructible regular polygons.
High school and college students as well as amateur mathematicians will appreciate this stimulating and provocative book, and its glimpses into the crucial role geometry plays in a wide range of mathematical applications.

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