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Ruler and the Round (Classic Problems in Geometric Constructions)
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Product Details
Author:
Nicholas D. Kazarinoff
Format:
Paperback
Pages:
160
Publisher:
Dover Publications (October 20, 2011)
Language:
English
ISBN-13:
9780486425153
ISBN-10:
0486425150
Weight:
6.4oz
Dimensions:
5.375" x 8.5"
Case Pack:
52
File:
Dover-Dover_08032024_P7614837_onix30_Complete-20240803.xml
Folder:
Dover
As low as:
$10.40
List Price:
$10.95
Publisher Identifier:
P-DOVER
Discount Code:
D
Audience:
College/higher education
Pub Discount:
65
Overview
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.
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.
