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Geometric Constructions (Undergraduate Texts in Mathematics)

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Geometric Constructions (Undergraduate Texts in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.

Synopsis:

Written in an informal style that intersperses history and philosophy with mathematics, this class-tested, self-contained book demonstrates how some simple construction tools can be associated with various fields of real numbers through coordinate geometry.

Synopsis:

Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.

Description:

Includes bibliographical references (p. [189]-197) and index.

Table of Contents

Euclidean Constructions.- The Ruler and Compass.- The Compass and the Mohr-Mascheroni Theorem.- The Ruler.- The Ruler and Dividers.- The Poncelet-Steiner Theorem and Double Rulers.- The Ruler and Rusty Compass.- Sticks.- The Marked Ruler.- Paperfolding - The Back of the Book.

Product Details

ISBN:
9780387982762
Author:
Martin, George Edward
Publisher:
Springer
Author:
Martin, George E.
Location:
New York :
Subject:
Applied
Subject:
Geometry - General
Subject:
Geometry
Subject:
Geometrical constructions.
Subject:
Mathematics-Applied
Copyright:
Edition Description:
Book
Series:
Undergraduate Texts in Mathematics
Series Volume:
333
Publication Date:
19971205
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
214
Dimensions:
235 x 155 mm 1090 gr

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Related Subjects

Computers and Internet » Computers Reference » General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Geometric Constructions (Undergraduate Texts in Mathematics) New Hardcover
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Product details 214 pages Springer-Verlag - English 9780387982762 Reviews:
"Synopsis" by , Written in an informal style that intersperses history and philosophy with mathematics, this class-tested, self-contained book demonstrates how some simple construction tools can be associated with various fields of real numbers through coordinate geometry.
"Synopsis" by , Geometric constructions have been a popular part of mathematics throughout history. The first chapter here is informal and starts from scratch, introducing all the geometric constructions from high school that have been forgotten or were never learned. The second chapter formalises Plato's game, and examines problems from antiquity such as the impossibility of trisecting an arbitrary angle. After that, variations on Plato's theme are explored: using only a ruler, a compass, toothpicks, a ruler and dividers, a marked rule, or a tomahawk, ending in a chapter on geometric constructions by paperfolding. The author writes in a charming style and nicely intersperses history and philosophy within the mathematics, teaching a little geometry and a little algebra along the way. This is as much an algebra book as it is a geometry book, yet since all the algebra and geometry needed is developed within the text, very little mathematical background is required. This text has been class tested for several semesters with a master's level class for secondary teachers.
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