The circle
Subtitle: a mathematical exploration beyond the line
By: Alfred S. Posamentier & Robert Geretschläger
Contributors: Geretschläger, Robert
Publisher: Prometheus Books
Published: 2016
Language: eng
Number of pages: 349
ISBN-13: 9781633881679
Subjects: Plane Geometry; Geometry; Circle; Circle packing
Description: The circle has fascinated mathematicians since ancient times. This entertaining book describes in layperson's terms the many intriguing properties of this fundamental shape. If math has intimidated you, this may be the ideal book to help you appreciate the discipline through one of its most important elements. The authors begin with a brief review of the basic properties of the circle and related figures. They then show the many ways in which the circle manifests itself in the field of geometryleading to some amazing relationships and truly important geometric theorems. In addition, they explore remarkable circle constructions and demonstrate how all constructions in geometry that usually require an unmarked straightedge and a compass can also be done with the compass alone. Among other things, the reader will learn that circles can generate some unusual curves -- many even quite artistic. Finally, the role of circles in art and architecture and a discussion of the circle's place on the sphere bring "full circle" this presentation of a key element of geometry. -- Provided by publisher.
Notes: Includes bibliographical references and index.
Table of contents: title: The circle relationships in basic plane geometry-and an extension; title: The circle's special role in geometry; title: Famous theorems about circles; title: Circle-packing problems; title: Investigation of equicircles; title: Circle constructions : the problem of Apollonius; title: Inversion : circle symmetry; title: Mascheroni constructions : using only compasses; title: Circles in art and architecture; title: Rolling circles : hypocycloids and epicycloids / by Christain Spreitzer; title: Spherical geometry : circles on the sphere; title: Afterword : A cultural introduction to the circle / by Erwin Rauscher.