The Circle: A Mathematical Exploration beyond the Line

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 geometry--leading 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.

Alfred S. Posamentier has published over fifty-five books in the area of mathematics and mathematics education, including, most recently, Numbers- Their Tales, Types, and Treasures (with Bernd Thaller). After having been on the faculty of the City College of the City University of New York for forty years, where he was a professor of mathematics education and dean of the School of Education, he subsequently held the same positions at Mercy College, New York, for five years. Robert Geretschl ger is a mathematics teacher at Bundesrealgymnasium Keplerstrasse in Graz, Austria. He is also an adjunct member of the mathematics faculty at the Karl-Franzens University in Graz, the coach of the Austrian International Mathematical Olympiad team, and the president of the "Kangaroo" student mathematics contest in Austria. He is the author of Geometric Origami, among other works.

""A fascinating book taking the reader full circle through the circle's baffling properties. As a layperson I was fascinated by the authors' subtle way of leading me through complex mathematical formulas--all connected with the circle but never circular. A cleverly written book offering new perspectives for the nonexperts." --Arthur Mettinger, professor, University of Vienna, Department of English and American Studies; and academic president, FH Campus Wien University of Applied Sciences "This book should be read by everyone who thinks math and geometry are difficult or boring. The authors, leading mathematicians themselves, have taken the topic of circles and shown us how fascinating--magic, indeed--and central to our experience of the world circles are. Posamentier and Geretschlager have explored the world of circles and their many applications in everyday life as well as in geometry, in a way that the most nervous layperson can understand and enjoy. I for one will never look at architecture or art in the same way after reading this book. I especially commend it to every teacher or confused student of mathematics." --Baroness Pauline Perry, former president of Lucy Cavendish College, Cambridge University "After reading this wonderful book, which helped me to recall my early memories of the geometry of circles, I was absolutely enchanted by the wonderful relationships involving circles--as well as their constructions and their appearances in our culture and on the sphere--that we should have been exposed to in our school days but never were! This is the book that all who have even the slightest interest in geometry will love, to have their knowledge of circles enriched. Great book!" --Charlotte Frank, PhD, senior advisor, McGraw-Hill Education; former director of curriculum and instruction, New York City Board of Education; and former regent, University of the State of New York "This is a remarkable addition to the geometry literature, giving a very incisive new insight into the role of the circle and how it relates to the line and other geometrical forms. Whatever your background, this is sure to help you reinforce your comprehension of all things geometric." --Peter Taylor (AO), emeritus professor, University of Canberra "Alfred S. Posamentier and Robert Geretschlager are a congenial mathematical author team; they are impressive not only for their superior content competence but also for their extraordinary talent to present mathematics to the general audience as a fascinating, enriching adventure. This book not only enhances the reader's knowledge but also is remarkable for its modest tone and splendid style." --Rudolf Taschner, professor of mathematics, Vienna University of Technology, and 2004 Austrian Scientist of the Year "This volume is a treasure trove on everything you want to know about circles. Starting from simple results in Euclidean geometry, it reaches far both in space and time, revisiting many famous historical problems and considering more modern topics such as inversive geometry and combinatorial geometry. . . . A fantastic collaboration between two noted mathematicians." --Andy Liu, Professor Emeritus, Department of Mathematical and Statistical Sciences, University of Alberta, and vice president, International Mathematics Tournament of the Towns