A History of the Circle: Mathematical Reasoning and the Physical Universe

by Ernest Zebrowski Jr

Overview

The concept of the circle is ubiquitous. It can be described mathematically, represented physically, and employed technologically. The circle is an elegant, abstract form that has been transformed by humans into tangible, practical forms to make our lives easier.

And yet no one has ever discovered a true mathematical circle. Rainbows are fuzzy; car tires are flat on the bottom, and even the most precise roller bearings have measurable irregularities. Ernest Zebrowski, Jr., discusses why investigations of the circle have contributed enormously to our current knowledge of the physical universe. Beginning with the ancient mathematicians and culminating in twentieth-century theories of space and time, the mathematics of the circle has pointed many investigators in fruitful directions in their quests to unravel nature’s secrets. Johannes Kepler, for example, triggered a scientific revolution in 1609 when he challenged the conception of the earth’s circular motion around the sun. Arab and European builders instigated the golden age of mosque and cathedral building when they questioned the Roman structural arches that were limited to geometrical semicircles.

Throughout his book, Zebrowski emphasizes the concepts underlying these mathematicians’ calculations, and how these concepts are linked to real-life examples. Substantiated by easy-to-follow mathematical reasoning and clear illustrations, this accessible book presents a novel and interesting discussion of the circle in technology, culture, history, and science.

Product Details

ISBN-13:	9780813528984
Publisher:	Rutgers University Press
Publication date:	06/01/2000
Edition description:	New Edition
Pages:	232
Product dimensions:	6.00(w) x 9.00(h) x 0.70(d)

About the Author

Ernest Zebrowski Jr. holds professorships in science and mathematics education at Southern University in Baston Rouge, and in physics at Pennsylvania College of Technology of the Pennsylvania State University. He is the author of Perils of a Restless Planet: Scientific Perspectives on Natural Disasters and several science textbooks. 

Table of Contents

The quest for pi
Rollers, wheels, and bearings
The celestial clock
Mathematics and the physical world
Charting the planet
Surface and space
Celestial orbs
From conics to gravity
Oscillations
Waves
Artificial and natural structures
The real and conjectured universe
Appendix A: Formulas for the areas of common shapes
Appendix B: Formulas for the volumes of common solids
Appendix C: Algebraic equations for the conic sections

What People are Saying About This

Eli Maor

From a history of pi to the workings of rollers and gears, from tsunami killer waves to the elusive waves of gravity, from the atom's nucleus to the structure of the universe—here is a fascinating tour de force of all things circular. After reading Zebrowski's account, you'll get answers to everything you've always asked about the circle—and much more!
(Eli Maor, author of e: The Story of a Number and Trigonometric Delights.)

Thomas Banchoff

The waves at the beach, the chariot wheels of the ancient Egyptians, the swirling of millions of stars in distant galaxies, the shape of puffball mushrooms, the structure of the atoms in our own bodies—all these and many other diverse physical entities become connected when we reduce their descriptions to mathematical language. But are the connections really there, and historically valid, or are they just artifacts of our limited way of thinking mathematically? I invite you to take this little journey with me and draw your own conclusions. An enjoyable readable treatment of the interaction between mathematical ideals and physical reality. Full of good stories. (Thomas Banchoff, author of Beyond the Third Dimension.)

Editorial Reviews

"From a history of pi to the workings of rollers and gears, from tsunami killer waves to the elusive waves of gravity, from the atom's nucleus to the structure of the universe—here is a fascinating tour de force of all things circular. After reading Zebrowski's account, you'll get answers to everything you've always asked about the circle—and much more!

author of e: The Story of a Number and Trigonometric Delights - Eli Maor

The book is insightful and clever. It blends the author's background in mathematics and physics to uncover natural occurrences of mathematics in the world around us.

E-Streams

Zebrowski is a wonderful storyteller, and his choices of topics reveal not only the depth of explanation afforded by the available mathematics but the beauty in the explanations; he succeeds in keeping the explanations accessible to the most general audience.

Choice

Throughout his book, Zebrowski emphasizes the concepts underlying these mathematicians' calculations, and how these concepts are linked to real—life examples. Substantiated by easy—to—follow mathematical reasoning and clear illustrations, this accessible book presents a novel and interesting discussion of the circle in technology, culture, history, and science.

Zentralblatt fnr Didaktik der Mathematik

This is an accessibly written investigation of how past attempts by scientists to discover the perfect circle led to major discoveries of the physical universe.

Technology & Society Bulletin of Science

I found the book to be fascinating, and the author's presentations and illustrations of the contrasts between mathematical reasoning and scientific reasoning were especially appealing. The book is rich in history, which is carefully integrated into the discussions, and it includes wonderful illustrations and stories.

Mathematics Teacher

An enjoyably readable treatment of the interaction between mathematical ideals and physical reality. Full of good stories.

author of Beyond the Third Dimension - Thomas Banchoff

After Zebrowski's well-received Perils of a Restless Planet (LJ 7/97), this new book is a disappointment. Only partially about circles, the text aims "to examine [for the general reader] the broader relationship between mathematical reasoning and the physical universe." Most of the physical examples are common ones, from historical models of the solar system to relativity theory, which standard physics and astronomy texts explain better and just as engagingly. An exception is an intriguing discussion of some techniques used in the construction of the pyramids. The level of exposition varies greatly: a whole chapter is devoted to the elementary relationships of linear dimension, area, and volume, whereas the discussion of wave phenomena uses partial differential equations. There are occasional errors, such as the statement that a neutron star comprises "billions of protons and neutrons," and curious terminology: the list of regular polyhedra repeatedly includes the hexahedron rather than the cube. The endnotes provide appropriate suggestions for further reading, some popular, some scholarly. For larger public libraries.--Kristine Fowler, Mathematics Lib., Univ. of Minnesota, Minneapolis Copyright 1999 Cahners Business Information.

Library Journal

From the ancient mathematicians to 20th-century theories of space and time, Zebrowski (science and mathematics education, Southern U., Baton Rouge and physics, Pennsylvania State U.) explores how investigating the circle has contributed enormously to knowledge about the physical universe in general. Among his examples are Kepler's questioning of a circular orbit for the earth, and Arab and European builders experimenting with something different for arches than the Roman semi- circle. He assumes no particular background in science or mathematics. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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