A history of the circle : mathematical reasoning and the physical universe / Ernest Zebrowski, Jr.

Format:

Book

Author/Creator:

Zebrowski, Ernest.

Language:

English

Subjects (All):

Cycles.

Pi.

Circle.

Genre:

Festschriften.

Physical Description:

x, 215 pages : illustrations ; 25 cm

Place of Publication:

New Brunswick, N.J. : Rutgers University Press, [1999]

Summary:

The concept of the circle is ubiquitous. It can be described mathematically, represented physically, and employed technologically. We drive cars that go on round tires, we operate our laundry machines with quarters, and we unscrew our ketchup bottle caps. 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 over time 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 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.

Contents:

Chapter 1 The Quest for Pi 1

Chapter 2 Rollers, Wheels, and Bearings 14

Chapter 3 The Celestial Clock 26

Chapter 4 Mathematics and the Physical World 39

Chapter 5 Charting the Planet 51

Chapter 6 Surface and Space 68

Chapter 7 Celestial Orbs 86

Chapter 8 From Conics to Gravity 104

Chapter 9 Oscillations 124

Chapter 10 Waves 144

Chapter 11 Artificial and Natural Structures 166

Chapter 12 The Real and Conjectured Universe 184

Appendix A Formulas for the areas of common shapes 201

Appendix B Formulas for the volumes of common solids 202

Appendix C Algebraic equations for the conic sections 203.

Notes:

Includes bibliographical references (pages 205-210) and index.

ISBN:

0813526779

OCLC:

39905900