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### Summary

### Summary

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.

### Author Notes

Ernest Zebrowski, Jr., holds professorships in science and mathematics education at Southern University in Baton 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 of several science textbooks.

### Reviews 2

### Library Journal Review

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.ÄKristine Fowler, Mathematics Lib., Univ. of Minnesota, Minneapolis (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.

### Choice Review

Eugene Wigner coined the phrase "the unreasonable effectiveness of mathematics" to call attention to the manner in which mathematics can be used to model the physical world better than anyone could reasonably expect. Here, Zebrowski takes up this theme and tells the history of some of the most celebrated and penetrating explanations of the natural world, all based on the oldest and best understood mathematical object, the circle. Reaching back to the oldest applications of mathematics--the building of large structures--he shows how mathematical knowledge of the circle, and its close relations the conic sections, has led to deep understanding of the planet, the heavenly bodies, time, and waves. The interaction between mathematical knowledge and physical questions is central to the story, an aspect of mathematics that is often neglected and rarely so well exposed. 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. A welcome addition to all libraries. General readers. J. McCleary; Vassar College

### Table of Contents

Preface | p. ix |

Chapter 1 The Quest for Pi | p. 1 |

Chapter 2 Rollers, Wheels, and Bearings | p. 14 |

Chapter 3 The Celestial Clock | p. 26 |

Chapter 4 Mathematics and the Physical World | p. 39 |

Chapter 5 Charting the Planet | p. 51 |

Chapter 6 Surface and Space | p. 68 |

Chapter 7 Celestial Orbs | p. 86 |

Chapter 8 From Conics to Gravity | p. 104 |

Chapter 9 Oscillations | p. 124 |

Chapter 10 Waves | p. 144 |

Chapter 11 Artificial and Natural Structures | p. 166 |

Chapter 12 The Real and Conjectured Universe | p. 184 |

Appendix A Formulas for the areas of common shapes | p. 201 |

Appendix B Formulas for the volumes of common solids | p. 202 |

Appendix C Algebraic equations for the conic sections | p. 203 |

Notes | p. 205 |

Index | p. 211 |