# Hesiod's Anvil: Falling and Spinning Through Heaven and Earth

MAA, Jul 26, 2007 - Mathematics - 344 pages
This book is about how poets, philosophers, storytellers, and scientists have described motion, beginning with Hesiod, a contemporary of Homer, who imagined that the expanse of heaven and the depth of hell was the distance that an anvil falls in nine days. This book is aimed at students who have finished a year-long courses in calculus, but it can be used as a supplemental text in calculus II, vector calculus, linear algebra, differential equations, and modeling. It blends with equal voice romantic whimsy and derived equations, and anyone interested in mathematics will find new and surprising ideas about motion and the people who thought about it. Some of the things readers will learn is that Dante's implicit model of the earth implies a black hole at its core, that Edmond Halley championed a hollow earth, and that Da Vinci knew that the acceleration due to the earth's gravity was a constant. There are chapters modeling Jules Verne's and H.G. Wells' imaginative flights to the moon and back, the former novelist using a great cannon and the latter using a gravity-shielding material. The book analyzes Edgar Alan Poe's descending pendulum, H.G. Wells' submersible falling and rising in the Marianas Trench, a train rolling along a tunnel through a rotating earth, and a pebble falling down a hole without resistance. It compares trajectories of balls thrown on the Little Prince's asteroid and on Arthur C. Clarke's rotating space station, and it solves an old problem that was perhaps inspired by one of the seven wonders of the ancient world. The penultimate chapter is a story, based upon the Mayans, that loosely ties together the ideas about falling and spinning motion discussed in the book. Nearly all the chapters have exercises, some straightforward and some open ended, that may serve as the beginnings of student's honors projects.

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### Contents

 preamble ii 15 preamble Hi 39 preamble iv 53 preamble v 67 preamble vi 83 preamble vii 97 Falling through a Rotating Earth 111 preamble ix 139
 preamble xi 185 preamble xii 205 preamble xiii 227 preamble xiv 257 preamble xv 275 Appendix 289 Comments on Selected Exercises 305 References 333

 preamble x 161