Hesiod’s Anvil

This book is about how poets, philosophers, storytellers, and scientists have described motion, beginning with Hesiod, who imagined that the expanse of heaven and the depth of hell was the distance that an anvil falls in nine days. The reader will learn 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 Earth\'s gravity was a constant. There are chapters modeling Jules Verne\'s and H.G. Wells\' imaginative flights to the moon and back, analyses of Edgar Alan Poe\'s descending pendulum, and the solution to an old problem perhaps inspired by one of the seven wonders of the ancient world. 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.

• Suitable as a supplemental text in calculus II, vector calculus, linear algebra, differential equations, and modelling • Lots of exercises that may serve as the beginnings of students’ projects • Blends with equal voice romantic whimsy and derived equations

Introduction; Preamble I. Good to fall; 1. Hesiod’s muses; Preamble II. Towers crash; 2. The gravity of Hades; Preamble III. A great fall; 3. Ballistics; Preamble IV. A new leaf; 4. Heavenly motion; Preamble V. Falling oars; 5. Pendulum variations; Preamble VI. Half to fall; 6. Retrieving H.G. Wells from the ocean floor; Preamble VII. Turned round and round; 7. Sliding along a chord through a rotating Earth; Preamble VIII. Fallen, fallen, fallen; 8. Falling through a rotating Earth; Preamble IX. Falling into naught; 9. Shadow lands; Preamble X. Spinning complete; 10. The Trochoid family; Preamble XI. The world turned; 11. Retrieving H. G. Wells from the moon; Preamble XII. Catch a star; 12. Playing ball in space; Preamble XIII. Turn a different hue; 13. The rotating beacon; Preamble XIV. Never turning; 14. The long count; Preamble XV. What a fall!; 15. Hesiod’s anvil; Appendix; Cast of characters; Comments on selected exercises; References; Index; About the author.