## Hesiod's Anvil: Falling and Spinning Through Heaven and EarthThis 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 |

333 | |

### Other editions - View all

Hesiod's Anvil: Falling and Spinning Through Heaven and Earth Andrew J. Simoson No preview available - 2007 |

### Common terms and phrases

angle approximately assume asteroid axis ball thrown barbell beach beacon bungee cord calculus cannonball Cavor cavorite Chapter chord circle constant coordinates core core-mantle boundary counterclockwise curve density derivative descent differential equation direction dropped earth earth's center earth's surface eastward displacement ellipse envelope epicycloid Exercise feet Figure 14 Figure 9 ft/sec Galileo given gives graph gravitational acceleration gravity field heaven Hesiod Hesiod's hole hollow earth illuminated spot Imagine initial conditions initial velocity ladder launch light linear mantle Maria mass mathematician mathematics Mayan miles moon moon's motion Newton's nine orbit ordinary points orthotomic parametrization path pebble pebble's Pellucidar pendulum perigee period polar pole poohsticks position Priscilla problem radius real number respect rotation rate Sarah Selenites shown in Figure shows signal speed simple harmonic motion sinker Snell's law solution solve story tandem spheres tangent terminal velocity throw trajectory trochoid vector Verne's