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A Wealth of Numbers

Book Description

Despite what we may sometimes imagine, popular mathematics writing didn't begin with Martin Gardner. In fact, it has a rich tradition stretching back hundreds of years. This entertaining and enlightening anthology--the first of its kind--gathers nearly one hundred fascinating selections from the past 500 years of popular math writing, bringing to life a little-known side of math history. Ranging from the late fifteenth to the late twentieth century, and drawing from books, newspapers, magazines, and websites, A Wealth of Numbers includes recreational, classroom, and work mathematics; mathematical histories and biographies; accounts of higher mathematics; explanations of mathematical instruments; discussions of how math should be taught and learned; reflections on the place of math in the world; and math in fiction and humor.

Featuring many tricks, games, problems, and puzzles, as well as much history and trivia, the selections include a sixteenth-century guide to making a horizontal sundial; "Newton for the Ladies" (1739); Leonhard Euler on the idea of velocity (1760); "Mathematical Toys" (1785); a poetic version of the rule of three (1792); "Lotteries and Mountebanks" (1801); Lewis Carroll on the game of logic (1887); "Maps and Mazes" (1892); "Einstein's Real Achievement" (1921); "Riddles in Mathematics" (1945); "New Math for Parents" (1966); and "PC Astronomy" (1997). Organized by thematic chapters, each selection is placed in context by a brief introduction.

A unique window into the hidden history of popular mathematics, A Wealth of Numbers will provide many hours of fun and learning to anyone who loves popular mathematics and science.

Some images inside the book are unavailable due to digital copyright restrictions.

Table of Contents

  1. Cover
  2. Half title
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. 1 “Sports and Pastimes, Done by Number”: Mathematical Tricks, Mathematical Games
    1. The Well Spring of Sciences
    2. Mathematical Recreations
    3. “How Prodigiously Numbers Do Increase”
    4. Profitable and Delightful Problems
    5. Lotteries and Mountebanks
    6. Dodging the Mastodon and the Plesiosaurus
    7. “Plenty of Interesting Things to Be Discovered”
  8. 2 “Much Necessary for All States of Men”: From Arithmetic to Algebra
    1. Addition and Subtraction
    2. Multiplication and Division
    3. Reducing Fractions
    4. Decimal Fractions
    5. Extracting Square Roots
    6. The Rule of Three
    7. The Rule of Three, in Verse
    8. “The First Analysts”
    9. Quadratic Equations
    10. Cubic Equations for the Practical Man
  9. 3 “A Goodly Struggle”: Problems, Puzzles, and Challenges
    1. The Ladies’ Diary
    2. The Girl’s Own Book
    3. The Boy’s Own Magazine
    4. “The Analyst”
    5. Can You Solve It?
    6. Mathematical Challenges
  10. 4 “Drawyng, Measuring and Proporcion”: Geometry and Trigonometry
    1. Points and Lines
    2. Squares and Triangles
    3. Pythagoras’s Theorem
    4. Trigonometrical Definitions
    5. The Resolution of Triangles
    6. Introduction to Spherical Geometry
    7. Napier’s Rules
  11. 5 Maps, Monsters, and Riddles: The Worlds of Mathematical Popularization
    1. The Athenian Mercury
    2. Newton for the Ladies
    3. Maps and Mazes
    4. “Einstein’s Real Achievement”
    5. Riddles in Mathematics
    6. Fermat’s Last Theorem
    7. Where Does It End?
    8. Yamátárájabhánasalagám
    9. Saddles and Soap Bubbles
    10. “The Monster” Unveiled
  12. 6 “To Ease and Expedite the Work”: Mathematical Instruments and How to Use Them
    1. “Cards for the Sea”
    2. Making a Horizontal Sundial
    3. Speaking-Rods
    4. Telescopes Refracting and Reflecting
    5. Scales Simple and Diagonal
    6. Making a Star Clock
    7. PC Astronomy
  13. 7 “How Fine a Mind”: Mathematicians Past
    1. The Labyrinth and Abyss of Infinity
    2. “It Must Have Commenced with Mankind”
    3. Kepler’s Astronomical Publications
    4. Isaac Newton, a Good and Great Man
    5. Pythagoras and His Theorem
    6. Seki Kōwa
    7. “Her Absolute, Incomparable Uniqueness”
    8. “One of Your Calculating Fits”
    9. Analysis Incarnate
    10. Hardy and Littlewood Rummage
  14. 8 “By Plain and Practical Rules”: Mathematics at Work
    1. High Marshal and Camp Master
    2. The Practical Gauger
    3. Geodæsia
    4. Plain Sailing
    5. High-Pressure Engines
    6. The Strength of Materials
    7. Plumbing and Hydraulics
    8. Automobiles and Printing
  15. 9 “The Speedier Expedition of Their Learning”: Thoughts on Teaching and Learning Mathematics
    1. “To Have Their Children or Servants Instructed”
    2. Euclid with Algebra
    3. The Idea of Velocity
    4. Mathematical Toys
    5. A Mother Explains Comets
    6. “Geometry without Axioms”
    7. The Game of Logic
    8. Higher Mathematics for Women
    9. A New Aspect of Mathematical Method
    10. New Math for Parents
    11. “Merely a Formal Statement of the Way We Think”
    12. Turtle Fun
  16. 10 “So Fundamentally Useful a Science”: Reflections on Mathematics and Its Place in the World
    1. The Myrrour of the Worlde
    2. “A Very Fruitfull Praeface”
    3. “Geometry Is Improving Daily”
    4. The Fifth Element
    5. Of Mathematics in General
    6. Lineal Arithmetic
    7. Astronomy in New South Wales
    8. The Advantages of Mathematics
    9. Sylvester Contra Huxley
    10. What a Mathematical Proposition Is
    11. The Character of Physical Law
    12. Our Invisible Culture
  17. 11 The Mathematicians Who Never Were: Fiction and Humor
    1. Spider-Men and Lice-Men
    2. In the Court of Lilliput
    3. Automathes
    4. The Loves of the Triangles
    5. Master Senex the Astronomer
    6. An Ode to the Mathematics
    7. “Some Veritable Urania”
    8. Fun
    9. A Sight of Thine Interior
    10. Scenes in the Life of Pythagoras
    11. Bao Suyo
  18. Index