Thursday, August 11, 2016

Book Review: The math book : from Pythagoras to the 57th dimension, 250 milestones in the history

Last weekend I finally had enough down time to read through The Math Book by Clifford Pickover.
Overall I thought it was a very good read. The book is structured as a chronological series of one page discussions of mathematical breakthroughs throughout history. Each article also includes a related illustration which I found both visually arresting and useful.

The articles range from pre-history (30000 year old bones engraved with tally marks) through modern day discoveries like the Lie Group E8. This format is good for getting an appreciation of the progress of mathematics through history without necessarily delving into details. In many ways this sense of scope and of Mathematics as a living field of research where discoveries are being made is what is left out of normal school textbooks. So any resource that breaks the static/linear impression students might have is useful.

Also because the articles don't necessarily relate to each other (although Pickover is very good about cross-linking related topics) you can jump around easily.  The first night I picked the book up from the library, I played a game with my kids where they picked a year in history and we looked at what had happened then.

A small sampling of topics:

  • Magic Squares
  • Zeno's Paradox
  • Archimedes Spiral
  • Al-Khwarizmi's Algebra
  • Fibonacci's Liber Abaci
  • Golden Ratio
  • Kepler Conjectur
  • Projective Geometry
  • Euluer-Mascheroni Constant
  • Goldbach Conjecture
  • Buffon's Needle
  • Bessel Function
  • Quarternions
  • The Mobius Strip
  • Pick's Theorem
  • Principia Mathematica
  • Hilbert's Grand Hotel
  • Cellular Automata
  • Ulam Spiral
  • Surreal Numbes
  • The ABC Conjecture
  • Perfect Magic Tesseract
  • Checks is Solved
Overall, for Math Club purposes this serves more as a starting point for thinking about what I might plan a day around. There's not enough  here to make anything complete but its a great survey of potential ideas. If you wanted to have kids do book reports or presentations (which is outside my thinking of  the scope for the club) this would also be a good resource. One other idea I came up with was reading or adapting a single individual page to the group from time to time. 

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