Adventures in Recreational Mathematics (Volume 2) – Stan Lipovetsky [PDF]

The second volume of the two-volume set contains 13 chapters on more recently posed problems which solutions require more special mathematics. It starts with Preface and Chapter 1 “Why Recreational Mathematics?” where the author explains that the puzzles should be understandable to a lay person, though the solutions may be harder and lead to real problems, like Fermat’s Last Theorem, Four-Color Theorem, or Mandelbrot Set. The recreational mathematics has the popular and pedagogic aspects, without a clear boundary between them and “serious” mathematics. It is also presented in games, mechanical puzzles, magic, and art. Various recreational topics developed to scientific problems and applications are discussed. Besides the ancient and medieval problems, the modern ones are known, for example, how a fisherman can mail a 2.5 m fishing pole if the post office accepts a maximum parcel length of 1.5 m? The fisherman makes a cubical box of edge 1.5 m, then its diagonal is longer by square root of three times, so 1.5*1.73 = 2.6 m. The post office also requires the total of length and girth to be at most 3 m. Then optimization leads to maximizing the volume leading to a cylindrical tube. Other problems include Rubik’s Cube known in versions 5 × 5 × 5, 8 × 8 × 8, and even 17 × 17 × 17, serving to development of problem-solving skills. Recreational mathematics is a useful source of mathematical models, techniques, methods, and it helps to appreciate the historical and multicultural aspects of human thought. The next chapters deal with dozens specific problems.

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