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Winter 2013 - 2014

Term Paper: Science of Magic

Course description

10 ECTS points. Time: Thursdays 3 pm s.t. Venue: SR1, physics high rise.

A range of non-trivial topics in math and physics can be discussed in the context of  magic tricks, artistry and entertainment.

Schedule (subject to change)

28.11. The Math of Juggling, Max Bergau
09.01. De Bruijn Sequences, Nikolaj Kulvelis
16.01. Hummer Shufles, Kai von Prillwitz
23.01. Picture Hanging Puzzles, Sabrina Fam & Nerissa Ng
30.01. Invisibility Cloaks, Andreas Reichert
13.02. Soap Bubbles and Minimal Surfaces, Jonas Wenzler

Possible Topics and Preliminary Literature

  • The Mathematics of Juggling
    (combinatorics of sequences)
  • Invisibility Cloaks
    (electrodynamics, metamaterials)
  • Banach-Tarski Paradox
    (measure theory)
    Won't earn you cheers at that children's birthday party - but serves as a stark reminder that there are limits to Wigner's Unreasonable Effectiveness of Math as the universal language of Nature.
    • S. Wagon, The Banach-Tarski Paradox, Cambridge University Press (1999)
  • Minimal Surfaces and Soap Bubbles
    (basic differential geometry, variational calculus)
    • C. Boys, Soap bubbles, their colours and the forces which mold them, Crowell (1962).
      Semi-scientific intro to the physics of soap bubbles.
    • C. Isenberg, The Science of Soap Films and Soap Bubbles, Dover (1978).
      A complete account of the physics of soap films.
    • Spivak, A comprehensive introduction to differential geometry, Volume 3, Publish or Perish (1975).
      Chapter 2 gives an account of minimal surfaces in three dimensions.
    • Meeks, Perez, The classical theory of minimal surfaces
      Survey of the mathematical theory of minimal surfaces. Might be a bit too advanced, but contains helpful references.
    • Both the geometry and application to soap films are covered in relatively elementary language in the textbook Differentialgeometrie und Minimalfl├Ąchen (2007) by Eschenburg und Jost.
      (The 1994 edition does not contain an explicit chapter about soap films!)
  • Picture Hanging Problem
    (would classify as algebraic topology, but some understanding of group theory is sufficient)
    Adventurous students aiming for more "physics" could also mention Dirac's String Trick (or why a Fermion looks different after having been turned by 360 degrees)
  • Card Tricks
    From the book by Diaconis and Graham (two eminent mathematicians), one could take presentations on Invariants of Hummer Shuffles, De Bruijn Sequences, and the Gilbreath Principle & Mandelbrot Set.
    • Persi Diaconis, Ron Graham, Magical Mathematics. Princeton University Press (2011).

 

The books listed below will be bought by the Physics Library specifically for this seminar. They will be available for participants before being entered into the general database. Please get in touch with Mrs Breuer at the Physics Library for details. Some texts are also available freely on the authors' websites.

Ulf Leonhardt: Geometry and Light
Stan Wagon: Banach-Tarski Paradox
Boys C V: Soap-Bubbles, Their Colours and the Forces Which Mould Them
Persi Diaconis: Magical Mathematics
Perez: Survey on Classical Minimal Surface Theory
Burkard Polster: Mathematics of Juggling
Fun with Algorithms (darin enthalten: Demain: Picture-hanging Puzzles)
 

 

 

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