# 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)

- Talk by Allen Knutson
- Burkart Polster,
*The Mathematics of Juggling*, Springer (2003).

Discusses the combinatorics of*juggling sequences*. The book

includes a chapter on the*physics*of juggling.

**Invisibility Cloaks**

(electrodynamics, metamaterials)- Ulf Leonhard,
*Optical Conformal Mapping*, Science Express (2006)

also have a look at the author's web site. - Leonahardt, Philbin,
*Geometry and Light: The Science of Invisibility*, Dover (2010). - Ergin et al.,
*Three-Dimensional Invisibility Cloak at Optical Wavelengths*, Science (2010).

Recent 3-D device built in Karlsruhe.

- Ulf Leonhard,
**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)

- S. Wagon,
**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 Minimalflächen*(2007) by Eschenburg und Jost.

(The 1994 edition does not contain an explicit chapter about soap films!)

- C. Boys,
**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)

- Demain et al.,
*Picture-Hanging Puzzles.* - A simple introduction to the
*fundamental group*is in the book by Allen Hatcher.

- Demain et al.,
**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).

- Persi Diaconis, Ron Graham,

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)