How to Introduce the Cyclic Group and Its Properties Representation with Matlab ? Thanks to Magic Using the Perfect Faro Shuffle

Author(s)
Pierre Schott

ABSTRACT

Why use Magic for teaching arithmetic and geometric suit, additive groups, and algorithmic notions through Matlab? Magicians know that, once the surprise has worn off, the audience will seek to understand how the trick works. The aim of every teacher is to interest their students, and a magic trick will lead them to ask how? And why? And how can I create one myself? In this article we consider a project I presented in 2009. I summarize the project scope, the students' theoretical studies, their approach to this problem and their computer realizations. I conclude using the mathematical complement as well as weak and strong points of this approach. Whatever the student's professional ambitions, they will be able to see the impact that originality and creativity have when combined with an interest in one's work. The students know how to “perform” a magic trick for their family and friends, a trick that they will be able to explain and so enjoy a certain amount of success. Sharing a mathematical / informatics demonstration is not easy and that they do so means that they will have worked on understood and are capable of explaining this knowledge. Isn't this the aim of all teaching?

Why use Magic for teaching arithmetic and geometric suit, additive groups, and algorithmic notions through Matlab? Magicians know that, once the surprise has worn off, the audience will seek to understand how the trick works. The aim of every teacher is to interest their students, and a magic trick will lead them to ask how? And why? And how can I create one myself? In this article we consider a project I presented in 2009. I summarize the project scope, the students' theoretical studies, their approach to this problem and their computer realizations. I conclude using the mathematical complement as well as weak and strong points of this approach. Whatever the student's professional ambitions, they will be able to see the impact that originality and creativity have when combined with an interest in one's work. The students know how to “perform” a magic trick for their family and friends, a trick that they will be able to explain and so enjoy a certain amount of success. Sharing a mathematical / informatics demonstration is not easy and that they do so means that they will have worked on understood and are capable of explaining this knowledge. Isn't this the aim of all teaching?

Cite this paper

nullSchott, P. (2011). How to Introduce the Cyclic Group and Its Properties Representation with Matlab ? Thanks to Magic Using the Perfect Faro Shuffle.*Creative Education, 2,* 27-40. doi: 10.4236/ce.2011.21005.

nullSchott, P. (2011). How to Introduce the Cyclic Group and Its Properties Representation with Matlab ? Thanks to Magic Using the Perfect Faro Shuffle.

References

[1] [1] Ammar, M. (1998). The complete cups & balls. L&L Publishing.

[2] Assaf, S., Soundararajan, K., & Diaconis, P. (2009). Riffle shuffles of a deck with repeated cards. DMTCS Proceedings, 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2009, 89-102.

[3] Boileau, N. (1740). La scolastique. Souchay, Paris.

[4] Chardiny, N., Dupin, B., & Grosgeorge, S. (2010). Utiliser les mathématiques pour créer un tour de Magie utilisant le mélange FARO. Mémoire de P.S.I, ESIEA.

[5] Diaconis, P., Graham, R. L., & Kantor, W.M. (1983). The mathematics of perfect shuffles. Advances in Applied Mathematics, 4, 175-196. doi:10.1016/0196-8858(83)90009-X

[6] Diaconis, P. (1998). From shuffling cards to walking around the building. An introduction to markov chain theory. Proceedings of International Congress, Berlin, I, 187-204.

[7] Diaconis, P. (2003). Mathematical Developments from the Analysis of Riffle-Shuffling. In A. Fuanou and M. Liebeck (eds.), Groups Combinatorics and Geometry (pp. 73-97). N.J.: World Scientific.

[8] Diaconis, P., & Graham, R. L. (2005). The solutions to Elmsley’s Problem. Mathematics magazine. doi:10.1142/9789812564481_0005

[9] Elmsley, A. (1957). Mathématics of the weave shuffle. The Pentagram, 11, pp.70-71.

[10] Erdnase, S. W. (1902). The expert at the card table. Chicago.

[11] Gardner, M. (1958). Mathematics, magic and mystery. Dover.

[12] Gardner, M. (2005). Martin Gardner's mathematical games : the entire collection of his scientific American columns. Mathematical Association of America.

[13] Gilbreath, N. L. (1958). Magnetic colors. The Linking Ring, 38, 60.

[14] Gilbreath, N. L. (1966). Second Gilbreath Principle. Linking Ring, June 1966.

[15] Gilbreath, N. L. (1989). Magic for an Audience. series of 3 articles in Genii, Vol. 52, No. 9-10-11, March, April, May 1989.

[16] Huet, G. (1991). The Gilbreath trick: A case study in axiomatisation and proof development in the Coq Proof Assistant. Proceedings, Second Workshop on Logical Frameworks, Edinburgh. doi:10.1017/CBO9780511569807

[17] Lachal, A. (2010). Quelques mélanges parfaits de cartes. Quadrature.

[18] Magid, A. (2005). Notices. American Mathematical Society.

[19] Mayol, H. (2000). La Magie des cordes Maestro, HBM Production.

[20] Poincaré, H. (1912). Calcul des probabilités. Rédaction de A. Quiquet. Deuxième édition, revue et augmentée par l’auteur, Gauthier-Villars, Paris.

[21] Mulcahy, C. (2003). Fitch Cheney's Five Card Trick. Mathematics Horizon, 10.

[22] Mulcahy, C. (2004). Top 5 reasons to like mathematical card tricks. 11.

[23] Mulcahy, C. (2007). An ES periment with cards. 14.

[24] Schott, P. (2010). The use of magic in optics in higher education. Creative Education, 1, 11-17.

[25] Schott, P. (2009). The use of magic in mathematics: From primary school to higher education. Proceedings of ICERI2009 Conference, Madrid, Spain, 58-70.

[26] Sheynin, O. B. (1991). H. Poincaré’s work on probability. Archive for History of Exact Sciences, 42, Berlin: Springer.

[1] [1] Ammar, M. (1998). The complete cups & balls. L&L Publishing.

[2] Assaf, S., Soundararajan, K., & Diaconis, P. (2009). Riffle shuffles of a deck with repeated cards. DMTCS Proceedings, 21st International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2009, 89-102.

[3] Boileau, N. (1740). La scolastique. Souchay, Paris.

[4] Chardiny, N., Dupin, B., & Grosgeorge, S. (2010). Utiliser les mathématiques pour créer un tour de Magie utilisant le mélange FARO. Mémoire de P.S.I, ESIEA.

[5] Diaconis, P., Graham, R. L., & Kantor, W.M. (1983). The mathematics of perfect shuffles. Advances in Applied Mathematics, 4, 175-196. doi:10.1016/0196-8858(83)90009-X

[6] Diaconis, P. (1998). From shuffling cards to walking around the building. An introduction to markov chain theory. Proceedings of International Congress, Berlin, I, 187-204.

[7] Diaconis, P. (2003). Mathematical Developments from the Analysis of Riffle-Shuffling. In A. Fuanou and M. Liebeck (eds.), Groups Combinatorics and Geometry (pp. 73-97). N.J.: World Scientific.

[8] Diaconis, P., & Graham, R. L. (2005). The solutions to Elmsley’s Problem. Mathematics magazine. doi:10.1142/9789812564481_0005

[9] Elmsley, A. (1957). Mathématics of the weave shuffle. The Pentagram, 11, pp.70-71.

[10] Erdnase, S. W. (1902). The expert at the card table. Chicago.

[11] Gardner, M. (1958). Mathematics, magic and mystery. Dover.

[12] Gardner, M. (2005). Martin Gardner's mathematical games : the entire collection of his scientific American columns. Mathematical Association of America.

[13] Gilbreath, N. L. (1958). Magnetic colors. The Linking Ring, 38, 60.

[14] Gilbreath, N. L. (1966). Second Gilbreath Principle. Linking Ring, June 1966.

[15] Gilbreath, N. L. (1989). Magic for an Audience. series of 3 articles in Genii, Vol. 52, No. 9-10-11, March, April, May 1989.

[16] Huet, G. (1991). The Gilbreath trick: A case study in axiomatisation and proof development in the Coq Proof Assistant. Proceedings, Second Workshop on Logical Frameworks, Edinburgh. doi:10.1017/CBO9780511569807

[17] Lachal, A. (2010). Quelques mélanges parfaits de cartes. Quadrature.

[18] Magid, A. (2005). Notices. American Mathematical Society.

[19] Mayol, H. (2000). La Magie des cordes Maestro, HBM Production.

[20] Poincaré, H. (1912). Calcul des probabilités. Rédaction de A. Quiquet. Deuxième édition, revue et augmentée par l’auteur, Gauthier-Villars, Paris.

[21] Mulcahy, C. (2003). Fitch Cheney's Five Card Trick. Mathematics Horizon, 10.

[22] Mulcahy, C. (2004). Top 5 reasons to like mathematical card tricks. 11.

[23] Mulcahy, C. (2007). An ES periment with cards. 14.

[24] Schott, P. (2010). The use of magic in optics in higher education. Creative Education, 1, 11-17.

[25] Schott, P. (2009). The use of magic in mathematics: From primary school to higher education. Proceedings of ICERI2009 Conference, Madrid, Spain, 58-70.

[26] Sheynin, O. B. (1991). H. Poincaré’s work on probability. Archive for History of Exact Sciences, 42, Berlin: Springer.