Using a Card Trick to Illustrate Fixed Points and Stability
Jyoti Champanerkar, Mahendra Jani · PRIMUS · 2015
Mathematical ideas from number theory, group theory, dynamical systems, and computer science have often been used to explain card tricks. Conversely, playing cards have been often used to illustrate the mathematical concepts of probability distributions and group theory. In this paper, we describe how the 21-card trick may be used to illustrate concepts such as a discrete dynamical system, a fixed point, and the stability of a fixed point. The 21-card trick is a way of dealing cards in order to predict a card that is selected by a volunteer, within three moves. The 21-card trick and its two generalizations are examples of piece-wise linear, non-homogeneous, discrete dynamical systems, all of which have a global stable fixed point.