‘In practical life we are compelled to follow what is most probable ; in speculative thought we are compelled to follow truth.’ —Spinoza


When a coin falls in water, its trajectory is one of four types determined by its dimensionless moment of inertia I∗ and Reynolds number Re: (A) steady; (B) fluttering; (C) chaotic; or (D) tumbling. The dynamics induced by the interaction of the water with the surface of the coin, however, makes the exact landing site difficult to predict a priori.

Here, we describe a carefully designed experiment in which a coin is dropped repeatedly in water to determine the probability density functions (pdf) associated with the landing positions for each of the four trajectory types, all of which are radially symmetric about the centre drop-line.

{ arXiv | PDF }