Theorem 1.In a uniform juggle with dwell time \(D\), vacant time \(V\), flight time \(F\) then$$\frac{F+D}{V+D}=\frac{B}{H},$$where \(B\) is the number of balls and \(H\) the number of hands.

Scientific Aspects of Juggling.

In Claude Elwood Shannon: Collected Papers. Edited by N.J.A. Sloane and A. D. Wyner. IEEE Press, 1993.