English: Map created from Claude Shannon's juggling theorem for the juggling pattern known as the Shower, synchronous (4x,2x). (F+D)H = (V+D)N.

F = time in air

D = time in hand

H = number of hands

V = time hand is vacant

N = number of balls

Thus for the three ball Shower: (2+1)2 = (1+1)3 = 6.

A three ball pattern for one person, we know that, H = 2 and N = 3, thus:

(F+D)2 = (V+D)3.

The LCD of 2 and 3 is 6. The only option for x*2 = y*3 is that x is three and y is two.

This means that V and D must equal 1 each, so that their sum equals two:

(F+1)2 = (1+1)3.

Since D = 1, the only option for F is 2, so that their sum is three, thus:

(2+1)2 = (1+1)3 = (3)2 = 2(3) = 6.