Image: Juggling Shannon's theorem Cascade

Description: Map created from Claude Shannon's juggling theorem for the juggling pattern known as the Cascade. (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 Cascade: (3+3)2 = (1+3)3 = 12. 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, and 6*2 = 12. The only option for x*2 = y*3 = 12 is that x = 6 and y = 4. This means that the sum of F and D must be 6 and the sum of V and D must 4: (6)2 = (4)3. The only options for D in (V+D)3 = 12 3, 2, and 1. If D = 2 then F must equal 4 and V must equal 2. (4+2)2 = (2+2)3 = 12 If D = 1 then F must equal 5 and V must equal 3. (5+1)2 = (3+1)3 = 12 Presumably neither of the above are possible since there are only 3 balls, there can't be values above three. If D = 3 then F must equal 3 and V must equal 1. (3+3)2 = (1+3)3 = 12 1st 2nd 3rd hand: D--VD--VD--V ball: D--F--D--F-- R L (F+D)H=(V+D)N (3+3)2=(1+3)3 6×2=4×3 12=12
Title: Juggling Shannon's theorem Cascade
Credit: Own work
Author: Hyacinth
Usage Terms: Public domain
License: Public domain
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