page_title: Juggling notation
hierarchical_section_title: Juggling notation
caption_attribution_description: English: 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
context_page_description: Juggling notation is the written depiction of concepts and practices in juggling. Toss juggling patterns have a reputation for being "easier done than said" – while it might be easy to learn a given maneuver and demonstrate it for others, it is often much harder to communicate the idea accurately using speech or plain text. To circumvent this problem, various numeric or diagram-based notation systems have been developed to facilitate communication of patterns or tricks between jugglers, as well the investigation and discovery of new patterns.
  A juggling notation system was first proposed by Dave Storer in 1978 and while the first juggling diagram, by Claude Shannon around 1981, was not printed till 2010, the first printed diagram and second oldest notation system were proposed by Jeff Walker in 1982.
context_section_description: Juggling notation is the written depiction of concepts and practices in juggling. Toss juggling patterns have a reputation for being "easier done than said" – while it might be easy to learn a given maneuver and demonstrate it for others, it is often much harder to communicate the idea accurately using speech or plain text. To circumvent this problem, various numeric or diagram-based notation systems have been developed to facilitate communication of patterns or tricks between jugglers, as well the investigation and discovery of new patterns.
  A juggling notation system (based on music notation) was first proposed by Dave Storer in 1978 and while the first juggling diagram (a ladder diagram), by Claude Shannon around 1981, was not printed till 2010, the first printed diagram and second oldest notation system were proposed by Jeff Walker in 1982.
caption: Shannon's theorem for the cascade pattern
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