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File:Juggling Shannon's theorem Cascade.svg

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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
Date
Source Own work
Author Hyacinth
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This media depicts a juggling pattern using one or more of standardized juggling notations (such as juggling ladder). Juggling pattern notation may be created identically for each juggling pattern (no "distinctiveness"), which consist of common knowledge ("common material"), and may be performed by anyone with the necessary skill. As such, ladder notation, which is considered too simple to be eligible for copyright protection, or which consists only of a system, with no original creative input.

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29 September 2017

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Date/TimeThumbnailDimensionsUserComment
current19:39, 17 September 2020Thumbnail for version as of 19:39, 17 September 20201,305 × 315 (14 KB)SVGWorkaroundBotWorkaroundForLibrsvgBugs ScourYES SVGCleanerYES User:SVGWorkaroundBot/source, solves bugs such as: phab:T55899, phab:T68672, phab:T43424, phab:T193929, phab:T35245 reduce invalid-Errors, convert flowRoot to SVG1.1-text, please see file-description-page on commons for the actual bug
00:15, 30 September 2017Thumbnail for version as of 00:15, 30 September 20171,305 × 315 (16 KB)HyacinthUser created page with UploadWizard
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