| 531 in action |
[Jul. 21st, 2013|09:36 pm] |
http://www.juggling.org/papers/science-1/mathematics.html
As an example, consider the pattern 531. Write the numbers 5, 3 and 1 a few times in a row, each digit under the next point in the number line starting at point 0 [see top illustration at right]. The number below point 0 is 5, so starting there, draw a semicircle five units in diameter to point 5, representing a throw that is high enough to spend five time units (beats) in the air. The number below point 5 is a 1, so draw a semicircle of diameter 1 from point 5 to 6. Point 6 has a 5 under it, so the next semicircle is from point 6 to 11. You have now traced out the path in time of the first ball, which happens to be the same as the first ball in the three-ball shower pattern 51 described above. Repeat the process starting at times 1 and 2, respectively, to trace out the path of the remaining two balls. The result is that the first and third balls both move in shower patterns but in opposite directions, and the second ball weaves between the two showers in a cascade rhythm. Leaving out this middle ball results in the neat and simple two-ball site swap 501.
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