RustyJuggling

Juggler. Decent but definitely a work in progress.
I like theory.

Recent theory developments that I don't want to make a special point of posting:
Relationships between Duration (a siteswap throw; 1,2,3...), Destination (The end position of a throw in the pattern; for 5 in 531 destination is 3 [lands on the 3rd throw]), Loops (The number of times a throw 'passes' its destination throw before landing), Period, and Order (What position a throw has in the pattern; 2 in 531 is the 2nd throw.
- Duration= y
- Destination= d
- Loops= L
- Period= P
- Order= x

- LP= y_x-y_x^L
- y_x^L= d_x^L-x

And with those you can make any number of interesting equations, including one where you can find the period of a pattern given a single throw's y, d, and L.


Also, one axiom that allows 333-> 441 is=
A: ss(Y₁ y_p)- ss((Y₁+1) (y_p+1-p)
where p is the period.

However, this is actually a composite of these axioms:
A:ss(y₁ Y_m y_p)- ss(y₁ Y_m (y_p-p))
A:ss(y₁ Y_m y_p)- ss((y₁ Y_m y_p)+1)
Where Y_m is all digits between the first and the last.

This is because y₁ with Y_m together is equal to Y₁. The +1 goes to both terms, the -p goes to just the last one.

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