A couple years ago when I was traveling through Africa, my host wrote a computer program for me that worked both as a poi simulator as well as a mathematical tool for measuring the distance a poi head travels in each hypo and epitrochoid pattern I could dream up at the time. After comparing a lot of the numbers the program created, it turns out there are some really fascinating harmonic relationships that emerge when you combine moves that normally wouldn't go together as a result of a lack of alignment with either the poi heads or hands.