State Diagrams - In the last 20 years, there have been many exciting new mathematical discoveries to the world of juggling. Possibly the most important of these was the discovery of siteswaps. These were developed by several different people at the same time. More recently, the discovery of State Transition diagrams has been very important. These ideas were developed by Jack Boyce. I will try to explain a little about these in the following article, and also include some discoveries that I have made.