Mathematics of juggling

Juggling involves coordinating the movement of objects—like balls or clubs—so they follow predictable trajectories. Mathematically, this can be modeled using principles of physics and algebra, where each object’s flight follows a parabolic path influenced by gravity and timing. Juggling patterns, or "siteswaps," are sequences of numbers representing the number of beats every object spends in the air, ensuring tosses are synchronized. These patterns help in planning throws so that objects are caught and thrown at the right moments, creating a seamless cycle. This combination of physics and pattern recognition makes juggling a fascinating practical application of mathematical principles.