Mathematics of juggling

Juggling is a physical skill, performed by a juggler, involving the manipulation of objects for recreation, entertainment, art or sport. The most recognizable form of juggling is toss juggling. Juggling can be the manipulation of one object or many objects at the same time, using one or many hands. Jugglers often refer to the objects they juggle as props. The most common props are balls, clubs, or rings. Some jugglers use more dramatic objects such as knives, fire torches or chainsaws. The term juggling can also commonly refer to other prop-based manipulation skills, such as diabolo, devil sticks, poi, cigar boxes, contact juggling, hooping, yo-yo, and hat manipulation.

The words juggling and juggler derive from the Middle English jogelen ("to entertain by performing tricks"), which in turn is from the Old French . There is also the Late Latin form joculare of Latin joculari, meaning "to jest". Although the etymology of the terms juggler and juggling in the sense of manipulating objects for entertainment originates as far back as the 11th century, the current sense of to juggle, meaning "to continually toss objects in the air and catch them", originates from the late 19th century.

From the 12th to the 17th century, juggling and juggler were the terms most consistently used to describe acts of magic, though some have called the term juggling a lexicographical nightmare, stating that it is one of the least understood relating to magic. In the 21st century, the term juggling usually refers to toss juggling, where objects are continuously thrown into the air and caught again, repeating in a rhythmical pattern.

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