| dc.description.abstract | As the subtitle clarifies this thesis is on the mathematics behind juggling.
Whenever we want to learn, talk about or describe something, we need a language which fits the subject well. Sometimes the language we speak suffices
and all we need is to find some common ground by developing terminology.
However, sometimes this does not suffice and we need to develop a language
to fit the subject, taking music as an example. Imagine having to communicate a piece of music without having a dedicated language and notation,
it’s very hard! A similar thing is to say for communicating juggling so a
language was developed. Given the precise nature of juggling, it is not much
of a surprise that this became a mathematical language.
Having a mathematical language means having definitions and we need to
check that these capture our phenomena we try to describe. We do so by
making sure that, given our abstract definition of a juggling pattern, we can
retrieve all the information necessary to actually juggle the pattern in the
detail we are aiming to describe it. We answer practical questions like how
many balls a pattern requires and where we need to start in the pattern.
Having a mathematical language also allows very well for seemingly nonsensical questions to be asked. Since we can be sure that we translated
juggling into a piece of mathematics which makes sense for our topic, we
can forget about the juggling for a moment and play around with just the
mathematics. The theorems we then prove might not have any interesting
physical interpretation at all, but sometimes we can relate these back to very
nice properties of the juggling sequences.
This thesis tries to explore all of these facets. It should be viewed as a
collection of theorems and proofs, which start rudimentary and build up to
more technical results, which are hopefully interesting and useful for mathematicians and jugglers alike. | |
