### Site swap practice

In laboratory one a quote from Freeman Dyson was used to start a journey through the mathematical models that explain physical systems. Dyson calculated how an electron ought to behave. Later someone went into a laboratory and the electron behaved as predicted by the mathematical model. In laboratory two a linear model predicted the location of a rolling ball. In laboratory three a falling ball obeyed a quadratic mathematical relationship. The behavior of a marble rolling off of a banana leaf obeyed a square root relationship. And in laboratory four the marbles knew what to do in order to mathematically conserve momentum. Sound, the relative depth of an image, and Ohm's law all exhibited linear relationships.

There are other mathematical relationships that govern physical systems. There are systems that are modeled by exponential and logarithmic functions. The path of a RipStik formed a sine wave on a sheet of paper. There are exotic functions such as the hyperbolic sine and hyperbolic cosine. Some systems are best described by complex variables that include a real and an imaginary component. Many of these systems are beyond the mathematical scope of this course.

The relationships described above are algebraic mathematical models. Much of the mathematics curriculum is centered on algebra in part because algebra is important to describing the physical world. There are, however, other mathematical models, non-algebraic models. This laboratory seeks to broaden the students mathematical horizons by introducing a mathematical model and notation that is not algebraic. In laboratory fifteen the students were introduced to the mathematics of site swaps.

In an attempt to connect site swap theory back to the language of algebraic equations, after introducing site swap notation I referred to sequences such as 33342333 as site swap equations. The sequence is a mathematical statement that can be true (juggable) or false (not juggable).

This laboratory continues to provide a fun way to wrap up a term of exploring the mathematics at the core of physical science while expanding the students thinking with a mathematics system like nothing they have ever seen before.

Although traditional site swap notation does not include multi-plexing, this term Carlyne demonstrated the usefulness of multiplex notation when she juggled four balls using a paired multiplex. While sitting down.

*Norma keeps three aloft*

*Achimy mastered three tennis balls and then three space balls*

*Sussy keeps up three small inflatable balls*

In an attempt to connect site swap theory back to the language of algebraic equations, after introducing site swap notation I referred to sequences such as 33342333 as site swap equations. The sequence is a mathematical statement that can be true (juggable) or false (not juggable).

This laboratory continues to provide a fun way to wrap up a term of exploring the mathematics at the core of physical science while expanding the students thinking with a mathematics system like nothing they have ever seen before.

Although traditional site swap notation does not include multi-plexing, this term Carlyne demonstrated the usefulness of multiplex notation when she juggled four balls using a paired multiplex. While sitting down.