# Reducing rotations to finite data

## Document Type

Presentation Abstract

## Presentation Date

10-3-2016

## Abstract

This talk will concern the age-old problem of codifying rotations.

For instance, every rotation of 2-dimensions can be approximated by a symmetry of a square; every rotation of 3-dimensions can be approximated by a symmetry of a cube; similarly for rotations of arbitrary dimensional data. The advantage here is that symmetries of a square, and of a cube, are finite and easily understood. The first part of this talk will explicate this by way of some light combinatorics and some pictures.

The real challenge, however, is not just to combinatorially reduce rotational data, but to do so in such a way that composing rotations is compatible with this reduction in a comprehensible manner. The second part of this talk will explain this challenge, and I will offer a complete solution (from joint work with John Francis).

I will assume the audience has facility with linear algebra; familiarity with topology and groups will be helpful, though not assumed.

## Recommended Citation

Ayala, David, "Reducing rotations to finite data" (2016). *Colloquia of the Department of Mathematical Sciences*. 511.

https://scholarworks.umt.edu/mathcolloquia/511

## Additional Details

Monday, October 3, 2016 at 3:00 p.m. in Math 103

Refreshments at 4:00 p.m. in Math Lounge 109