### Water Measuring, Skew Billiards and Euclid's Algorithm - David Lewis

##### 25th October 2014

This is a presentation concerned with how you transfer something (in this case water) in specific and limited, fixed integer, amounts from some given initial state to a some given final state. This idea is closely tied up with finding integer solutions (positive and negative) for (x, y) which satisfy equations likeN = Kx + My where (K, M, N) are all positive integers. We will see how this is tied up with Euclid's famous algorithm for deciding if a pair of integers are co-prime. And hopefully have some fun at the same time.