LSU Mathematics Contest for High School Students
High School Mathematics Contest

Spencer Roby


2019 Contest Logo

This years contest logo was developed by Professor Padmanabhan Sundar of the LSU Mathematics Department. The logo design gives a three-dimensional picture of collision dynamics of two colliding particles that travel in a vacuum. Here, \(u\) and \(v\) denote pre-collision velocities, and \(u^*\) and \(v^*\), post-collision velocities. On account of conservation of momentum and energy, they lie on a sphere with center at \(\frac{(u + v)}{2}\) and diameter equal to \( |v - u| \). One may take \(u\) as the south pole and \(v\) as the north pole. While the conservation laws provide us with four equations, \( (u^*, v^*) \) is six dimensional. Hence, in writing \(u^*\) and \(v^*\) as functions of \(u\) and \(v\), one needs two parameters. If the unit vector in the direction of \(v^* - v\) is called \(n\), then it enables one to write \(v^*\) in terms of \(u\), \(v\) and \(n\). In spherical coordinates, \(n\) is written as a function of \(\theta\) and \(\xi\) where \(\theta\) is the co-lattitude and \(\xi\) is the meridian for the velocity \(v^*\).