High School Mathematics Contest

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## 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 $$v^*$$.

 Contest organizer: Contest e-mail:   Contest web-page: Mark Davidson, phone: (225) 578-1581 contest@math.lsu.edu www.math.lsu.edu/~contest