Geodesics on a hot plate: an example of a two-dimensional curved space

The equation of the geodesics on a hot plate with a radially symmetric temperature profile is derived using the Lagrangian approach. Numerical solutions are presented with an eye towards (a) teaching two-dimensional curved space and the metric used to determine the geodesics (b) revealing some characteristics of two-dimensional curved spacetime and (c) providing insight into understanding the curved space which emerges in teaching relativity. In order to provide a deeper insight, we also present the analytical solutions and show that they represent circles whose characteristics depend on curvature of the space, conductivity and the coefficient of thermal expansion