The 2-torus is homeomorphic to a doughnut which can be modelled by rotating a circle along a circle (see [1, Example 3.22]).

The main idea for the proof is based on the observation that both are modelled by two angles (see [1, Proposition 3.36]).

References Link to heading

1. J. Lee, Introduction to Topological Manifolds. New York, NY: Springer New York, 2011. doi:10.1007/978-1-4419-7940-7