The torus is one of the most important geometrical objects in mathematics. As a topological space it is just a product of two circles. The is a natural continuous mapping from the real plane to the torus which is called the exponential map. It is of interest to understand the image of a line through the origin in the plane in the torus under the exponential map. If the line has irrational slope its image in the torus is dense, that is it approaches every point arbitrarily closely. If time permits few more facts about the winding line will be mentioned.
