The Whitney-Graustein Theorem states that two plane curves can be smoothly deformed into each other if and only if they have the same winding number.
The original proof of Whitney from 1937 is one of the first occurrences of Gromov’s h-principle, and it is semi-algorithmic. In this talk, after setting up the scene, I will give an algorithmic proof for this theorem that uses contact topology. The talk gives a gentle introduction into the field of contact topology with an emphasis on Legendrian knots, and it should be accessible even for students.