How To Parallel Park Your Car: Another Mystery Solved with the Theory of Lie Groups

How big does a car space have to be to fit your car into if you must parallel park? Is it the length plus half the width, as advised by driving instructors? What does the theory of Lie Groups tell us? <img alt="" src="https://miro.medium.com/v2/resize:fit:700/0*49YM_-6QN7dC5EA6" style="height:467px; width:700px" /> Photo by <a href="https://unsplash.com/@averieclaire?utm_source=medium&utm_medium=referral" rel="noopener ugc nofollow" target="_blank">averie woodard</a> on <a href="https://unsplash.com/?utm_source=medium&utm_medium=referral" rel="noopener ugc nofollow" target="_blank">Unsplash</a> A car can’t drive directly sideways, or turn around on the spot. Its possible motions are all isometries in 2D Euclidean Space, but its basic controls, “steer” and “drive” are only a tiny, tiny subset of these isometries. Lie Theory can explore how complicated motions can be built from a small subset, and thus how even simple, seemingly inadequate controls can achieve complicated motions in mechanics and robotics. In particular, it tells us the surprising answer to the question: How big does a car space have to be to fit your car into if you must parallel park? How even do you parallel park your car? <a href="https://www.cantorsparadise.com/how-to-parallel-park-your-car-another-mystery-solved-with-the-theory-of-lie-groups-28db7d4fb6f2">Read More</a>