There’s a lot of simple geometric problems like this that don’t have known closed form solutions. A lot of simple geometric time to intersection problems (comes

There’s a lot of simple geometric problems like this that don’t have known closed form solutions. A lot of simple geometric time to intersection problems (comes up a lot in game physics) don’t have known explicit solutions for example. Finding them is interesting but once you have something you can use an iterative algorithm on to find a solution at arbitrary precision the pressure/incentive to solve them is reduced quite a lot. Generally mathematicians would consider the number that answers this problem to be “known” in the colloquial sense, even before this better form.