This has an answer, but it makes a nice puzzle for the mathematically inclined so I'm presenting it as a riddle. You have a hypersphere of n dimension and you want a function which describes a non-geodesic line which never crosses itself in the space of the sphere. Questions: What is the smallest number of dimensions such a sphere can have? How do you construct the function that describes such a line? Enjoy. I'll give the answer if you get stuck.