Please forgive me...I am not a mathematician, but I have a couple questions that have been puzzling me. In theory, can a circle be so large that connecting 3 points on that circle result in a degenerate triangle? If the length of a straight line drawn between two points on a circle is Planck distance, how can another point fall between those 2 points? Do such questions cause problems using math as a descriptive tool in physics, or are there fudge factors? One more thing...does the Poincaré conjecture factor into these questions in any way? Thank you.