- #1

pmsrw3

- 459

- 0

I want to get three numbers that contain all the rotation and translation-independent information in (x1,y1), (x2,y2), (x3,y3). This is easy. I would also like the mapping to be continuous. That is, I would like to have a continuous injection from ℝ^2×ℝ^2×ℝ^2/E+(2) -> ℝ^3. This, I believe, is impossible. Am I right? I have a feeling this is basically Borsuk–Ulam, but like I said, I'm pretty ignorant of topology.

Thanks for any help.