24 Apr
2014
24 Apr
'14
12:01 p.m.
Well, Adam solved the recent surface puzzle with what is probably a "book proof" à la Erdős. (As well as a follow-up puzzle in a similar vein.) Here's one in a different vein. Puzzle: ------- It's well known that if you identify a (2D) the opposite edges of the square [0,1]x[0,1] by (x,0 ~ (x,1), and (0,y) ~ (1,y), 0 <= x,y <= 1, the result is a torus. Suppose instead you use the identification (x,0 ~ (x+.5,1), and (0,y) ~ (1,y+.5), 0 <= x,y <= 1, where addition is mod 1. QUESTION: Which surface does this result in? --Dan