nostr:npub154rl37l9zpl5enrvd937ullp6q8kd5q3f46dmf05h0tt02a2y80q3av0lk wrote: " I wonder how we can distinguish the black and yellow regions in your figure, since they are combined into the fundamental region of SL(2, Z)."

If you read my article you'll see the answer to this explained in detail:

https://johncarlosbaez.wordpress.com/2023/09/23/the-moduli-space-of-acute-triangles/

In brief the answer is GL(2,Z), a group which is 'twice as big' as SL(2,Z).