If I understand correctly, the surface of a
Möbius ring is mathematically speaking
endless? Well, then. Take any length of
toiletpaper, fashion a Möbius ring out of
it
and hey presto! Mathematical thriftyness
galore! Enjoy!

Better yet, after using your mobius strip of toilet paper, cut it down the middle with a pair of scissors and voila! you now have a ring twice as big and you can continue wiping.