I got so excited that I bought a box of my own,
and I've been making my own "mobius music". But
I use math to make the music we play as a
mobius band (since I haven't any talent as a
composer...).
Now we want to connect our mobius bands up with knots:
What kind of a knot is the edge of a Mobius band? (Cut one
in half!)
Do you get a knot with a twice-twisted Mobius band? (Cut one
in half!)
What kind of a knot do you get when you cut the alternative recycling symbol
shown above? How many twists does it have?
Give a band four twists! Cut it in half. What do you get?
What do you suppose that you'd get if you cut one with
five twists?
What objects (knots, links) do we get by cutting the
Mobius band in "thirds"?