- Your homework on the
"Knotty Tale" is due today, along with your homework on knots.
- You also have an assignment due this coming Tuesday, which concerns Mobius bands. We'll spend more time on Mobius bands today.
Question of the day:
- Mobius bands are a part of geometry, but relate to a special area
called "topology" -- the study of form and shape.
The Topologist's favorite riddle: What's the difference between a donut and a coffee cup?
Answer: There isn't any! (to a topologist....)
- What is a Mobius band?
- Let's make some!
- A mobius band is made from a regular band using only a single twist.
- By the way, did you know that there are two different
Mobius bands? They're mirror images of each other! (Symmetry, again....)
- Check yours against someone else's, and convince yourself that they're really different.
- Make one of each!
- Properties of a mobius band:
- A mobius band has only one side.
- A mobius band has only one edge.
- Cutting a band:
- What happens when you cut a mobius band "in half"? Let's check out a bug on a band....
- What if you cut it into "thirds"?
- Applications of Mobius bands:
- Conveyor belts
- Kazakhstan's National Library in Astana
- Recycling Topology
- The official recycling symbol is mobius, but over
time an alternative has crept in:
- My dad loved mobius bands so much....
- a history of the recycling symbol
- AARP article on the history of the creation of the recycling symbol
- Recycling -- Mobius, or only Seemingly Mobius?
- The official recycling symbol is mobius, but over
time an alternative has crept in:
- A joke: "Why did the chicken cross the Mobius band?"
- Mobius music:
- First of all, Vi Hart's most beautiful performance of Music Box music: Pachelbel's Music Box Canon in D
- But what really got me excited was when Vi introduced me to "mobius music"
- 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?
