- You have a homework due Wednesday. There will be one more
homework, due the last week of finals.
- Logo day is coming up: Wednesday, 4/29.
From our syllabus:
Companies have logos; you should have one, too! Your math logo will be something (like a family crest)
that represents you. It will be created using elements from this course (or other mathematical elements of your own choosing). You will type up a one-page sheet, illustrating and explaining your choice.
- Rectangular Mosaic Tiles and symmetry
- We can use them to make any knots: try your hand at
- They can help us to draw Borromean Rings, for example: use your Mosaic Graph Paper to create your own version of the Borromean Rings.
- 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...).
- How does the Mobius band relate to knots and links?
- 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 objects (knots, links) did we get by cutting the Mobius band in "thirds"?
- What kind of a knot is the alternative recycling symbol shown above?
