- There is key for the last test on-line.
- You have a new reading assignment.
- Sorry: I've got behind in my homework grading! I'll get it to you on Tuesday.
- That being said, you do have a new homework due to be handed in next time: our Knotty Tale.
- Kyle V. provided copies of the Led Zeppelin album, showing that there is no distinction in crossing of the Borromean rings:
Here is an image of the Symbols (Does this give you any ideas for your personal logo?)
- Reminder: on 4/26, we'll have "Logo Day". It's about time that you
began wrapping up your logo. What -- you haven't started yet?! Time to
get started....
From the syllabus:
LOGO: 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 write a one page sheet, illustrating and explaining your choice. These will be presented the last day of the course.
Let's start today with a little "knot equivalence" practice. I'll give you a few twisted bands, and you tell me what kind of knots they are, using
- Reidemeister moves, and
- tricolorability.
Question of the day:
- Mobius bands are a part of geometry, but relate to a special area
called "topology". Your reading concerns topology
generally, and mobius bands as a particular example.
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"?
-
My dad loved mobius bands so much....
- 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:
- 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?"
- 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?
