- You have a new assignment: keep visiting Schedule and Assignments page to keep track of these.
- Timeline of Lewis Carroll's life
additions:
- Everyone has discharged their duty!
- On a slip of paper, write your favorite's number
- For Tuesday, 9/8: submit
- your calculations (sheet of paper) and checks for each poem
- A short (half page) description of why you chose your favorite. This should be typed and well-written. These will distributed to the authors of each.
- A short (half page) description of your own, including the calculation.
- More Mobius band applications, and whatnot:
- Dylan: "My application of the Mobius strip is in velocity and acceleration studies. Based on my limited knowledge of physics, I know that a velocity is a vector and that acceleration is the derivitive of said vector. I also know that in order to change velocity you change either it's speed or direction. Since a Mobius band has only one side, and is a continuous curve, if a track could be built in the shape of one, the object on it would neither change direction nor need to slow down, giving physicists an ideal method of studying velocity or acceleration. Why they couldn't use a circle was not part of the assignment, and has therefore gone unaddressed.""
- Ryan: A team of scientists came up with a geometric method of mapping out music in coordinate space, and according to their findings, for music made of chords containing two notes, all musical possibilities take the shape of a Mobius strip/band. (source)
- Kayla: Apparently there have been a few different designs for toys that include a Mobius Band. One in particular was a railroad in the shape of a Mobius Band that had magnets so that the train could go upside down. (source)
- Holly: Mobius buildings!
- Hannah: a wedding ring, or a noodle -- like a circular rotini twist (ooohhh! I like that!).
- Two (Karrissa and Annna) chose the recycling symbol: e.g.
One application I have found is the use of the Mobius Band design as the universal symbol for recycling. I chose this because we see this symbol used nearly everyday. (source). Annna added the history of the recycling symbol.
- Several (Barbara, Annie, Amanda) mentioned its role in conveyer belt technology: here's one reference:
- According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Mobius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Mobius strips, and they appear in his woodcuts "Mobius Strip I" and "Mobius Strip II (Red Ants)" (Bool et al. 1982, p. 324; Forty 2003, Plate 70). (source, with beautiful illustrations from Escher)
- According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Mobius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Mobius strips, and they appear in his woodcuts "Mobius Strip I" and "Mobius Strip II (Red Ants)" (Bool et al. 1982, p. 324; Forty 2003, Plate 70). (source, with beautiful illustrations from Escher)
- Jessica: One practical application of the mobius band that I found was that the concept can be used to created half-twisted, continuous-loop recording tapes. Applying the idea of the mobius band is useful because it allows for almost twice the playing time of a normal recording tape. It also allows for the same amount of tape to be used letting companies save money. (source - with construction tips and other nice applications. Also a joke: "Why did the chicken cross the Mobius band?")
- Klein bottles (Fortunatus's purse)
- Results of your Mobius exercise
- How do you know that the Mobius band and the ordinary band are not topologically equivalent?
- What are the two forms of a Mobius band?
- What happened when you "cut a Mobius band in half"?
- How about "thirds"?
- Let's make Fortunatus's Purse (sort of...)
- How would you describe Charles's upbringing? (Evidence!)
- How would you describe his character? (Evidence!)
- We'll take a look at a few of the problems in the Arithmetic text (p. 30).