- Announcements:
- Sorry, the exams aren't graded yet: Wednesday.
- Homework for section 5.4: Mindscapes pp. 383-, #4, 10, 11,
13, 15, 16 (type up #20)
Due Monday, 4/7 - Outline revisions due.
- Sorry, the exams aren't graded yet: Wednesday.
- More on the Moebius band: the Band that keeps on playing.
- Recycling -- Moebius, or only Seemingly Moebius? (p. 350)
- Three-dimensional Thoughts
- Some people think that the universe is Moebius in
structure: that if you go off in one direction, you may come back, with your
right-and-left handedness reversed. I read a copy of Science News and was
surprised to find that there's speculation that the Universe is in the
shape of a Dodecahedron! (a local copy)
"This is what got Giordano Bruno burned at the stake," said Dr. Max Tegmark, a cosmologist at the University of Pennsylvania. "Is space infinite or not?" (the New York Times)
- In the same issue of Science News there is a story about a Snail with Sulfide Shingles: it reminded me of the use of Fibonnaci in two different ways:
- the logarithmic spiral,
- and the spiral patterns of the pine cone. (a local copy)
- What is a Klein bottle?
- A special one-sided surface
- A pair of anti-symmetric Moebius bands taped together (but you can't do it!)
- Some people think that the universe is Moebius in
structure: that if you go off in one direction, you may come back, with your
right-and-left handedness reversed. I read a copy of Science News and was
surprised to find that there's speculation that the Universe is in the
shape of a Dodecahedron! (a local copy)
- Knots and Links (Section 5.4)
- Knot Theory
- Not-a-knot
- Unknot
- Trefoil Knot
From the "Why Knot Art?" gallery of Cliff Long:
- Figure-Eight Knot (aka the "four-knot")
- Let's show that our authors screwed up the figure-eight knot, and actually produced a trefoil knot (p. 377)
- Here's the figure-eight knot.
- 5-Knot
- Links: Borromean
Rings:
- "Is it possible to link three rings together in such a manner that they are indeed linked, yet if we remove any one of the rings the other two become unlinked?"
- Yes!
Standard diagram of the Borromean rings
A realization of the Borromean rings as ellipses
Coat of arms (of the municipality of Hallsberg, Sweden) showing padlocks in Borromean rings configuration
(Thanks Wikipedia!) - icosahedra, golden rectangles, and interlocking rings!
- Knot Theory
