- Sorry -- tests aren't graded yet. Hope that it went well for you!
- You had a new reading assignment for today: visit this website and read about "human knots": have you ever played this before?
- Notice her graphs in the first part of the video: those are the two non-planar graphs, and the graph of an octahedron!
- By making a closed-curve squiggle graph, you're creating a knot.
- "Borromean snakes": "No two snakes are actually linked to each other".
- Just before the Borromean snakes there is a trefoil snake.
- "What kind of knots are you drawing and can you classify them?"
(an example of Solomon's Knot -- which you might notice is actually a link!)
- Celtic Knot Mosaic Examples: (not quite the same idea, but pretty! And again, you'll see that there are links contained therein -- including Borromean rings)
- Knot Mosaics
- help us to draw Borromean Rings, for example: use your Mosaic Graph Paper to create your own version of the Borromean Rings.
- Rectangular Mosaic Tiles and symmetry
- We can use them to make any knots: try your hand at
- We begin with the "unknot", of course: a circle. This is the simplest knot, but not very interesting.
- Trefoil Knot -- the simplest interesting knot. It has three crossings, and there's no way to make it any simpler! We will also call it the 3-knot.
- Can we make a simpler knot -- one with either 1 or 2 crossings? Why not?
- There are two different ways to think about making the trefoil knot: as a
- twist knot, and as a
- torus knot.
- figure-eight knot
- So: can we make a human knot in the shape of a trefoil knot? If so, then we won't be able to undo it -- they'll be knotted together forever!
- 5-Knot
- Actually, there are two kinds of 5-knots
- To help you, we have the Rolfsen Knot Table
- The cinquefoil knot
- The 3-twist knot
- How can we tell them apart? Are they really different? For that we need to study knot equivalence, and our primary tool, the Reidemeister moves.
