Day 30, MAT115

• There is an assignment (due this Friday, 11/4)

• You had a reading assignment for today: to visit this website and read about "human knots".

• Question of the day: What are the two distinctly different five knots?

• Knot Mosaics:
  

  (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
    • We use five different square Mosaic Tiles and symmetry
    • We can use them to make any knots or links: at
      • the trefoil knot
      • the figure-eight knot

• Knot Theory
  • Trefoil Knot

    From the "Why Knot Art?" gallery of Cliff Long:

    • Spanning Surface of a Trefoil Knot (wood)
    • Same thing, in Marble
    • Some twists on a Trefoil Knot....

  • Figure-Eight Knot (aka the "four-knot")
    • Here's the figure-eight knot, in more detail.

  • Now: let's make some human knots! The trefoil and figure-eight knot.

  • 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.

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