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It will be over fractals, wallpapers, Platonic solids, and symmetry.
We'll review shortly, after we wrap up something with a little knot...
Then we'll have another art contest.
which I always think of in the context of this quote:
"We must all hang together, or assuredly we shall all hang separately." Benjamin Franklin, at the signing of the Declaration of Independence.
We saw how many different groups have used it in their logos, whenever three things are intimately intertwined.
How can we turn a trefoil knot into other knots (and the Borromean rings)?
We begin with the 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 (since it's the only knot with three crossings):
The twist formulation is a good place to start in order to draw the Borromean rings:
You only need to know the first row!:) But can you see some of the other toroidal and twist knots down the road?