All knots start with from an unknot – a torus in mathematical terms.
Back to Null 52 weeks and 52 mathematical knots later circling the globe on the equator line, it’s time to conclude with one last knot. The Clifford’s torus is the simplest most symmetric embedding of 2 circles. Or in the KnotGeometryProject terms: one unknot for the beginning of the year, and one for today. This torus is also the transition to many new shapes I’ll explore next year.
Thank you for having followed the Knot geometry project this year. I hope you enjoyed it as much as I did. With my best wishes for a very happy and safe 2021.
A C4 Conway knot converted in Knotplot. C4 also identifies tetragonal structures in the mineral world. As the knot-journey is passing over Tshuapa, next to the mighty Congo river. Good occasion to celebrate the ample supply of cassiterite ore buried in the local river beds.
A handsome 8.2.3 knot made of Mugumo wood to celebrate the knot geometry project passing over Mount Kenya. The Mugumo fig tree is a sacred tree for the Kikuyu communities living near Mt Kenya. They’re also known for their basketry skills and knot making expertise as the image background can tell.
Thanks, Cyan LeMonnis for the inspiration & your tasteful Kiondo bags.
Things to do on the ocean: watch a sphere travel around an endless Morin eversion, under a starry sky.
Named after Morin, a blind mathematician who was a member of the group that first exhibited an eversion of the sphere, this topological metamorphosis starts with a sphere and ends with the same sphere but turned inside-out.
Time flies quickly – 4 weeks to NulL, after this year-long Knot journey circling the planet on the equator line…
The ocean takes on a strange shape when it enters the fourth dimension – so does this Hopf fibration. Some say there are no knots in the 4th dimension. How do you unknot such a knot?
“In general, we can regard hyperseeing in our three-dimensional world as a more complete all-around seeing from multiple viewpoints. Since knots can look so different from different viewpoints, knots are excellent examples of interesting forms on which to practice hyperseeing. Knots are also open forms that one can actually see through.”
This one is for Nat Friedman who opened so many of us to the beauty of hyperseeing and hyperspace.
When planets turns into beams and the water start spiraling down – we know we’re entering another universe.
That’s where the Breathers solitons, the ultimate self contained 4D knots, grow in clusters.
These soliton solutions are characteristically different in that the associated space curve is knotted—a simple overhand knot that occurs periodically (as is expected of a breather) as the curve evolves in time.
I’m posting this week iteration of the knot-geometry series a little early because of an unplanned coincidence.
Call it serendipity, I just passed over Pontianak today. Pontianak is the name of a town in Malaysia – but it is also the name of one of the fiercest ghoul of ancient local lores. She comes at night to haunt and frighten whoever’s in sight. Not to worry, if you can prick a needle in the nape of her neck, she turns into a beautiful and kind lady!
The L6n1 knot seems like a perfect fit for that story – Happy Knot-Halloween all!