Celebrating a double-unknot

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.

Fang knot

Fang mask created filling the empty space of a 6.1 knot. 

As the Knot geometry project is passing over the Lome National park in Gabon,  I discovered a 6.1 knot had all the components of an interesting Fang wooden sculpture. 

Traditional Fang and Ntumu art was very popular in the early 19200 with the modernists and the like of Klee and Picasso

Tshuapa dances

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.

More on the Knot-Geometry project on Patreon

Mugumo knot carving

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.

Endless eversion

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…

Wind-knot

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.

More on the knot geometry project on Patreon.

Breather knot

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. 

Indian nights

Moonlight over the Indian Ocean when knots turn into 4D. manifolds. 

This is a variation of an L5a1 knot – or maybe two iterations of this knot romancing each other under the full moon?

Last leg of the Knot-Geometry project, 3,500 some (nautical) knots to Turdo, Somalia and back to Null in a few weeks.

More on the Knot-Geometry project on Patreon