Endless knot

Endless like this knot, the waves keep weaving their pattern forever.

The Knot geometry project is now sailing toward Macapa – Cidade das Mangueiras (the city of Mango ). No known relationship between the mango tree grain and the 7 – 4 knot, but it was fun to look into it to see if there was any.

In mathematical knot theory, the endless 7 – 4  knot is a 7-crossing knot which can be visually depicted in a highly-symmetric form and is one of the oldest known knot on the planet. It was found on clay tablets over 2500 years (BC) ago and its symbol is featured in many Eastern and Western religions.

Was it at the origin of weaving? It maybe since it is made from a single strand weaved and reweaves symmetrically.

Doing a symmetrical tiling was tempting. But in the context of this project project, I let the waves inspire me and take us into a more complex beadlike composition.

More details on this knot and the knot geometry project @http://bit.ly/knotgeometry



120-cell knot

The famous 120-cell 4D polytope is a 120 dodecahedral cells. Pick an arbitrary dodecahedron and label it the “north pole”. Twelve great circle meridians (four cells long) radiate out in 3 dimensions, converging at the fifth “south pole” cell. 

Perfect topic for a slow day in the middle of the ocean 18.42º West from the American coast


Isabella’s brooch

Knot geometry project, month of February, 1,650 knots west of Null.

What better place than the middle of the ocean to dream of the 4th dimension. A hologram of Queen Isabella jewelry left by conquistadors on their way west? Actually, the real 4D knot (lower left) is a construct  by mathematician Rob Kusner requiring a 4 dimensional approach to geometry. 50 components, 600 beads, 21,600 polygons went into this model.

More on the Knot geometry project on Patreon