The 8.8 knot

Variation on the 8.8 knot in honor of Dunkel, et al. the MIT team who demonstrated knots various strength according to a clever color changing fiber scheme.

Basically, a knot is stronger if it has more strand crossings, as well as more “twist fluctuations” — changes in the direction of rotation from one strand segment to another. If a fiber segment is rotated to the left and to the right as a knot is pulled tight, this creates a twist fluctuation and thus opposing friction, which adds stability to a knot.

Wisely, the authors point out that there is no winning knot in this. It all depends what the knot is used for: suturing, sailing, climbing, construction and all other areas depending on knots to keep volumes bound to each other.

Visually I borrowed the background from the Knot Atlas, arc presentation  of a 8.0 knot. The planar picture of the knot in which all arcs are either horizontal or vertical creates very dynamic lines  explored based on a Mango-based color theme.

I figured that sailing toward Macapa, the city of Mangos, after 7 weeks and 2,800 miles from Null on the ocean, any sailor would be looking forward to taste that succulent fresh fruit plentiful on Macapa’s food stands.

02-23

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

02-16

 

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

02-09

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

02-02

 

Inverted Möbius

Week 3, 1,200-some (nautical) knots from Null island.

Reflection of an inverted Moebius strip on my compass box. Virtual knot such as this one are made possible using parameters of longitude and latitude on a 3D sphere. The Möbius transformation minimize area distortion and is used to converts 3D brain scans in 2D readable maps.

In addition,  in stereovision,  the 3-rung Möbius ladder helps chemists synthesize molecules. Quite an impressive resume for a surface discovered by German mathematician Möbius in the mid 1800s.

More on the Möbius strip and the Knot geometry project on Patreon @@http://bit.ly/knotgeometry

01-26

Seafaring cinquefoil

Week two of the Knot geometry project, 800 (nautical) miles from Null island. Leaving the gulf of Guinea entering the open ocean. A school of Cinquefoil knots are jumping on and off the water around me!

In mathematics, this prime knot also named pentafoil or seal of Solomon, can’t be built from smaller knots and is only one of two knots with 5 crossings. Its dynamic and fluid shape creates a polished geometry and its surface glistens like water  on a dolphin’s skin.

More on the cinquefoil and the Knot geometry project  @http://bit.ly/knotgeometry

01-19

Knot in a box

Square knots, a sailor’s best friend. They’ve been around for 4,000 years or more. Mathematicians found that square knots are the sum of two trefoil knots mirroring each other. Or are they? This is what I saw in the sky, 0º S, 6ºW , 410 (nautical) knots from Null island.
More details on the journey and the Knot geometry project on my Patreon page
01-12