The legend of Baku

I’ve had a hard time focusing on my Knot-geometry project this week, for reasons we all know & share.

However, I am sailing over the Japura river by now. This area of the Amazon at the edge of the  Brazil – Colombia border has a very large concentration of tapirs. Tapir have for unique feature four toes on the front feet and three on the hind feet. Great for an all-terrain run stability. That’s where I found my bridge to a 4 and 3 Conway knot visualization.

The background is a repeat tiling of Conway notation 4 and  the two knots (4&3) were done in stereography,  to give an idea of what an abstract representation of a tapir emerging from  its frame could look like.

Even better, as Do- Mana explains, tapirs are mythical creatures in many Asian lores known for devouring bad dreams and nightmares. Very timely indeed.



The unbreakable knot

Sailing over the Tumucumaque National Park this week inspired me to carve this 7.7 knot in one of the planet most hardest and most precious wood – lignum vitae (tree of life).

This is a nod to our fragile ecosystem as well as its often forgotten dwellers. For good measure, I borrowed for my background a local symbol I found in a wonderful booklet on the heritage of the WAYANA E APARAI culture published by the Brazilian Indian Museum in Rio. 

More details on the Knot-Geometry project, on Patreon


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.


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 @@


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  @


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

Setting sail

Change of mind, I’ll take WordPress around the globe with me, after all!

Knot #1. Latitude 0º,  longitude 0º, a lone buoy in the Gulf of Guinea. First knot of the series: the unknot.

More details on this visualization, the unknot, and the island of Null @


Knot story


Jan. 1st, 2020. 400 knots a week

Like many of you, I’ve been a long time WordPress content creator & user.

Simple, clean and robust, I tolerated their putting ads on my site, nothing is really for free, I guess. Big conundrum lately – no more free site option on WP. What shall I do for my upcoming 2020 project? Can’t use the old sites templates, and I’m not ready to pay a fee either. The next to best thing to do is to take the plunge and move to Patreon   I got the idea from Tatiana Aleksina & Tony Single. Thanks for it guys!

I’ll be maintaining & updating each of my WP sites as needed to give you updates relevant to each particular project. Otherwise, join me on my new home for a one knot a week for 52 week project that will take us sailing around the planet Earth for the entire year.

I’ll be missing you WordPress, thanks for having been such a pleasant host all these years. And to all, thanks again for your long following & support. Best to each one of you in 2020

Jean Constant

Summer months

A selection of the Geometry of Nature project images from the summer months (June, July, August) is now available at Saatchi Art – aluminum, canvas or paper. Look for collection – Geometry of Nature