Part IV

The beauty of ideal knots

Let me change the mood.
From the gloomy one to more optimistic.
Untangling knots is neither easy nor safe, but the result - ideal knots - are worth the risk: they are pretty!
Some artists knew this before the scientists started to think about them.
There are many wonderful examples of  ideal knots depicted in the most precious pieces of art.
Being Polish, I went through the art galleries trying to find ideal knots in pictures painted
by Polish artists, in particular those, whom I like most: Wyspianski, Axentowicz, Zmurko.
I think I have found some interesting pieces.
Let me start with Zmurko. He is less known, but as I find, his knowledge of ideal knots was deep.
One of his paintings can be seen as a proof of the existence of ideal knots. I like the proof.
In contrast to the proof by Cantarella, Kusner and Sullivan, Zmurko's proof is full of warmth and feelings.
(CKS, sorry, but this is true.)

A cigarette, a fan and an ideal trefoil
(based on: A fan and a cigarette by Franciszek Zmurko)

It seems that many Polish artists who spent some time in Paris were aware of the existence of ideal knots.
Certainly, Wyspianski knew they existed. More. He was apparently aware that the path leading to the ideal
conformation could be blocked by the misleadingly beautiful, local minima.
Looking at his Girl with a knot you will certainly recognize the Gordian Unknot.
Neither I, nor anybody else was able to provide a formal proof of its existence.
Wyspianski's approach is different: "The proof of the pudding is in eating".
He simply portrayed it.

Girl with the Gordian Unknot
(based on: Girl with a flowerpot by Stanislaw Wyspianski)

As we are with Wyspianski, my favorite painter, let me tell you something more about him.
His intuitive knowledge of the knot theory must have been a good one.
In one of his paintings, we find a clear image of a nicely tightened, big achiral knot.

Girl with an achiral knot
(based on: Girl in a hat by Stanislaw Wyspianski)
 

In another, I recognize a toy in form of a cable knot.

Sleeping Mietek with a cable knot
(based on: Sleeping Mietek by Stanislaw Wyspianski)

To end with something special, let me introduce to you another remarkable Polish painter, Jozef Mehoffer.
In Friburg, Switzerland, you may find his wonderful stained glass pictures. Here, I would like to make you
acquainted with one of the most unusual piece of his work, a dream-like picture of a garden.
It would be strange, if there were no ideal knots in it. There are two, both trefoils.