In the icons of the saint, scientists have found perfect knowledge of the laws of mathematics

Incredibly interesting in this regard is the article by the candidate of historical sciences, art historian R.A. Suslova, published in 2021. In it, the author analyzes the miniatures illustrating the Khitrovo Gospel and compares them with Andrei Rublev’s “Holy Trinity”. Let me remind you that the Khitrovo Gospel is a luxurious handwritten Gospel created at the very end of the 14th – beginning of the 15th century for one of the Kremlin cathedrals. The last owner of the masterpiece was the boyar Bogdan Khitrovo, who received the manuscript as a gift from Tsar Feodor Alekseevich in 1677 – hence the name. The ancient handwritten Gospel is decorated with an image of an Angel, four evangelists and their symbols, as well as figurines of animals and scenes of their struggle. Some of the miniatures are presumably made by Andrei Rublev. Having conducted a detailed analysis, R.A. Suslova found confirmation of this hypothesis. Having studied the composition of the images of the evangelists, the art historian proved that it is based on the strict application of mathematical and drawing methods, namely the construction of the Fibonacci spiral, parallel and central projection. These same methods are used in Rublev’s icon “Holy Trinity”.

Andrei Rublev’s icons were the result of a genius’s insight

And now it’s time to exclaim: “Stop! What are you talking about? Where is the Russian Andrei Rublev, and where is the Italian merchant and mathematician Leonardo of Pisa, son of Bonacci, nicknamed Fibonacci!” Let’s figure it out. In 1202, that is, two centuries before the creation of our Gospel, the Khitrovo merchant and mathematician Leonardo of Pisa wrote the main work of his life, “The Book of Abacus” – “The Book of Calculations” (Leonardo of Pisa called arithmetic calculations “abacus”). In his book, the Italian convinced readers of the advantages of the decimal system of calculation, and did it so successfully that all of us, except for programmers, still use it to this day – it’s convenient, after all, we also have ten fingers on our hands. Leonardo was not the author of the decimal system, he spied it on Eastern mathematicians. The merit of the work was that it clearly explained to traders, architects, builders, sailors – everyone who had to deal with arithmetic – the rules of addition, subtraction and multiplication in a system of calculation new to the Italians. Leonardo did not stop there, he explained the theory of divisibility and even described the properties of a number series, which was later called the Fibonacci numbers. What kind of beast is this? It’s simple, the Fibonacci numbers are a series of numbers where the first number is 0, the second is 1, and each subsequent number is equal to the sum of the two previous ones. That is, the series: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on. The Fibonacci sequence was also not invented by an Italian, it was known in Ancient India. But Leonardo of Pisa included this sequence of numbers in his book as a problem about continuously reproducing rabbits, and centuries later the problem, or rather the sequence of numbers revealed in it, interested mathematicians so much that they began to study it closely. And they still can’t stop. And when European mathematicians began to study Fibonacci numbers, this led to grandiose discoveries that turned both science and art upside down.

At first, inquisitive minds noticed that if any number in the Fibonacci sequence is divided by the previous number in the sequence, the result will tend toward the number 1.618. Moreover, the further the dividend and divisor are from the first members of the sequence, the closer the result of their division will be to the number 1.618.

For example, if we divide 2 by 1, we get 2, but if we divide 89 by 55, we get 1.618181. You may ask: “What does Andrei Rublev have to do with this?” Be patient for a minute, especially since we are finishing with mathematics for now. The year is 1509, and the monk Luca Pacioli in his book “Divine Proportion” puts forward the theory of “Divine Proportion” and defines the number 1.618 as “the number of God”. Why? Because this is the number of ideal proportion. Subsequently, the name of God disappeared from the “ideal Divine proportion”, and the proportion itself began to be called the golden ratio. And the golden ratio is such a ratio of parts to the whole, when the larger part relates to the smaller in the same way as the whole to the larger. And surprisingly, this ratio is the number we are already familiar with – 1.618.

The treatise of monk Luca Pacioli “Divine Proportion” was illustrated by none other than Leonardo da Vinci himself, who drew the ideal proportions of a human being. The drawing is widely known as “Vitruvian Man”. Like Leonardo of Pisa, Luca Pacioli was not the inventor of the Divine Proportion, it had already figured in the works of mathematicians and philosophers of Ancient Greece, but after Leonardo da Vinci, both the principles of the golden section and the Fibonacci sequence itself became the object of particularly close attention. Leonardo himself used the canons of the golden section and the geometric spirals of the Fibonacci sequence in “The Last Supper” (1495-1498). After Leonardo, the process of creating a painting or fresco could not do without solving geometric problems, and Albrecht Durer, for example, even used the proportional compass he invented to determine the points of the golden section…

And now it’s time to remember our genius Andrei Rublev. To do this, let’s return once again to figures and numbers – only now analyzing dates.

Presumable dates of Andrei Rublev’s life: 1360-1430. Place of birth and work – Moscow or Moscow region. “Monk Andrei” did not travel abroad, therefore he was not familiar with “The Book of Abacus” and the problem about breeding rabbits. Moreover, in Rus’ of that time they used their own, Cyrillic system of calculation, based on the alphabetical recording of numbers using Cyrillic or Glagolitic. Rus’ learned Arabic numerals only in the 18th century. Let us also pay attention to the fact that the monk Luca Pacioli published his book “Divine Proportion” in 1509.

The icon “Holy Trinity” by Andrei Rublev (early 15th century) is also perfect from a mathematical point of view. Photo: Social networks

Then where does the knowledge of these Divine proportions come from in the icon painter’s works? The Golden Section? Where does the applied and such talented use of the patterns resulting from understanding the properties of the Fibonacci sequence come from? The most obvious answer is that the Byzantine masters from whom Andrei Rublev studied could have passed on this unique knowledge of the Divine proportions – after all, Ancient Greece knew and used the rules of the Golden Section. Yes, that could have been the case. Art critic R.A. Suslova notes in her article: the author of the miniatures from the handwritten Gospel knew both Greek mathematics and examples of Byzantine art well. But then – attention! – important! It turned out that neither in Russian nor in Byzantine art could one find analogs to the drawing and graphic methods used by the author of the miniatures for the Gospel, Khitrovo. But “many methods of constructing the composition and the details of the image in the miniatures are similar to those present in the icon of St. Andrei Rublev “The Holy Trinity”.”

I think that in the article by R.A. Suslova, what is interesting and important is not only the conclusion that the author of some of the illustrations of the famous handwritten Gospel of Khitrovo is Andrei Rublev. Yes, one mystery has been solved, but the solution itself gives rise to new questions. And the main one – from where? How did the monk Andrei Rublev know about the Fibonacci numbers and their geometric spirals that organize the composition? And about the Divine proportions and such complex drawing methods of their implementation? And about the ways to solve the problem of squaring the circle?.. And how did he know about the Trinity? About the fact that God’s peace is love. And also harmony, built on the fundamental laws of mathematics. It must have been that a light-winged Angel quietly whispered in our genius’ ear. What do you think?