The Well of San Patrizio In Orvieto, Umbria, it was built by Antonio da Sangallo around the 1530. Behind its construction, the fibonacci sequence could hide, or more precisely the Aurea section. This is the declaration of Luciano Cencionia doctor passionate about history which, through calculations, noticed the presence of a correspondence between the well of the well and a numerical succession similar to the sequence of fibonacci, that is, one of the most narcotic mathematical structures that we know that, starting from 0 and 1, it builds a succession of numbers in which each number is given by the sum of the previous two.
Let’s see in this article because it is more correct to speak of the golden section and it is not a sequence of fibonacci, according to which calculations the well of San Patrizio can be considered associated with one of the most famous mathematical constants in the world and because it could be a simple coincidence.
The well of San Patrizio and the golden section: what is the connection?
These days are the declarations of Luciano Cencioni, a doctor passionate about history who has studied the proportions of the well of San Patrizio, according to which the famous Pozzo di Orvieto is not only an incredible work of Renaissance engineering, but also a “harmoniously perfect” work. This is because, according to Cencioni’s calculations, there would be a link between the proportions of the well and the golden section, also called constant of Fidia φ. It is a constant mathematics of approximately 1.618 and corresponds to the ratio between two lengths necessary so that the lesser length is to the greater one like the greatest one is to the sum of the two lengths.
This said, it might seem like any relationship, but it is instead one of the most important constants in mathematics, but also in architecture, art and … in nature! In short, the golden section is often considered a synonym for harmony of proportions.
The ratio between the diameters of the well is equal to 1+φ
The calculation of Cencioni was the following:
If we take the diameter of the internal cylinder, equal to 4.65 meters, and we multiply it by the constant of Fidia φ (1,618), we get about 7.5 meters. Adding this value to the internal diameter, we reach 12.17 meters, practically that of the external cylinder, which is 12.20 meters and this shows that the golden proportion is present in the well of the well, although probably in an unconscious way by Sangallo (author of the well).
We try to understand in a nutshell what we have just read and what is the role of the golden section (or constant of Fidia). Let’s start with a premise: the well of San Patrizio is cylindrical cava, as often happens for well and as you can see in the image below. This means that there is a internal diameter and a external diameter of the cylinder that composes the well, whose difference in size determines the thickness of the “walls”.
According to calculations, the external diameter (12.20 meters) can be obtained by multiplying the internal diameter (4.65 meters) by a constant equal to 1 + φ, that is “1 + golden section” or about 2.618. By rereading the statements of Cencioni we can translate them into “mathematician” as follows: if we call dthe the internal diameter (equal to 4.65 meters) and dAnd external one (equal to 12.20 meters), we have that:
This proportion makes us think that even if the golden section is actually present in the relationship between the two diameters, we are not in front of a golden proportion because the constant of multiplication is not actually the constant of Fidia φ. As Cencioni himself says in his statements, it can be said that the architectural proportions of the well of San Patrizio are casuallymore than deliberately, connected to the golden section.
What does the Fibonacci sequence have to do with the San Patrizio well?
In the declarations, however, the Fibonacci sequencewhich is actually linked with a double wire with the golden section. It is a succession of numbers that, starting from 0 and 1, is built so that each number of the sequence is given by the sum of the two previous numbers. So, so to speak, let’s start with 0 And 1then we still have 1 (= 0+1), then 2 (= 1+1), 3 (= 1+2), 5 (= 2+3), 8 (= 3+5), 13 (= 5+8), 21 (= 8+13) and so on. Thanks to Kepler we know today that the relationship between two subsequent terms of the Fibonacci sequence tends to infinity precisely in the golden section φ. In mathematical:
In the case of the Pozzo di San Patrizio we can see that the two internal and external diameters are part of a numerical sequence that – attention – is not that of Fibonacci, but which has the same fundamental property of the sequence: in fact, we note that 12.20 (the external diameter) is about 4.65 (internal diameter) + 7.5. In fact, the calculation of Cencioni follows the definition of a succession defined as that of Fibonacci, but which does not start from 0 and 1 as it happens by definition for the famous succession. Let’s see how:
- Starting from the internal diameter 4.65, we obtain the number 7.5 by multiplying it by φ (approximate to 1.618). In this world, we have just defined two consecutive terms of a series similar to that of Fibonacci, where the relationship between two subsequent elements is precisely φ;
- At this point, they add up to them 4.65 and 7.5, we get 12.17, an approximation of the external diameter. In this way, we have defined a new term of our succession following the rules of the Fibonacci sequence according to which the sum of two consecutive terms defines the subsequent term of the series.
In short, we can say that the architectural dimensions that characterize the well of San Patrizio, if adequately manipulated, can lead us to connections with the golden section and with the fibonacci sequence. This manipulation, however, is far away From being a direct application of the golden section, which represents precise harmonic canons. We cannot say with certainty that Sangallo, the author of the well, was aware of the “semi-aureeous” proportions that he was using and that the relationship between the two diameters was intentionally 1 + φ.
In any case, with a little confidence in the beauty of mathematics and our perception of “perfection”, we can think that consciously or unconsciously we are led to research the golden section even where there is not!
