Three Old Arches



In August 2022 the Daily Mail published a story which reported that a "scientific" study "has revealed that the walled cathedral city, in the northwest of England, has the highest percentage of buildings - 83.7 percent - that align with the 'golden ratio'." Venice came second, and London third. Back in November 2021 Cheshire Live posted essentially the same story and provided some further information on "the most beautifull buildings in Britain" based on a very similar study. Chester had the second highest scoring building in the study, Three Old Arches, in Bridge Street which scored "99%". The 13th Century stone frontage at the street and row levels of No. 48 is also considered to be the earliest shop front still surviving in England.

The "judge" is this supposedly "scientific" study was a computer program which compared the dimensions of the front-facing profile of the building (as it appeared in Google Street View) with the 'golden ratio' and used this as a test of "beauty".

The Golden Ratio
The ratio is the number x such that 1/x = x-1. It also happens to be close to the ratio of the lengths of the sides of a credit card (85.6 mm x 53.98 mm).

The Golden Ratio. is commonly represented by the Greek letter phi ( ϕ ). Ancient Greek mathematicians first studied the golden ratio because of its frequent appearance in geometry. It is sometimes said that the 5th-century BC mathematician Hippasus of Metapontum discovered that the golden ratio was neither a whole number nor a fraction (and therefore an "irrational" number), surprising Pythagoreans. Euclid's Elements (c. 300 BC) provides several propositions and their proofs employing the golden ratio, and contains its first known definition. The golden ratio was studied peripherally over the next millennium. Abu Kamil (c. 850–930) employed it in his geometric calculations of pentagons and decagons; his writings influenced that of Fibonacci (Leonardo of Pisa) (c. 1170–1250), who used the ratio in related geometry problems but did not observe that it was connected to the Fibonacci numbers. Luca Pacioli named his book Divina proportione (1509) after the ratio, and explored its properties including its appearance in some of the Platonic solids. Leonardo da Vinci, who illustrated the aforementioned book, called the ratio the sectio aurea ('golden section'). German mathematician Simon Jacob (d. 1564) noted that consecutive Fibonacci numbers converge to the golden ratio; this was rediscovered by Johannes Kepler in 1608. The first known decimal approximation of the (inverse) golden ratio was stated as "about 0.6180340.." in 1597 by Michael Maestlin of the University of Tübingen in a letter to Kepler, his former student. In fact the ratio has an infinite number of decimals without any repeating pattern.

In Mathematics and Nature
The ratio has many interesting mathematical properties. For example, it is defined in a unique way by a very simple equation. There is also a special relationship between the Golden Ratio and Fibonacci Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). When we take any two successive (one after the other) Fibonacci Numbers, their ratio is very close to the Golden Ratio and gets closer as the numbers get bigger. The Fibonacci Numbers also appear in biological settings, such as branching in trees, the arrangement of leaves on a stem, the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern, and the arrangement of a pine cone's bracts. The reason why this type of mathematics turns up in nature is that it is the result of a simple process which repeated.

In Art
The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."

The idea that the Golden Ratio is somehow connected to visual beauty is frequently repeated in "popular science" books and articles. These frequently refer to the "Divina proportione" (Divine proportion), a three-volume work by Luca Pacioli, was published in 1509. Pacioli, a Franciscan friar, was known mostly as a mathematician, but he was also trained and keenly interested in art. Divina proportione explored the mathematics of the golden ratio. Though it is often said that Pacioli advocated the golden ratio's application to yield pleasing, harmonious proportions, Mario Livio points out that the interpretation has been traced to an error in 1799, and that Pacioli actually advocated the Vitruvian system of rational proportions that can be expressed as exact fractions, which is quite different to the Golden Ratio.

Psychologist Adolf Zeising brought a resurgence in the popularity of the golden ratio in the 1854, writing of a universal law for “beauty and completeness in the realms of both nature and art”, after noting the golden ratio’s appearance in plants. Publications since have labeled many of these claims as simply misconceptions.

Livio states:


 * "literature is bursting with false claims and misconceptions about the appearance of the Golden Ratio in the arts (e.g. in the works of Giotto, Seurat, Mondrian). The history of art has nevertheless shown that artists who have produced works of truly lasting value are precisely those who have departed from any formal canon for aesthetics. In spite of the Golden Ratio's truly amazing mathematical properties, and its propensity to pop up where least expected in natural phenomena, I believe that we should abandon its application as some sort of universal standard for ‘beauty,’ either in the human face or in the arts."

Sources and Links

 * Chester Lifestyle on the story;