I believe that your article is based on Dr. Murkowsky's 1992 article, "Misconceptions about the Golden Ratio", which like your article, is dismissive of applications of the Golden Ratio to art in architecture in western culture starting with Classical Greece. Devlin, who often quotes Murkowsky's article, seems to attribute the "popularization" of the Golden Ratio to the minor character Adolf Zeising.
I believe this dismissive arguments are in error. First, artists and architects are not usually in the habit of explicitly documenting their reasoning behind their creative decisions and leaving behind such written evidence for historians. Secondly, during the European Renaissance, Euclid's Elements was the foundational textbook on geometry and mathematics. This textbook has no less than ten references to the "Extreme and Mean Ratio", and any student of geometry learning from this text would have had to work through the several propositions that required the Golden Ratio.
Euclid's Elements was required study in European universities up until the mid 20th century, and it would be hard to explain why the "Extreme and Mean Ratio" would not have an undue influence on western art and architecture, since I imagine these learned artists and architects of the past all having a copy of this textbook on their bookshelves.
The Parthenon, built only two centuries before Euclid of Alexandria summarized ancient Greek knowledge of geometry in Elements, does have elements of the Golden Ratio in its design, the most obvious are within inscribed artwork within the upper facade, where many golden rectangles are found. Murkowsky's dismissal of the front of the Parthenon having Golden Ratio proportions have to do with the convenient subtraction of the stylobate (the base foundation and the series of steps of that lead to the level where the columns are placed), and he makes no further investigation into application of the Golden Ratio in the Parthenon's architecture. This dismissal has been repeated by Devlin and Livio and others, and is unfortunate, as it is reaching mythical proportions.
The Golden Ratio has been found throughout Renaissance art and architecture and beyond. For instance, consider the Pyramide du Louvre, which was constructed at the entrance to the Louvre Museum in Paris, and was designed by 20th century chinese-american architect I.M. Pei. Pei has stated that the design of this pyramid was not based on dimensions of the Great Pyramids of Egypt, but instead on the Golden Ratio.
Finally, I present for consideration the architecture and street layout of Washington, D.C., the early 19th century preplanned city which is the capital of the United States of which there are many obvious manifestations of the Golden Ratio. Although the design decisions were not explicitly documented, it may be deduced that since many of the founding fathers of the United States were freemasons, a secret society originating in Renaissance stonemason guilds, inclusion of this "sacred geometry" is not to be unexpected.
I believe that your article is based on Dr. Murkowsky's 1992 article, "Misconceptions about the Golden Ratio", which like your article, is dismissive of applications of the Golden Ratio to art in architecture in western culture starting with Classical Greece. Devlin, who often quotes Murkowsky's article, seems to attribute the "popularization" of the Golden Ratio to the minor character Adolf Zeising.
I believe this dismissive arguments are in error. First, artists and architects are not usually in the habit of explicitly documenting their reasoning behind their creative decisions and leaving behind such written evidence for historians. Secondly, during the European Renaissance, Euclid's Elements was the foundational textbook on geometry and mathematics. This textbook has no less than ten references to the "Extreme and Mean Ratio", and any student of geometry learning from this text would have had to work through the several propositions that required the Golden Ratio.
Euclid's Elements was required study in European universities up until the mid 20th century, and it would be hard to explain why the "Extreme and Mean Ratio" would not have an undue influence on western art and architecture, since I imagine these learned artists and architects of the past all having a copy of this textbook on their bookshelves.
The Parthenon, built only two centuries before Euclid of Alexandria summarized ancient Greek knowledge of geometry in Elements, does have elements of the Golden Ratio in its design, the most obvious are within inscribed artwork within the upper facade, where many golden rectangles are found. Murkowsky's dismissal of the front of the Parthenon having Golden Ratio proportions have to do with the convenient subtraction of the stylobate (the base foundation and the series of steps of that lead to the level where the columns are placed), and he makes no further investigation into application of the Golden Ratio in the Parthenon's architecture. This dismissal has been repeated by Devlin and Livio and others, and is unfortunate, as it is reaching mythical proportions.
The Golden Ratio has been found throughout Renaissance art and architecture and beyond. For instance, consider the Pyramide du Louvre, which was constructed at the entrance to the Louvre Museum in Paris, and was designed by 20th century chinese-american architect I.M. Pei. Pei has stated that the design of this pyramid was not based on dimensions of the Great Pyramids of Egypt, but instead on the Golden Ratio.
Finally, I present for consideration the architecture and street layout of Washington, D.C., the early 19th century preplanned city which is the capital of the United States of which there are many obvious manifestations of the Golden Ratio. Although the design decisions were not explicitly documented, it may be deduced that since many of the founding fathers of the United States were freemasons, a secret society originating in Renaissance stonemason guilds, inclusion of this "sacred geometry" is not to be unexpected.