Editor's Pick: The Square/Circle Dual Module: Design Principle of the "Eighth Wonder of the World"

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Almost fifteen hundred years since its construction in the center of ancient Constantinople, the Hagia Sophia has divulged the secret of its design principle. Volker Hoffmann, professor at the Institute for Art History at the University of Bern, deciphered this using state-of-theart 3D laser technology.

Due to its vast dome, which appears to be floating almost weightlessly over the open main room, the cathedral erected at the commission of emperor Justitian in the late antiquity period was regarded as the eighth wonder of the world. The "Aya Sofya" was built in a period of just six years between 532 and 537 AD according to the plans drafted by the mathematician Anthemios von Tralles and the architect and structural engineer Isidoros von Milet. However, the plans to this highly significant building and what is today a U N E SCO world cultural heritage site remain lost. For hundreds of years, experts have tried to fathom just how these scientists and artists working in the 6th century managed to construct a freely suspended dome measuring almost 56 meters high and 31 meters wide, supported only by four pillars. Considering the technical facilities available at the time of its construction, many experts still regard this building even to this day as one of the boldest feats of construction to have ever been achieved by human hand.

Bewildering Phenomena
"The key experience on entering the main room through the emperor’s gate, which immediately presents itself in full view exposing its full width and height up to the vertex of the huge dome, is the impossible task of finding a clear relationship to the dimensions and an accurate calculation of the dimensions. This phenomenon, which was intended by its architects, is produced by the spatial structure, the apparent weightlessness of the dome, and the bewildering abundance of direct and indirect lighting effects", writes the guide Marco Polo. Thanks to the work of the Bernese art historian, insights into these dimensions and their consistent application by the architects and builders of the day are now available.

Ancient Projection Technique
Volker Hoffmann, working together with engineer Nikolas Theocharis in a research project sponsored by the Swiss National Fund, found out that the entire design of the Hagia Sophia is based on an analemma. This is a projection technique that had already been described by Ptolemaeus, which involves subsequently a square and circle and overlapping and penetrating each other three-dimensionally in the form of a cube and sphere. For the Hagia Sophia, according to Volker Hoffmann’s findings, Anthemios and Isidoros had devised a crossed-over double-square analemma as a uniform design shape for the ground plan and the elevation of the cathedral. After performing 3D laser measurements with the aid of a H DSTM Leica 2500 laser scanner and a Leica Disto™ handheld laser meter in the Hagia Sophia, the two scientists from the University of Bern used the technique known as reversed engineering to decipher a "master plan" what is now some 1470 years later. It is based on a heightwidth ratio of 1 to 1.06 of the small square to the larger square. On the basis of the investigations they have performed to date, the researchers have arrived at the conclusion that "there are no building plan related points or lines in the Hagia Sophia that cannot be deduced from this master plan using geometric logic."

Ingenious Design Principle
This design and building principle describ ed by Volker Hoffmann as the "master plan" of the Hagia Sophia is truly ingenious. "Putting it simply, it can be said that the master plan was marked out with pegs and strings on the building site, meaning that the master builder then only had to measure in the double square, which in turn allowed him to transfer across very precisely all the other points (pegs) and lines (strings and/or lines of bearing) of the Hagia-Sophia architectural elements", says the professor for architectural history and preservation of historical monuments from the University of Bern. Next year, following the completion of the laser evaluations and after consulting the museum’s director Mustafa Akkaya, results of this research work are to be presented in the form of an exhibition for the 14 million inhabitants of Istanbul and for the numerous visitors that flock to the Hagia Sophia.

A 354Kb PDF of this article as it appeared in the magazine—complete with images—is available by clicking HERE