Basic dimension of the Hagia Sophia deciphered

Square/circle dual module was the design principle of the “Eighth Wonder of the World.”  Almost one and a half thousand years since its construction in the center of ancient Constantinople, the Hagia Sophia has divulged the secret of its design principle.

Istanbul/Bern/Heerbrugg, July 14, 2004 – Almost one and a half thousand 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-the-art 3-D laser technology. Some of the first laser evaluations are to be shown for the first time in mid-July 2004 in Istanbul at the Congress of the International Society for Photogrammetry and Remote Sensing (ISPRS).

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 UNESCO world cultural heritage site have always remained lost without trace. For hundreds of years, experts have tried to fathom out 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.

The “impossible task” of determining the dimensions
“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.

Constructional wonder of the world from one to one point zero six
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 3-D laser measurements with the aid of a HDS™ 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 height-width 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 reconstructed
This design and building principle described 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. The some two thousand photogrammetry and remote sensing experts who have traveled to the ISPRS Congress taking place in July 2004 will receive the first insights this year in Istanbul at the Leica Geosystems exhibition stand.

To date, nobody had uncovered the secret of the design principle used in this building devoted to Divine Wisdom, the Hagia Sophia. That was until Volker Hoffmann, together with his employee Nikolaos Theocharis, finally succeeded in deciphering it using state-of-the-art 3-D laser measurement techniques some 1470 years later.

  Each point of the Hagia Sophia main dome is recorded in 3D in this HDS laser scan file. Using the Cyclone software, it is possible to view on the PC the building from various perspectives and to measure the coordinates of each point recorded. © Hoffmann-Theocharis/Leica Geosystems



  Just like the entire Hagia Sophia, the south wall is also based on the dimensions of a figure of circles and squares. © Hoffmann-Theocharis/Leica Geosystems 






   The pillar heights also follow the uniform design principle to the precise centimeter of the “master plan” deciphered by Volker Hoffmann. © Hoffmann-Theocharis/Leica Geosystems 








  The south wall of the Hagia Sophia recorded true to scale using laser measuring techniques and Cyclone software also reflects the design principle documented by the master plan in the cross-sectional view to the precise centimeter. © Hoffmann-Theocharis/Leica Geosystems 



  Professor Dr. Volker Hoffmann, engineer Nikolaos Theocharis and art historian Dr. Francine Giese at the Bern Institute for Art History discussing the proportions of the laser images of the Hagia Sophia and how these confirm the dimensions of the “master plan”. Photo: Leica Geosystems



Prof. Dr. Volker Hoffmann, Institut für Kunstgeschichte, Hodlerstrasse 8, CH-3011 Bern
Phone +41 31 631 4743 – Fax +41 31 631 8969 – E-Mail: