Squaring the Circle of Sophia

This article is dedicated to the Hagia Sophia in Istanbul, Turkey. It illustrates how the geometry of the building is in a stunning and mind blowing way based on ‘squaring the circle’, circles and squares of identical circumference and perimeter. From the date of its construction in 537 AD it served as a Christian cathedral and was dedicated to the Wisdom of God. Its full name in Greek is Naos tēs Hagias tou Theou Sophias, "Shrine of the Holy Wisdom of God" (squaring the circle?). This article is dedicated to the Hagia Sophia in Istanbul, Turkey. It illustrates how the geometry of the building is in a stunning and mind blowing way based on ‘squaring the circle’, circles and squares of identical circumference and perimeter. From the date of its construction in 537 AD it served as a Christian cathedral and was dedicated to the Wisdom of God. Its full name in Greek is Naos tēs Hagias tou Theou Sophias, "Shrine of the Holy Wisdom of God" (squaring the circle?).

In 1453, Constantinople (present day Istanbul) was conquered by the Ottoman Empire and the cathedral was converted into a mosque. Famous in particular for its massive dome, it remained the world's largest cathedral for nearly a thousand years, until Seville Cathedral was completed in 1520. In 1931 it was secularized and opened as a museum on 1 February 1935. On 24 July 2020 it was turned into a mosque again - edit 2020. The Hagia Sophia is considered the epitome of Byzantine architecture and is said to have "changed the history of architecture".

Let's start with squaring the circle. The circumference of the circle below is identical to the perimeter of the square.

We add two circles that are identical to the first circle, while the arrows (see above) indicate their locations.

The two circles are used to construct two new squares, based on ‘squaring the circle’.

We now construct a square that exactly encompasses the central circle.

This new square is used to construct yet another circle based on ‘squaring the circle’. Not only is the circumference of this new circle identical to the perimeter of the square, the circle also intersects the previous diagram as indicated by the arrows.

When we take the lines out that we don’t need any more, we get the following (the top and bottom lines of the central square have been extended).

If we now superimpose the above diagram on the floor plan of the Hagia Sophia, we get the diagram below. Please, take your time to study this diagram and be amazed about the amount of indicators that show that the floor plan is based on ‘squaring the circle’ in many ways.

Also the extended squaring the circle diagram fits perfectly over the floor plan. See diagram below on the left.

Even a side view reveals many ‘squaring the circle’ connections as can be seen in the diagram on the right. © Bert Janssen, 2017. Edited in 2020. In my book 'the Organizing Principle', I elaborate on this and other comparable subjects. Read also Secret and Sacred Architecture - part 1