The central part of Hagia Sophia is a cubical shell obtained by removing the interior of the cube
and parts of its walls. On top of it we have a flat cube in which two cylindrical shapes were
removed. Finally on top of this element we have a half sphere from which the interior was
removed. In a similar way the two parts adjacent to the central nave were constructed. Again we
have here two halves of cubes and two quarters of a sphere. Overall, Hagia Sophia is a very
complex and at the same time visually very clean assembly of geometric objects. There is also
hidden geometry that a normal person may not see even after careful examination of the building.
Locations and sizes of particular elements, e.g. entrances, columns, niches, arches, were established
using Euclid’s mean and extreme ratio property (see [4]). Sizes of major part of the basilica were
established using the side-and-diagonal numbers.