photo above of Umayyad Mosque, Damascus by Bernard Gagnon for Wikipedia CC BY-SA 3.0.
In previous articles on double squares and then St Peter’s Basilica, it became clear that squares and double squares have been embodied, within sacred buildings and art, because circles can then spawn golden rectangles from them. A golden rectangleA rectangle whose sides are in the ratio of the Golden Mean (1.618034) or a Fibonacci approximation to the Golden Mean. has one dimension related to its other dimension as the golden meanThe Golden Mean is that unique ratio {1.618034}, relative to ONE {1}, in which its square and reciprocal share the same fractional part {.618034}. It is associated with the synodic period of the planet Venus, which is 8/5 {1.6} of the practical year {365 days}, by approximation. It is a key proportion found in Greco-Roman and later "classical" architecture, and commonly encountered in the forms living bodies take. {1.618034…}. Firstly, the original square plus golden rectangle is a larger golden rectangle but, secondly, the new golden rectangle (beside the square) shares its side length as one unit {1} but its other side is then the reciprocal of the golden mean (0.618034).
The golden mean is the only irrational number whose reciprocal, and square share its fractional part {0.618034 1.618034 2.618034}: there can be only one real number for which this is true. But it is in its geometrical expression, living structure and aesthetics (as in classical architecture) that lead its uniqueness to be seen as a divine ratio. Therefore, it seems, ancient human civilizations sought this golden form of harmony within the form of the Temple, especially in Dynastic Egypt and Classical Greece. The planet Venus must have reinforced this significance since its synod {584 days} is 8/5 of the solar yearFrom Earth: the time in which the sun moves once around the Zodiac, now known to be caused by the orbital period of the Earth around the Sun. {365 days} and its manifestation such as evening and morning stars, move around the zodiacThe 12 constellations through which the sun passes in the solar year of 365.2422 days tracing out a pentacle or five-pointed star, the natural geometry of the golden mean.
The natural geometry of the Golden Mean is the Pentacle, traced out by planet Venus upon the Zodiac as evening and morning star. (from Sacred Number and the Origins of Civilization)
In the renaissance, the Classical tradition of Ancient Greece and Rome was reborn as neoclassicism, a famous proponent being Palladio, and further neo-classicism arose in the 19th Century and continues in the United States. From this, the previous article on St Peter’s saw its original square become rectangular in a golden way. The whole basis for this is due to the nature of squares and circles, that is: golden rectangles are easily formed geometrically through squares and circles.
The extension of St Peter’s from a square, by adding a golden rectangle, can be seen to also apply within the original square. Furthermore, there is a medium-sized square within the golden rectangle plus a small golden rectangle (see below).
The overall golden rectangle of St Paul’s of a square and golden rectangle below. Using the square within the golden rectangle, the original square above can have four such overlapping squares, to create a cruciform pattern, the upper part of which was used to lay out the Umayyad Mosque.
The medium square can be tiled four times within the large square to overlap the other medium squares, as shown above. This creates a small central square while the four regions that overlap are smaller golden rectangles. The lower golden rectangle is also repeated four times with overlapping, twice horizontally and twice vertically. It is seen that squares and golden rectangles can recede within a square, into smaller sizes, or expand around a square. It is as if all levels of scale hold a kind of fractal, based upon the golden mean.
The top six elements of the square can be seen to match the site plan of the Great (Umayyad) Mosque of Damascus, built 900 years before St Peter’s Basilica, on the site of an Orthodox Cathedral and, before that, a Roman temple to Jupiter. In other words, any golden rectangle design can contain resonances of somewhat different golden mean designs, that may express a different meaning or context; in this case the Mosque gives the notion of two squares overlapping to generate an intervening region of blending and the rectangle of overlap will then be phi squared in height (shown yellow below) relative to the width being unity – the central square’s side length.
The geometry of the Umayyad Mosque
My thanks to Dan Palmateer, for his emails and diagramming whilst on this theme of golden rectangles. One of his own pictures (below) shows the central square of the main square, by tiling the main square with the small golden rectangle.
The central square within the greater square is revealed in St Peter’s as a square within a circular area, noting that this plan (held by The Met Museum) was made after the building had been completed.
There was obviously a vernacular of golden rectangular building in Islam which was carried forth in Renaissance Europe. The potential for golden rectangular building can be all-embracing, as it is a property of space itself, due to numbers.