Photos

HM Emperor of the Holy Roman Empire, Frederick II, built the Castel Del Monte in the 1240s. In a land where snow is rare, it reminds us of the fractal shape of snowflakes. It's a perfect octagon, 123 feet across, with an octagonal center court. Octagonal towers on each corner carry the octagonal theme downward in scale. Its floor plan reflects octagonal Islamic tile work.

The building draws on the most powerful thinking about design and mathematics in the Islamic world. The ground plan, seen clearly in aerial shots of the citadel, perfectly illustrates all possible forms of an eight-sided polygon: four symmetrical axes, simple octagon, eight-pointed star formed by two intersecting squares and the pointed star polygon, universally known as the Islamic eight-pointed star. Castel del Monte is a fractal whose iterations are immediately apparent, one of the most beautiful structures ever to rise from the human mind, and the mind, recognizing it, is naturally captivated.

Frederick II was also a friend to the great mathematician Leonardo Fibonacci, who introduced the Arabic representations for zero and ten into European calculation.
For several years Leonardo Fibonacci corresponded with Frederick II and his scholars, exchanging problems with them. Fibonacci dedicated his Liber quadratorum (1225; "Book of Square Numbers") to Frederick; quite famous are the talks between them. Frederick had in his Court astronomers, philosophers and astrologers of whom he asked very sophisticated questions, ranging from anatomy to ethics, the relationship between body and soul, the essence of elements and agricultural practices. His correspondence on scientific matters with the Arab world was intense and viewed with great suspicion by the Italian Catholic culture.

Some astronomic and mathematical "odds" about Castel del Monte:

1. The presence of the golden ratio in the main portal.
2. The plane of the sundial coincidences with the plane of castels's courtyard.
3. The courtyard at the aequinoxes, noon. Note: the shadow line of the roof coincideces exactly with the edge of the walls; all wall structures are merely texture - and bump - mappings at midsummer solstice, noon and at midwinter solstice, noon.
4. The hidden astronomical characteristics of Castel del Monte courtyard form a rectangle with an aspect ratio of the Golden Number.
5. A nautilus is sculpted into an interior wall at the castle. On the inner wall of the nautilus are inscribed the Fibonacci Numbers.
6. The Fibonacci numbers grow at a rate measured by a certain mathematical constant called the Golden mean. The Golden mean is thought by many people to describe the most aesthetically pleasing rectangle. Starting with such a rectangle, you can partition it so that it circumscribes a logarithmic spiral, which in turn models the shape of a shell of a chambered nautilus.
7. One can go upstairs through the nautilus shaped stairs that are made in counter clockwise sense as to indicate that from that moment on, all the knowledge will be turned over.
8. There may be a mathematical link between the anatomical structure of the cochlea and the theoretical structure of our tonal musical system. The mathematician Pythagoras believed that music was a musical expression of numbers. He discovered that the same ratios of the consonances in our current musical system have the capability of reproducing themselves (the ratio can reproduce itself within itself). These ratios are referred to as "golden ratios" or "golden rectangles". Interestingly, the structure of the cochlea also exhibits ratios of a "golden rectangle".

One question still remains: the number eight. Castel del Monte has a total of 56 facets (8 walls, with 48 sides on the 8 corner towers)."The fact that the number "eight" keeps cropping up in the structure has made some people suppose that such an obsession concealed a magic significance. In the esoteric doctrine, "8" symbolized INFINITY both horizontally and vertically, and is also the number of the wind-rose…"

One such chart is the Carta Pisana, drawn at the end of the thirteenth century. an interesting depiction of an octagonal compass that exactly matches the shape of the layout of the Castel del Monte. A mosaic of similar form in the Alhambra exhibits an additional step in the development of the 8-pointed star figure.

Modern geneticists have found that the DNA-RNA "dialogue" - the molecular information system governing life and evolution - is transmitted by 64 (8x8) codons.

Can be continued infinitely…

The aerial photos show that the tangents of the octagon forming the inner courtyard intersect at the centers of the octagonal corner towers: they form an eight-pointed star whose tips lie at the centers of the towers. Eight-pointed stars may also be drawn around the corner towers. The close geometric connections between the 8 stars thus created provide evidence that the size of the towers was not chosen arbitrarily, but follows a precise geometrical system. The geometric design of Castel del Monte is an example of a configuration with an inner aesthetic.


Hope you'll enjoy it.

This is for my friend Professor Atalay.

* in the ws the origial photo *