Geometry Art Nave, Monreale Cathedral, Sicily and Golden Rectangles

Successive Golden Rectangles dividing a Golden Rectangle into squares.

Monreale Cathedral and Golden Rectangles

Monreale Cathedral
The Cathedral of Monreale is one of the greatest extant examples of Norman architecture in the world. It was begun in 1174 by William II, and in 1182 the church, dedicated to the Assumption of the Virgin Mary, was, by a bull of Pope Lucius III, elevated to the rank of a metropolitan cathedral. The church is a national monument of Italy and one of the most important attractions of Sicily. Source: Wikipedia, Monreale.

Photo credit: David Stephenson.

Golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

Droste Effect
The Droste effect is a specific kind of recursive picture, one that in heraldry is termed mise en abyme. An image exhibiting the Droste effect depicts a smaller version of itself in a place where a similar picture would realistically be expected to appear. This smaller version then depicts an even smaller version of itself in the same place, and so on. Only in theory could this go on forever; practically, it continues only as long as the resolution of the picture allows, which is relatively short, since each iteration geometrically reduces the picture's size. It is a visual example of a strange loop, a self-referential system of instancing which is the cornerstone of fractal geometry. Source: Wikipedia, Droste Effect.

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