Geometry in the Real World

Dubai: Burj Al Arab Hotel at Night and Golden Rectangles, HTML5 Animation for iPad

Successive Golden Rectangles dividing a Golden Rectangle into squares (logarithmic spiral known as the golden spiral).


Burj Al Arab
Burj Al Arab is a luxury hotel located in Dubai, United Arab Emirates. At 1,053 ft, it is the fourth tallest hotel in the world, however 39% of its total height is made up of non-occupiable space. Burj Al Arab stands on an artificial island 920 ft from Jumeirah beach and is connected to the mainland by a private curving bridge. The shape of the structure is designed to mimic the sail of a ship. Source: Wikipedia, Burj Al Arab.

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.
 

Dubai: Burj Al Arab Hotel at Night and Golden Rectangles

 

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