Geometry in the Real World

Dubai: Jumeirah Beach Hotel and Golden Rectangles, HTML5 Animation for iPad

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


Jumeirah Beach Hotel
Jumeirah Beach Hotel is a hotel in Dubai, United Arab Emirates. The hotel, which opened in 1997, is operated by the Dubai-based hotelier Jumeirah. The hotel contains 598 rooms and suites, 19 beachfront villas, and 20 restaurants and bars. This wave-shaped hotel complements the sail-shaped Burj Al Arab, which is adjacent to the Jumeirah Beach Hotel. The hotel occupies a location on the beach. Visitors to the hotel have at total of 364,000 sq ft of beach for their use. Beside the hotel is the Wild Wadi Water Park. All guests in the hotel have unlimited access to the waterpark. Source: Wikipedia, Jumeirah Beach Hotel.

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: Jumeirah Beach Hotel and Golden Rectangles

 

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