Geometry in the Real World

Dubai: Burj Khalifa and Golden Rectangles, HTML5 Animation for iPad

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


Burj Khalifa
Burj Khalifa, known as Burj Dubai prior to its inauguration, is a skyscraper in Dubai, United Arab Emirates, and is the tallest man-made structure in the world, at 2,722 ft. The building officially opened on 4 January 2010, and is part of the new 490 acres development called Downtown Dubai.

The tower was designed by Skidmore, Owings and Merrill, who also designed the Willis Tower (formerly the Sears Tower) in Chicago and the new One World Trade Center in New York City. The Burj Khalifa uses the bundled tube design, invented by Fazlur Rahman Khan. Proportionally, the design uses half the amount of steel used in the construction of the Empire State Building thanks to the tubular system.

To support the unprecedented height of the building, the engineers developed a new structural system called the buttressed core, which consists of a hexagonal core reinforced by three buttresses that form the Y' shape. This structural system enables the building to support itself laterally and keeps it from twisting. Source: Wikipedia, Burj Khalifa.

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 Khalifa and Golden Rectangles

 

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