Machu Picchu, Geometry, Online Education

The Taj Mahal and Golden Rectangles, Droste Effect, Fibonacci Spiral, HTML5 Animation for Tablets, iPad and Nexus

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

Taj Mahal
The Taj Mahal is a mausoleum located in Agra, India, that was built under Mughal Emperor Shah Jahan in memory of his favorite wife, Mumtaz Mahal. While the white domed marble and tile mausoleum is most familiar, Taj Mahal is an integrated symmetric complex of structures that was completed around 1648. Ustad Ahmad Lahauri is generally considered to be the principal designer of the Taj Mahal.

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.

 

The Taj Mahal and Golden Rectangles, HTML5 Animation for iPad and Nexus