The Golden Rectangle is a rectangle that is based upon the Golden Mean, which is a number that is represented by the Greek Letter phi (F) or represented decimally 1.6180339887499 etc. The dimensions of a Golden Rectangle are 1.618, therefore a rectangle made using the Golden Mean for example be 13 feet by 8 feet. Other examples are 1 X 1, 2 X 1, 3 X 2, 5 X 3, 8 X 5, 21 X 13 and 34 X 21. The reason why all those dimensions make golden rectangles is that 21/13 comes out to be around 1.61904, a few decimal places away from the exact number of the Golden Mean. In nature the numbers contained within the Golden Mean occur again and again in many diverse things. If you start with the numbers 0 and 1, then make a list where each number is the sum of the previous two you have a list like the one below:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on to infinity...
The above numbers are called a Fibonacci Series, after Fibonacci, an Italian painter who while studying the way plants grew, realized they followed the above sequence perfectly. After a plant grew one flower, it would have to grow one more, then two more, and so on, following the pattern exactly. A few more examples of this numerical series in nature are the way a Nautilus constructs its shell, each time growing larger on each spiral using the Phi ratio. And, a sunflower which has 55 clockwise spirals overlaid on either 34 or 89 counterclockwise spirals, again following the Fibonacci series perfectly.
In architecture, the Golden Mean has been used widely throughout history. Originally discovered by Pythagoras, the ancient Greeks constructed their temples to fit the Golden Mean, the classic example of this being the Parthenon in Athens, which makes a perfect golden mean square. The reason why the Golden Mean was used for architecture was that the ratio was very easy to reproduce accurately without using highly technical methods of calculation due to the fact the Golden Mean ratios all differ from the number representing the Golden Mean by less than 0.003. After the fall of Rome, knowledge of the Golden Mean was lost until the Renaissance, when many Italian painters rediscovered the ratio, using it to create perspective in their paintings, to construct buildings and decorate rooms.