The Golden Ratio and Rectangle

The golden ratio is such that the biggest length divided by the medium length is equal to the medium length divided by the smallest length. The value of the golden ratio is 1.618 and can be found throughout the universe. The golden ratio is fractal in form. For example, the smallest length on a large scale can become the biggest length on a smaller scale. This scaling of length can continue ad infinitum, creating fractal designs. Since mass in the expanding universe is fractal, being composed of both matter and light, the golden ratio can be found readily where matter exists. The golden ratio is the basis for many fractal forms. One example is the golden rectangle. This rectangle is constructed based on the golden ratio. Dividing the long side by the short side results in the golden ratio. The golden rectangle is fractal in nature. If a square having sides equal to the length of the short side is inscribed inside the golden rectangle, then the left over piece of the rectanle is another golden rectangle. This subdividing of the golden rectangle can continue ad infinitum. There are many other examples of figures that are based on the golden ratio, but Aatucagg is particularly interested in the golden rectangle, since this is the geometry from which the golden spiral can be created. However, there is another way to create the golden spiral using a tiling of fibonacci numbers. The fibonacci numbers is a sequence of numbers such that dividing each successive number by the previous number converges on the golden ratio of 1.618. For example, in the fibonacci sequence 5 is followed by 8. Dividing 8 by 5 yields 1.600, which is a poor approximation if rounding to the nearest one thousanths. In the fibonacci sequence 144 is followed by 233. Dividing 233 by 144 yields 1.618, which is an accurate approximation for rounding to the nearest one thousanths. Where as the construction of the golden rectangle begins with the fully formed rectangle and is then subdivided, the fibonacci tiling starts from the inside and builds towards the fully formed rectangle. The more tiling that is used, the larger the rectangle will grow and the more accurately it will take on the dimensions of a true golden rectangle.

IMAGE LINKS:
Golden Rectangle

VIDEO LINKS:
The Golden Ratio and Rectangle
Golden Mean