Interesting Facts About the Golden Ratio in Nature, Art, Math and Architecture
What is the Golden Ratio? If you ask different people you might a find a few that have been exposed to it in their field of work or in their hobby. If you ask an artist, you might be told that the golden ratio is a method of geometrical use of space in a painting. A biologist will explain how the golden ratio is found in the beauty of nature. A mathematician can provide solutions ranging from simple algebraic and geometric problems to more advanced problems in number theory. A medical doctor will share with you how the golden ratio is found in human body’s anatomy. What is truly amazing is that all these explanations, and many others, for the golden ratio are all correct!
In fact, the ancient Greeks saw this ratio as being so special they gave it its own name and they called it Phi (Greek symbol:φ). The same name still used today. The mathematical value is approximately 1.618….
The Greeks used this ratio to construct proportional rectangles which they believed as being the “most beautiful rectangles” These rectangles have their sides formed using this ratio. See figure below: (With figure "b" just a 90 degree rotation of the smaller rectangle to the left in figure "a".
Figure #1 Credit Reference #1
If you insert rectangle (b) into rectangle (a), the resulting space will be a square of sides “y.”
Figure #2 Credit Reference #1
As shown in the figure above, this process can be repeated over and over again resulting in smaller and smaller rectangles. This spiraling effect is what makes these rectangles so unique and the reason the Greeks saw this ratio as being so important. Let us explore a few examples is architecture:
The Golden Ratio in Architecture
1) The Great Pyramid of Giza
The Great Pyramid of Giza in 4700 B.C. with proportions according to a "sacred ratio."
Picture #1, Credit Reference #2
In above figure, “h” is the height of the pyramid, “b” is half the length of the base, and “a” is the height of a triangular face. The ancient Egyptians constructed the Great Pyramids in such a way that the ratio (b : h : a) is approximately equal to (1 : √φ : φ).
The Greek sculptor Phidias sculpted many things including the bands of sculpture that run above the columns of the Parthenon.
Picture #2, Credit Reference #3
See how each major portion of the design fits into a red box or rectangle.
3) United Nations Building
The ratio for width to height for every 10 floors is the golden ratio.