Chapter Thirty-Six: The Golden Ratio The Golden Ratio
The Golden Ratio is known by many other names, such as the golden mean, the divine proportion, or the golden proportion. It is represented by the Greek letter Phi (φ), and is an irrational mathematical constant approximately equal to 1.6180339887.
The Greek mathematician Euclid defined the golden ratio over two thousand years ago, in 300 BC, while working with ratios present in geographic figures. For those who forget what a ratio is, it's a proportion used to describe two things, mathematically speaking. For example, 12 is to 4, what 6 is to 2. This statement is valid because the relationship that exists between 12 and 4 (12 divided by 4 equals 3) is the same as that between 6 and 2 (6 divided by 2 equals 3). Particular attention was being given to the structure of the pentagram, due to the magical properties being attributed to it. During his calculations, he defined what is now called the golden ratio:
"A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." ~Euclid
How it works:
What this means is that if you divide a line into two segments, the ratio of the larger of the sections in relation to the entire segment, is equal to the ration of the smaller section, to the longer section. Or, if you were to look at the above line, and create 2 segments within it according to the golden ratio, the total length "a+b", is proportional to segment "a" in the same way that "a" is proportional to the shorter segment, "b".
What is incredible about this number, and what freaked out many mathematicians of the time, is that the number is irrational. There is an infinite number of decimal places, which is really mind-boggling if you think about it. The reason why Phi is such an intriguing number, is that it has a phenomenal way of popping up where it is least expected. In fact, our entire view of the world is changed by the fact that everything and anything can be represented by a number or a fraction, such as phi.
Examples of where its found:
The number phi is frequently found in geometry, especially in figures that have a pentagonal symmetry. If you look at only one point of a five-pointed star, you are looking at an isosceles triangle, which means that two of its sides are of equal length. If you draw a line down the middle of this triangle, such as you would to obtain its height, the ratio of the height to the base of the triangle is none other than phi.
People often wonder why certain shapes are more appealing. While we don't know for certain, there is tremendous evidence that the Golden Ratio is omnipresent in the natural world. In fact, some people have called in Nature's perfect number.
Look at your fingers closely. If you measure the length of the longest finger bone, and then the length of the finger next to it, and then divide the longer length by the shorter one, you should get a number close to 1.168. All parts of the human body are proportional to this number. In fact, if your face is symmetric and follows this ratio, you are often said to be of exquisite beauty.
NOTE: Most information in this Chapter must be credited to
ArithmancyHOL by Rosa Gullveig.