5/11/14

Math is Golden


You are probably guessing from the title that I'm talking about the Golden ration or phi, the Greek letter. The golden ratio is equal to 1.61803398875 and so on and so forth. More information on phi here. Don't get phi and pi mixed up. Phi is the golden ratio, pi is related to ovaloid things. Got it?
The idea behind the golden ratio is that, if you divide a line into two sections, the longer part divided by the smaller part will equal the whole length divided by the longer part. In this way, you can create a perfect rectangle, one that pleases the eye.
The golden ratio is found everywhere, it appears in nature as well as human made constructions. While it isn't as famous as pi, it is pretty important.
Most animals are built according to the golden ratio. Shells, seeds, pine cones, hurricanes and spiral galaxies are shaped according to the golden ratio. The number of flower petals on different flowers respond to the Fibonacci sequence. DNA follows the Fibonacci sequence! The golden ratio is everywhere! (15 examples)
And the Fibonacci sequence. The Fibonacci sequence is a sequence which Leonardo Fibonacci came up with when trying to calculate the ideal expansion pairs of rabbits over the course of one year. Each number is the sum of the two numbers that precede it, for example:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.
How is this related to the golden ratio?
Well, when you take a successive pair of numbers, the ratio is very close to the golden ratio. The larger the pair, the closer it is.
The golden ratio is thought of as the most pleasing to the eye. Many people try to use the golden ratio, such as the ancient Greeks with the Parthenon.
What I find is the most fascinating is the fact that the golden ratio is found everywhere in nature, everywhere you look. The golden ratio isn't close to a fraction like 3.14 is, it slips between fractions.
What do you admire about this golden ratio?


UPDATE: Next time, the Goldbach Conjecture and the Weak Goldbach Conjecture

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