Golden Ratio
The Full Story and Applications in Real Life
Greatest mind of the Earth from all ages, from eminent mathematicians like Euclide or Pythagoras to modern artists, physicists have spent hours to work on this ratio's properties.
For two quantities x and y (x>y), they are in golden ratios if their ratio equals to the ratio of their sum to the number x:
Because of its definition, the ratio has a complex relationship with the Fibonacci sequence as whenever we take the ratio of any two successive Fibonacci numbers, it gets closer to the Golden Ratio.
The ratio has been applied not only to math but also to artists, designers, and scientists. One of the famous examples of this ratio, as I have collected, is the sequence of flower: lily (3 petals), buttercups (5 petals), chicory (21 pedals), and daisy (34 pedals).
The unique property is also applied to snail shells for the logarithmic spiral, the shape of the rectangles that depicts precisely the golden ratio.
Other examples can be found in astronomy, etc:
Spiral Galaxy
Hurricane Katrina
The Pine Cone
Last but not least, beauty. Faces are also bounded with famous examples of Golden Ratio. Each part on one's face is positioned at sections in the Golden Ratio. Although there are differences between people, as the population gets higher, that average ratio limits to the phi number. People have been said to be more attractive to people whose "ratios" are closer to phi.
The mysterious painting of Mona Lisa