What is the Golden Ratio

Question

 what is the golden ratio and how is it used in the human body and everyday life?

Answer 1

The Golden Ratio is (1 + √5)/2 = 1.61803398874989... ≈ 1.618

 

American researcher, Jay Hambridge, established that the Golden Ratio can be found no only in Greek temples and sculpture, but also in the proportions of the human skeleton. The ratio of the total height to the height of the navel is a close approximation to the Golden Ratio. Other researchers have claimed that ratios of many other parts of the human body are also in the Golden Ratio, such as the following: length of an index finger and the distance from the finger tip to the big knuckle, length of a leg and the distance from the hip to the kneecap, length of an arm and the distance from the finger tips to the elbow.

 

There are also rectangles that exhibit the golden ratio and are called Golden Rectangles. They can be found in playing cards, windows, book covers, file cards, ancient buildings, and modern skyscrapers. Renaissance artist Leonardo da Vinci and modern artist Piet Mondrian have incorporated the Golden Rectangle into their works because of its aesthetic appeal. It is believed that classic Greek sculptures of the human body were proportioned so that the ratio of the total height to the height of the navel was the Golden Ratio.Polycleitos (c450-440BC) used the Golden Ratio in creating the proportions for his Doryphoros, the Spearbearer. The Golden Rectangle was also used many times in the design of the Greek temple, the Parthenon. 

 

The Golden Ratio can also be found in the Fibonacci Sequence: 1,1,2,3,5,8,13,21,35,55,89,144,233,...

3/2 = 1/5,

5/3 = 1/6666...

8/5 = 1.6

13/8 = 1.625

21/13 = 1.6153...

233/144 = 1.618055...377/233 = 1.618025...

 

Also it is found in a sunflower. There are 55 clockwise spirals and 34 counterclockwise spirals. 55/34 = 1.617647...

 

The pentagram, famous as a magical or holy symbol contains the Golden Rectangle.

whole length/long part = long part/short part = 1.618

 

In Trigonometry 2sin54° = 1.618033989

 

As you can tell, I'm a little obsessed with the Golden Ratio. I'm a former geometry teacher and used to have my students gather in groups and measure all those different parts of their bodies. That was much more fun than listening to me lecture. They were amazed how those body parts actually did approximate the Golden Ratio.