# The Golden Ratio

by
**ZachWech**

Last updated 5 years ago

** Discipline: **

Math ** Subject: **

Geometry
** Grade:**

11

The GoldenRatio

What is it?The Golden Ratio (Also known as Phi and the Divine Proportion) is a special irrational number found by taking a line and cutting it into a long section and a short section. When you divide the long section by the short section it gives you the same number as dividing the whole length by the long section (That number being Phi). The value of the Golden Ratio is 1.618 or (1 + √5) 2

Where is it?The Golden Ratio is found in many places like architecture, nature, and, most importantly, in the human body.

The TeethAs seen to the right the height of the central incisor to the width of the two central incisors gives a golden proportion. Also, the four front teeth, from central incisor to premolar are the most significant part of the smile and they are in the Golden Proportion to each other.

The Hands/ArmsThe golden is found in your hand. Each section of your finger, from the tip to the base of the wrist is larger than the preceding one by about the golden ratio of 1.618. Also in all adjacent sections of your fingers, the section closest to the wrist is larger than the next section by approximately 1.618.The golden ratio is also in your arm. If you measure your hand from the tip of your middle finger to the wrist, multiply by 1.618 and you will end up with a number close to the distance between your elbow and your wrist.

The number 5The golden ratio is also connected to the number 5 as there are 5 appendages to the body (the head, arms, and legs). There are then 5 appendages on each of those (the 5 fingers and toes). Also there are 5 openings on the face which are the mouth, nose, and eyes. Lastly, the 5 senses (sight, sound, touch, taste, and smell)

The FaceMany proportions on the human face give phi. The proportions of the length of the nose, the position of the eyes and the length of the chin, all conform to some aspect of the Golden Ratio. As shown to the right.

Phi and The Fibonacci SequenceThe Golden Ratio is very related to The Fibonacci Sequence. When you take any two sucessive numbers from the sequence and divide the bigger number by the smaller the number is approximately Phi. The further down the sequence you go the more and more close the number gets to being exactly Phi.

www.Mathisfun.com

www.Goldennumber.net

www.Goldennumber.net

http://jwilson.coe.uga.edu/EMAT6680/Parveen/GR_Dentistry.htm

www.goldenspiralmarketing.com

www.artofraz.com

The Human EmbryoDuring the human embryo development, the human embryo gradually unfolds itself in a such way that it is exactly similar to the the golden spiral unfolds itself as it spins farther away from its center.

http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Hekimoglu/emat6700/golden%20ratio/goldenhuman.html

Sources:- http://jwilson.coe.uga.edu/EMAT6680/Parveen/GR_Dentistry.htm- http://goldenratioiseverywhere.weebly.com/armhand.html- http://www.intmath.com/numbers/math-of-beauty.php- http://www.goldennumber.net/five-phi/- http://www.mathsisfun.com/numbers/golden-ratio.html-

qurangoldenratio.blogspot.com

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