The Golden Ratio is Everywhere!

Ben Ochsner&

Amber Story

Background

If one were going to design a rectangular TV screen or swimming pool, would a particular shape be more appealing in terms of the overall pleasing affect it has on the human eye? Since the time of the Greeks, the ratio of length to width, approximately 1.618 has consistently been considered the most visually appealing. This ratio, termed the “Golden Ratio” not only appears in art and architecture, but also in specific natural structures. A golden rectangle is such that its side lengths are in the proportion of 1.618:1; the length of any golden rectangle is a little more than 60% greater than the width.

Background

Civilizations dating as far back as the Ancient Egyptians, the Mayans, as well as the Greeks all discovered the significance of the Golden Ratio and have thus incorporated it into their art, architecture, and structural designs. They discovered that the Golden Ratio happens to be nature's perfect number. For some reason, it just seems to appeal to our natural instincts. This project attempts to look deeper into that significance over which the Golden Ratio has impacted human understanding insofar as where it can be seen, how it can be used, and why it is so appealing to the human eye.

Phi and the Fibonacci Series

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, . . .• The ratio of each successive pair of numbers in the series

approximates phi (1.618. . .) and as the numbers get larger the closer to phi the ratio gets.

For example:2:1 = 1 3:2 = 1.55:3 = 1.668:5 = 1.613:8 = 1.62521:13 = 1.615***After the 40th number in the series, the ratio is accurate

to 15 decimal places.

Divine Proportions

One concept of the Golden Ratio that became immediately interesting to our research was the idea of divine proportions. As such and from a section in the book The Golden Ratio and Fibonacci Numbers, by R. A. Dunlap, the author discusses how the “Golden Ratio” was used divine proportions and thus proved in the composition of the human body. To get a better understanding of this concept, one has to know how the measurements evolved in this specific way.

Divine Proportions

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The Divine Proportion in the Body

• The black line is the body's height.

• The blue line, a golden section of the black line, defines the distance from the head to the fingertips

• The yellow line, a golden section of the blue line, defines the distance from the head to the navel and the elbows.

• The green line, a golden section of the yellow line, defines the distance from the head to the pectorals.

• The magenta line, a golden section of the green line, defines the distance from the head to the base of the skull.

Divine Proportions

Person: Ben Katlyn TJ Mark Aaron AmberBody Height 65 53 62 75 74 52Head to Finger Tips 37 1.76 32 1.66 37 1.68 46 1.63 45.7 1.62 32 1.63Head to Navel 23 1.61 24 1.33 23 1.61 28.5 1.61 28.3 1.61 19.8 1.61Head to Pectorals 17 1.41 16 1.5 14.2 1.62 17.5 1.63 17.5 1.62 12.2 1.62Head to Base of Skull 9 1.89 9 1.78 8.5 1.65 10.8 1.62 10.8 1.62 7.6 1.61

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Phi = 1.618033988749895...

See the Golden Ratio is

Everywhere!!!