The Golden Ratio

Dating back to over 2,400 years ago, famous mathematicians including Pythagoras and Euclid have dedicated countless hours into the study of what is now referred to as the Golden Ratio. This perfect ratio has been a topic of interest for mathematicians, philosophers, architects, and even artist. Ancient Greeks used mathematics to develop a relationship between beauty and truth. Aristotle believed in the existence of an ideal median that divided two extremes of a single entity. This perfect balance between excess and deficiency must satisfy properties such as symmetry, proportionality, and harmony. The Golden Ratio encompasses all of these characteristics and has been the cornerstone for architects and artists due to its aesthetically pleasing visual representations. The Parthenon is believed to have been designed using approximations of the ratio. Renowned artists such as Leonardo DaVinci and Salvador Dali are believed to have incorporated the ratio into some of their most famous artwork. The Golden Ratio, represented by the Greek letter Φ, is approximately 1.61803...or [ (1+√5)/2 ]. This is an irrational constant, meaning that it can’t be plotted on a number line because its decimal places go on infinitely, never converging to a finite value. By many, the Golden Ratio is thought to be a preexistent model for the natural balance of equilibrium that is a part of any changing life form. Below are several geometric representations of the ratio, and how it is found in the human body. Next post I am going to touch on how this ratio is found in countless mathematical sets including the Fibonacci Sequence. Because some of these pictures are difficult to understand I have included the verbal proportions of the body as well.
*Note all of the following ratios are equivalent, but the perfect ratio can only be approximated based on how close your body is to having the ideal proportions.
Length of face: width of face
Distance between the lips and where the eyebrows meet: length of nose
Length of face: distance between tip of jaw and where the eyebrows meet
Length of mouth: width of nose
Width of nose: distance between nostrils
Distance between pupils: distance between eyebrows