Leonardo da Vinci’s famous depiction of Vitruvius encodes geometrical gnosis that’s hidden deep beneath the collective unconscious. Let’s man handle these esoteric concepts and bring light to where there is darkness
Leonardo was familiar with the golden ratio and modeled Vitruvian’s square and circle off it.
It turns out that this Phi ratio is almost exactly smack dab in the middle of the two solutions of ‘squaring the circle’, that is drawing a square that is commensurate to a circle, either by having equal areas, or equal perimeters ( or lengths).
If the circle has a radius of 1, and thereby a diameter of 2, a square with the same area has a width of the square root of π. A square that has the same perimeter as the circle has a width of π divided by 2.
The square with the same area as the circle (in blue) is wider than the square that has the same perimeter (in green). The square Leonardo used (in gold) is just about half way between these two different geometrical formulas. Since the human body, as well as all life, utilized phi ratios in its construction, Leonardo decided to use this prolific ratio for the width of Vitruvius’ square.
The circle extends 12.8379% beyond the width of the blue square (equal areas).
The circle extends 27.32395% beyond the width of the green square (equal perimeters).
The golden square, which is in Phi proportion, extends 23.60679% beyond the width of the circle. (The square root of five is 2.2360679..)
The golden square lies in between these two geometrical solutions. But isn’t not perfectly in the middle. If you want to say it is, well that would only be a 97.08% correct statement.
The circle extends almost exactly 20% (20.0809%) beyond the mean of the blue and green squares (not shown). What’s interesting is that this is the ratio of 6/5, which is ubiquitous in the study of ancient cultures and geometrical/mathematical esoterica. This is a 99.93% accurate correlation, using the traditional value of π. (3.14159265..)
“I see 6/5 more as a resonance built into the architecture of the universe.” – Scott Onstott
”He who joins the hexagram and pentagram has solved half of the sacred secret.” –Eliphas Levi (19th century magician)
The Snowflake and the Flower (six and five)
“ [The existence of pentagons and hexagons] doth neatly declare how Nature Geometrizeth and observeth order in all things.”
– Sir Thomas Browne
“Squaring the circle” is the alchemical process of transferring an airy concept from the mental plane to the physical dimension so that objective conception and birth become a demonstrative reality. – Dr. John Munford
“The squaring of the circle is a stage on the way to the unconscious, a point of transition leading to a goal lying as yet unformulated beyond it. It is one of those paths to the centre.” – Carl G. Jung
Leonardo Da Vinci’s ‘Vitruvian Man’ displays Man within a circle and a square. The square he used is a consolidation, a duality of two distinct solutions to ‘squaring the circle’, or obtaining the unobtainable. We can never truly square the circle due to the nature of π. Did Leonardo hide the solution of this ancient philosophical quandary by suggesting that man is the mean between two transcendental impossibilities?
“Squaring the circle was a problem that greatly exercised medieval minds. It is a symbol of the opus alchymicum, since it breaks down the original chaotic unity into the four elements and then combines them again in a higher unity. Unity is represented by a circle and the four elements by a square. The production of one from four is the result of a process of distillation and sublimation which takes the so-called “circular” form: the distillate is subjected to sundry distillations so that the “soul” or “spirit” shall be extracted in its purest state. The product is generally called the “quintessence,” though this is by no means the only name for the ever-hoped-for and never-to-be-discovered “One.” It has, as the alchemists say, a “thousand names,” like the prima materia.”
— Carl Jung