Nearly 500 years after his death, we still admire Leonardo da Vinci’s many and varied accomplishments in painting, sculpture, architecture, science, and quite a few other fields besides, most of which would have begun with his putting down some part of the formidable contents of his head on to a piece of paper. (As we’ve seen, sometimes he needed to draw up a to-do list first.) Some of those works remained on paper, and even became famous in that humble form. If you’ve only seen one of Leonardo’s drawings, for instance, it’s almost certainly Vitruvian Man.
Leonardo’s circa-1490 study of the proportions of the human body — or to put it in more common terms, the picture of the naked fellow standing inside a square and a circle — stands at an intersection of art and mathematics, one at which Leonardo spent a great deal of time throughout his life. The Ted-ED lesson above, written by educator James Earle, gets into “the geometric, religious and philosophical significance of this deceptively simple drawing” whose title references the first-century BCE Roman architect and civil engineer Marcus Vitruvius Pollio, who claimed that “the navel is the center of the human body, and that if one takes a compass and places the fixed point on the navel, a circle can be drawn perfectly around the body.”
Vitruvius also realized that “arm span and height have a nearly perfect correspondence in the human body, thus placing the body perfectly inside a square as well.” Both he and Leonardo saw real implications in this alignment between anatomy and geography, beginning with the notion that buildings and other works of man should also take on these “perfect” proportions. All of this ties in with the problem, first proposed by ancient geometers, of “squaring the circle,” that is, finding a procedure to hand-draw a square and a circle both of equal area. Leonardo used Vitruvian Man to point toward one possible solution using the human body.
You can learn more about the importance and legacy of the drawing in the BBC documentary The Beauty of Diagrams, available on Youtube (part one, part two). “Although the diagram doesn’t represent some huge scientific breakthrough,” says its host, mathematician Marcus du Sautoy, “it captures an idea: that mathematics underpins both nature and the manmade world. It represents a synthesis of architecture, anatomy, and geometry. But it’s the perfection and elegance of Leonardo’s solution to this riddle of the square and the circle in Vitruvius which gives the diagram its power and its beauty.” And judging by the unabated popularity of Vitruvian Man parodies, it looks to have at least another half-millennium of relevance ahead.
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Ralph Steadman’s Wildly Illustrated Biography of Leonardo da Vinci (1983)
Based in Seoul, Colin Marshall writes and broadcasts on cities and culture. His projects include the book The Stateless City: a Walk through 21st-Century Los Angeles and the video series The City in Cinema. Follow him on Twitter at @colinmarshall or on Facebook.
…except, of course, that Leonardo abandoned this avenue of reasoning when he realised the perfect proportions he assumed Vitruvius had found were wrong. The diagram, although famous, shows nothing about human anatomy. It’s 500-year old #FakeNews. Just ask the curator of the Queen’s collection of Leonardo da Vinci works…I paraphrase what he told me 5 years ago:
Roman architect Marcus Vitruvius Pollio who suggested that somehow the perfect man could with arms and legs akimbo transect a perfect circle and a perfect square. In his work, Leonardo measure lengths, ratios and angles but could not find the perfect ratios suggested by Vitruvius 1500 years before. Instead, he obtained odd fractions 5/11’s, 7/17th’s none of which seemed to point to the perfect circle or the perfect man and Leonardo turned back from this dead-end.
https://www.sciencebase.com/science-blog/the-rights-and-lefts-of-leonardo-da-vinci-anatomist.html
thank you, a lot of information made available in one place, let me add to the discourse (for your consideration):
Having actually seen Di Vinci’s Vitruvian Man on display in an Italian museum (Venice) decades ago I realized copies/drawings of it do not reveal the hidden genius of Di Vinci (it was carved into the thick paper not merely drawn on it). It is a masterfully drawn “rebus” of sorts, causing many a learned man/woman has gazed up on its likeness thinking it was a 3D man inside a 2D square and 2D circle (mental gymnastics ensued … about rounding the square or squaring the circle. All missing what was actually there. The 3D man is drawn in a 3D cube and 3D sphere of equal volumes (that is but one of their relationships); proved by the math:
…Di Vinci’s nod to Archimedes AND Vitruvian, if not to Trismegistus too (ternary hides the quaternary):
the cube volume (L*W*H) 6*6*6= 216 and
the sphere volume (radius cubed*pi*4/3) 3.722(cubed)*3.142*(4/3)= 216 (all rounded numbers from the hundredths!)
…rounding the square/squaring the circle (nonsense):
circumference of the square (6*4) would require the circumference of the circle to have a diameter of 7.64 (24/3.142),
Di Vinci’s circle has a diameter of 7.444 it’s a non-starter.
.. along those lines, the golden ratio is also encoded (in plain view, not just encoded in the pyramid math)
Di Vinci’s Vitruvian Man (from the center of the circle/sphere down = 61.8% of the square!
I did pen online (decades ago) my observation of Di Vinci’ ‘Vitruvian Man’ to be in a 3D cube and sphere of equal volumes but was ignored by the academic dogma champions (doggedly hanging on to their “alleged consensus”) squaring the circle (its side is 24.075% longer that the square’s side) or rounding the square (a myopic view to be sure) … much like Stratfordians insisting Shakespeare is magically the work of a lone minor actor/wool merchant (Shak spar) attributing him alone the pseudonym/pen-name and there can be no other (???). Like the surgeon responding to President Reagan’s question (as he lay wounded at hospital after an assassination attempt), “are you a republican?” … the response was, “we are all republicans now” … WE ARE ALL OXFORDIANS NOW TOO (those of us that can smell what the Rock is cooking, in the vernacular of the day).
…drawing a square and circle of equal areas, not a problem… clearly not what he did. Likewise, drawing a cube and sphere of equal volumes math is easy if you know the math. The RELATIONSHIP BETWEEN THEM HAVING BEEN REVEALED in DaVinci’s Vitruvian Man is NO ACCIDENT/MERE COINCIDENCE, others assume he was rounding the square etc. (all the while ignoring the obvious). It is an illusion to think the 3D man is in merely in a 2D square and a 2D circle… he is in a 3D cube and 3D sphere of equal volume values 6*6*6=216=radius cubed*pi*(4/3). KISS (keep it simple) … hidden in plain sight…genius.
DID YOU NOTICE: the sphere’s radius cubed (rounded at thousandths) equals the degrees and minutes of GIZA’s pyramid slope?!?!
…there are TOO MANY “COINCIDENCES” in the Vitruvian man to be mere coincidences…
…there is a lot “more” going on here than just a guy in a couple rudimentary geometric shapes…
…in addition to di Vinci’s “rounding to in his head” accuracy:
another proof (concealed concept?) about volume:
SINCE: L*W*H= volume of cube and radius cubed*pi*(4/3)= volume of sphere
THEN: the diameter sphere that equals any side of cube (it fits into) a sphere will always be 52.359% of the cube … pi/6=.52359
radius cubed*pi*(4/3)= volume
(3.722 cubed*pi*(4/3))= volume
51.562*3.142*1.333=215.956 (who wouldn’t rounded that to 216)
(note: pyramid angle 51.84 … is 3.72867 cubed maybe Da Vinci was off by a few hundredths from his radius)
using his diameter for the volume of the imaginary square that sphere occupies 7.445*7.445*7.445= 412.661646125
…imbedded pattern coincidence: I doubt it to be a parity check but worth noting.
instruction:
sequence of 4 #‘s follow) (1+2=) 3. (skip 6’s) 1 (skip 6) 4 (skip 6) 2 (rounded up form 5) “3.142”
or
(4–1) 3. (instruction: skip next two (66)) 1 (skip one) 4 (skip one) 2 (rounded up from 5) “3.142” is what he used … coincidences do happen it appears (be aware when they are not).
REMINDES ME OF…ONE OF THE IMBEDDED CODES IN REVELATIONS”:
3 separate passages refer to the same period of time “differently””
ONCE WITH GREAT SPECIFICATION (1260 DAYS),
ONCE GENERICALLY (42 MONTHS … a 30-day window), and
ONCE CRYPTICALLY (A TIME, TIMES, HALF TIME … 3.5 years).
…concealing pi masterfully…
numbers used in the ternary (3) concealing the quaternary: 01223456 and a decimal somewhere
… zero thru six with two twos ??? perhaps something is squared or rooted, but what?
… BEYOND ODDLY SPECIFIC THERE IS NO 7,8 or 9 (deliberately out of sight out of mind!!!)
… rev 13:18 (of 666 fame) 13x18=234
… like Da Vinci’s backwards writing (he didn’t do it all the time, so I doubt it was to avoid smearing as he wrote
… 234 becomes 432, add them together viola “666”
…a parity check like rev 12:6 containing 1260
…now you know the real reason for the addition of chapter and verse numbers to the bible in the 1500’s
… reversed the missing 789 to get 987
… 9.87 with the decimal … AND IT IS THE SQUARE OF 3.142 … PI
BACK TO DI VINCI…squares in circles in squares, etc. (aka flower of live in a circle):
volume of a sphere (that has the diameter of 7.445)/volume of a cube (7.445 cubed) = % of cube’s volume occupied by sphere
216.02486/412.5785=.52359 (conversely, volume of sphere*.52359=volume of cube that contains it)
((pi/6= .52359 …))
Archimedes used a cube occupied by a sphere cut in half to determine the relationship between them
(having a flat side (slice) to work with):
volume of sphere with same diameter as a 6x6x6 cube: 113.083722 (who wouldn’t round that to 113)
…113 is the 30th prime number (perhaps he used prime #‘s as we used logarithms … short cuts???)
…113.083722/(6squared)36=3.1412
(5th century AD Chinese mathematician calculated pi to seven places)
(perhaps Da Vinci was oblivious to Chinese advancements)
(though Da Vinci 15th century AD/CE pi looks better than Archimedes 4th century BC/BCE approximations)
(being between 22/7 (3.1428) and 223/71 (3.1408))
(was Da Vinci mocking Archimedes with his improved sphere volume accuracy … Archimedes’ excelled in volume)
(by the 15th cent AD/CE 3.1415926 was known in Europe, something already known in China since 3rd cent AD/CE)
Look, several hundreds of years and none of our mathematicians have stumbled on Da Vinci’ truths in The Vitruvian Man (surely, I am not the 1st, mere decades ago). Archimedes was ham strung with his pi (22/7, 222/7); Da Vinci was not merely regurgitating something others built upon, he found a way to encode it in plain view.