Monday, January 30, 2012


I'll get back to politics soon. Right now, I'm working on Leonardo stuff in my spare time -- to the degree that I can spare some spare time. Which brings us to our poser for the day:

Look at the Vitruvian Man drawing. Question: How many of you know why the circle is where it is? And why it is the size it is?

For some reason, you won't find the answer anywhere on that Wikipedia page. Neither will you find it in most other websites and books which talk about this drawing.

Yet the solution is childishly obvious.

If you're tempted to blather on about the "golden ratio" or the pentagram or the heptagram -- FAIL! The answer is a lot more obvious than that. What puzzles me is why more people don't see fit to mention it.
A continuation of the arcs described by the movement of the four limbs?
First prototype of American Gladiators Atlasphere?

It's centered on his navel.
Good catch, Viowacity. But why is the circle that size?

Hint: The answer has nothing to do with the drawing of the man. Even if there were no guy in the picture, Leonardo still would have derived that circle from that square -- same sizes, same positions, same relationship between the two geometrical objects.

The answer is so insanely simple you'll just crap when you find out.
The circle has the same area as the square.

One takes the square, rotates it 45 degrees, and the top of the rotated square becomes the top of the circle. Then, one finds the middle-point between the bottom of the middle square (at the center) and the top point of the rotated square. Once that middle-point is found, one can take a compass & draw the circle starting from either the top or the bottom/center.
A guide?
Hoarseface -- you got it! There's only one problem with what you say: The circle and the square do NOT have the same area.

"Squaring the circle" is an ancient problem, and Leonardo was obsessed with it. After his time, it was proven to be impossible to square the circle.

However, there's a fellow on the net -- I don't have the link at the moment -- who has used the Vitruvian Man glyph to create a circle with the same area as the square. It's more complicated than I can go into here.

A geometer would not simply rotate the square, of course. You're supposed to create an octagram using just a compass and straight edge. You do this using a technique you learned about in high school -- and promptly forgot. (If you're like me, that is.)

Basically, you place the point of the compass on one corner of the square, then draw an arc that passes directly through the center. You'll divide the line in a ratio known as "the sacred cut."

Sorry -- I know that term sounds new agey. But the nomenclature is ancient and thus pretty much inescapable.

Leonardo was obsessed with octagons. You see octagon after octagon in his notebooks. I haven't seen any evidence that he cared about any other geometrical construction. All this talk about Leonardo's use of the so-called "golden ratio" is hooey, as far as I can see.

There is a LOT more to be said about this -- especially in regard to the Last Supper and the de Ganay version of the Salvator Mundi. (Hint: Look closely at the design in the leather band of the Salvator Mundi -- either the de Ganay or the "authenticated" Cook version.)

"owever, there's a fellow on the net -- I don't have the link at the moment -- who has used the Vitruvian Man glyph to create a circle with the same area as the square."

I should have said that he claims that he can do this with 99 percent accuracy. No one can devise a 100 percent accurate method.

Basically, there are two small dots on or near the clavicles of the Vitruvian Man. Place the point of the compass there.

That's a hint.
Link to the article by Tom Pastorello, saying Leonardo squared the circle with straightedge and compass (or rather, he almost did, because it's impossible).
Templar crosses and the Dome of the Rock and Ishtar and stuff.
Is this something to do with the Platonic Solids?

Synchronicity at work:
FWIW, I didn't know the answer ahead of time - but when the initial comments didn't provide an answer, I went looking for it myself.

And while I didn't mention that the areas of the square and circle were not perfectly equal, I was aware of it when I posted my comment and chose to omit that detail.

I was aware of it because it's addressed in the page I found that gave me the answer:

Which, for someone like myself who didn't want to spend too much time on the matter, gives a pretty good summary of the geometry involved along with helpful visual aides.

So it's not that I already knew the answer because of the profound breadth and depth of my knowledge, it's that I took the 10 minutes to do some Googling to find it.
Apropos pretty much nothing:

I think "Vitruvian" is an excellent name for an erectile dysfunction drug.
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Well, Sextus, if memory serves, Vitruvian was a Roman architect. Which would mean that he was an expert at erecting things.
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