fig. 1
fig. 2 Below is a line with the "real" Golden Section of 1:1,6180339: the line b-c has the same ratio to the line a-b as the line a-b has to the line a-c (or the shorter line has the same ratio to the longer line as the longer line has to the whole line): (see fig. 3) fig. 3 Of course we can now look at the ratio of the distance between the lines with the smallest distance (blue lines in fig. 2) and the distance between the lines with a little more distance (red lines in fig. 2), as mentioned in the website in which the ratio between the distance from the fingertip and the wrist to the wrist and the elbow was allegedly 1:1,618. (We have to take the average of the distances between these lines, because da Vinci drew this lines apparently by hand, so the distances differ a little.) This ratio is 1: 2,66. Again here is no ratio of 1:1,618. Luckily, da Vinci made notes above and beneath the drawing, so we can see whether these will give more information concerning the used proportions In fig. 4 we can see what da Vinci wrote beneath the drawing. For those who cannot read his notes or cannot read Dutch it says: (sentence with large letters directly under the line with markings): "The length of the spread arms of a man equals his height."
fig. 4 The notes (which are above the drawing of the Vitruvian man) in fig. 5:
Although da Vinci knew Pacioli and in fact worked with him during a few years, there is no evidence that Pacioli used the Golden Section in other fields than mathematics. Pacioli asked da Vinci to illustrate his work "The Divine Proportion", but there is no evidence that da Vinci used the Golden Section in his own work. So far as we can see (by studying all the available texts), the navel in the drawing of Homo Quadratus is just the middle of the circle and that is all. And so it is with many human bodies, but not with all human bodies. Also, when we measure the proportions of the body in the drawing by da Vinci exactly, we can see that the navel does not lie on the exact spot where it should lie according to the Golden Ratio. fig. 6 Also, we can see three points, in stead of one point, depicting the navel. When da Vinci would want to make a point using the Golden Section, it would be more logical, to draw one precise point on the right spot. But he did not. Besides, who needs three navels? One should be enough. I used the middle of the circle to place the red line. I could also have placed the red line on one of the "other navels", since many people state that "the navel" is on the spot, marking a point of the Golden Section. Text by Vitruvius When we see the text written by Vitruvius himself, the matter becomes more clear. ``In the human body the central point is naturally the navel. For if man be placed flat on his back with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.´´ Conclusion The most logical conclusion is that Leonardo da Vinci did not use the Golden Section anywhere in his work, and this includes the drawing of the "Vitruvian Man". It is clear, when we see the drawing, and his connotations on the very same paper, that he used the ratio's of the architect Vitruvius, and that he also did not alter these; he just copied them. In his other works, like the painting "Mona Lisa", the Golden Section is also not to be seen. (But there is another method, which can be seen in his work, and that is the Diagonal Method. See the links page.)
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