In this video, I'd like to take you through a quick tour of the history of Western art, starting with Leonardo da Vinci and going forward through time. So in this image here, we have LaBelle Ferren year around 1490. And I've overlaid this geometry on the canvas, and I've anchored it right there at the top of the railing and the top of the canvas itself. And what's amazing is that the, the convergence point of the Golden spiral converges right on that piece of jewelry on the woman's forehead, this Farren year, which was a popular adornment in those times. And so also notice that her eyes are also framed by the vertical divisions within that golden rectangle. Let's move forward to 1490 to the year that Columbus discovered America.

Here we have the most iconic Image perhaps in the entire world, the vitruvian man. So Leonardo was depicting the ideal proportions of man based on the writings of the ancient Roman architecture vitruvius. And he's showing that the human body is framed by the square and the circle. But what is really amazing is if you analyze this with the golden rectangles, you can see that the golden ratios shown in the yellow arrows point to significant features within the body. For example, the golden ratio on the square points to the center of the circle. The Golden Ratio on the circle points to the heart center, which is the central chakra in the energetic system of the body.

So we have the we have the physical and the spiritual centers identified with golden ratios. Here's my analysis of the Mona Lisa showing this method of constructing the golden rectangle from the square. And the square is shown with a circle inscribed in it. And you can see that the center of that points right at her eye, and the arc, which is what is used to create the golden rectangle perfectly frames her head. Her body is within the square down below her head up above. Here's another image by Leonardo da Vinci and 1515.

And it's really amazing how precise This is the point of his finger points exactly at that point where we have golden ratios both vertically and horizontally. The golden rectangle is framed on three edges of the canvas. In this image we have john the baptist sometimes called Bacchus pointing to As above, so below or perhaps In the Christian mode on earth as it is in heaven, and it's fitting very well in with this theme of the Golden spiral, which is something that is self similar, that is the same, above and below. This is Michelangelo's Creation of Adam fresco in the Sistine Chapel. a whole series of authors, which I included on this slide, discovered this proportion by measuring the ceiling and they know, they noted that the point where the fingers come together is precisely at the Golden Ratio. I'm just illustrating it here with my proportion, or to call that out graphically.

This is perhaps the second most popular artwork in the world after the Mona Lisa. And you have to ask yourself, why is that so popular? Perhaps it has something to do with the hidden goal. ratio proportions of these images. Here's Vermeer's girl with a Pearl Earring. And you can see when the golden rectangle is framed the top and the bottom of the canvas that these vertical divisions seem to point out her eyes.

And the horizontal division of the golden rectangle goes right through one of her eyes. Also by Vermeer, we have the geographer and the eye of the geographer and the eye of the compass are precisely indicated by golden ratios above and below. Moving forward in history, we're looking at the death of Socrates by Jacques Louis dahveed at the end of the 18th century, and you can see with the golden rectangle framed at the top and the bottom of the work The Golden Ratio runs right through all of the figures heads. That's the horizon line. And the diagonal of the golden rectangle above is what controls the angle of Socrates finger. As he's pointing to truth, right before he dies, that points to the convergence point of that golden spiral.

Here we have another painting about a death, the death of Caesar this time, the end of the 18th century. And the golden ratio is point right to the center of Caesars head, where his third eye would be also one of his killers arm, his arm is following that arc of the golden ratio. The figure on the extreme right seems to be framed by in his elbow touching edge of that golden rectangle. It's very resonant with this proportion. So I believe that this art started with this geometry and then proceeded to flesh out the artwork from there. Here we have the grand odo leads by ONC.

In the beginning of the 19th century, we have this golden rectangle framed on three edges of the canvas and the arc being a mimic of the woman's back and the curve of her back is very much like an arc. Also her face and the details there of her mouth and chin, framed very nicely by the divisions within the golden rectangle. Here we have Salvador Dali's corpus hypercube is in the mid 20th. And I've shown Golden Ratio divisions in the gold color here, both vertically and horizontally, both sides of them and you can see from this grid, the entire artwork was planned using this golden ratio proportion So in the end, we have to recognize that geometry is very much a part of our aesthetic appreciation of artwork. It's something that we might not understand consciously. But some of the most important works in western history.

Were structured using this proportion on the canvas. And I believe the reason that we find them so attractive is because that proportion resonates with something in us with something in our visual subsystem in our brains, or perhaps even deeper, perhaps even in our DNA. There is something that resonates with the golden ratio.