Probably the most famous example is The Vitruvian Man (pictured left), upon which, three sets of golden rectangles can be superimposed, covering the head, torso and legs.
Remarkable, I think you'll agree.
But wait, there's more. If we take the Mona Lisa, and draw a rectangle whose base extends from her right wrist to her left elbow, and vertically to the top of her head, we get a golden rectangle! Furthermore, if we draw nested squares inside this rectangle, the edges of these squares touch all the important focal points of the painting. (See below.)
But, alas Leonardo was an intellect the like of which we will not see again for millennia. Who now would have the precision, imagination and lightness of touch necessary to combine the aesthetically pleasing with the geometrically exact? Who would have the subtlety, the grace, the wisdom?
Oh, never mind...
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