Of great symbolic significance, a first application comes immediate, going to navigate in the coveted structure of the famous
Vitruvian Manto discover – not less by the golden circles expansion map – new amazing proportions resulting inside the ideal figure of the human body.
In his celebrated “De architectura” Book III, Chapter 1, Vitruvius mainly points out these proportions of the average adult body (plus many others, for who'd want to prosecute):
“§3. Thus, the navel is naturally the center of the body. In fact, if a man were placed supine with his hands and feet stretched out and the center of the compass was put on the navel, tracing a circumference would tangentially touch the fingers and toes. But that's not all: beyond the scheme of the circle, the figure of the square will also be found around the body. In deed, if we measure from the plane of the feet to the apex of the head, and then we transfer this measurement to the hands outstretched, a length equal to the height will be found, so that distances at right angles to each other, will delineate a square enclosing the figure…”Upon these writings Leonardo da Vinci based his Vitruvian Man. However, a circumference that tangentially touches the toes, to also touch the fingers requires, as we can see, the rotation of the arms of an arc with radius half side of that square, arc approximately (but not rightly) centered about the crossing of the two lines as they were measured to define the square itself, suitable to reach the circle with the extension of an arm.
Here is the basic facility; but how to get the navel to draw the circle?