8:01am (56 notes)
Fig. 17. Geometric constructions of square, √2 rectangles, and octagons, graphite by Mark A. Reynolds
These things are geometric, not natural, and so with the few aforementioned items and with the major exception of the octave in music, we could say then that octagonal systems are mainly a human construct, and we find them frequently used in those contexts. In Leonardo’s day, horoscopes were drawn not as they are today, but in squares, with diagonals and squares rotated through 45 degrees, the basic structure of octagonal symmetry. European philosophers emerging out of the Middle Ages discussed the four seasons and the “Four Cross Quarters” marking the eight major points of a year, the four elements plus their four states diagrammed within an octagon, and the eight major winds of Vitruvius; and on the subject of Vitruvius, we need only look at Leonardo’s now famous Vitruvian Man to grasp the idea. Vitruvius stated that the outstretched arms of a man are very nearly equal in length to that figure’s height; that is, he fits into a square. And when his arms and legs are outstretched to the sides, he fits into a circle. If we reduce these two positions to mathematical signs, the human figure assumes the plus sign and the multiplication sign. Translated to the anatomy of a square, these two symbols are then the midlines and the diagonals in the square’s make up.