# PENTAGONAL SYMMETRY IN PAINTING - COSMIC HARMONY

The analyses of paintings by Renaissance artists revealed that the composition of their works is based on a rotational pentagonal symmetry very similar to that found in our solar system.

In the Renaissance period, it was widely believed that the Earth was flat and the center of the Universe. No one was allowed to contradict the new scientific discoveries without running the risk of capital punishment for the audacity.

Leonardo had one of the best scientific minds of his time, he was very creative and fond of studying; he tried to depict his cosmic discoveries in his paintings. Not only him, but his contemporaries as well: Raffaelo, Michelangelo and others. These artists did not make their works inside the geometric frame of the central linear perspective, but rather on it, in order to eliminate the hardness and the static resulting from purely geometric lines.

The pictorial space divided into three successive planes was worked as follows: the 2nd and 3rd planes performed by central linear perspective. The 1st one by a two-dimension-cyclical symmetry coupled to the central linear perspective. This is the origin of the third dimension found in Leonardo’s works.

This geometric frame performed mainly in Leonardo’s work called “The Last Supper” was the origin of the baroque. We note in it the static of the background constructed by the linear perspective and the dynamism of the figures and their robes represented in first plane by rotational symmetry.

In his book “Leonardo” (Gráf.Univ.M. Gerais – BH 1995), Santiago Americano Freire discloses his discovery: the invisible structure existing in the great master’s works. He called it stereo perspective and defined it as follows: “Stereo-perspective (new for us) results from a cyclical symmetry of non-finite groups of possible rotations at two dimensions, coupled with the central linear perspective”.

It is interesting to note that the overlapping of images that makes up the new basic concept of my new linear perspective has a pentagon “coupled” to it. It is not a pentagon inscribed in a circle as in Santiago’s stereo perspective, but it is a pentagonal figure with five equal sides. The entire geometric frame of this new exact perspective is performed between the two lines generated by this imaginary pentagon: the line of its base and the line that joins its two opposed lateral vertices.

The stereo perspective will not be covered in this book because it is the work by another author. However, I would like to mention that the harmony and rhythm that it confers to the composition, either figurative or non-figurative and to the third dimension, when it is coupled to the linear perspective, is something that the painter can not ignore.