ANCIENT GEOMETRY, 4. RENAISSANCE

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The Renaissance saw a rebirth of Classical Greek and Roman culture and ideas, among them the study of mathematics as a relevant subject needed to understand nature and the arts. Two major reasons drove Renaissance artists towards the pursuit of mathematics. First, painters needed to figure out how to depict three-dimensional scenes on a two-dimensional canvas.

Second, philosophers and artists alike were convinced that mathematics was the true essence of the physical world and that the entire universe, including the arts, could be explained in geometric terms. In light of these factors, Renaissance artists became some of the best applied mathematicians of their times.

divine proportiondivine proportion

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The first printed illustration of a rhombicuboctahedron, byLeonardo da Vinci, published in De divina proportione.

Written by Luca Pacioli in Milan from 1496–98, published in Venice in 1509, De Divina Proportione was about mathematical and artistic proportionLeonardo da Vinci drew illustrations of regular solids in De divina proportione while he lived with and took mathematics lessons from Pacioli. Leonardo’s drawings are probably the first illustrations of skeletonic solids, which allowed an easy distinction between front and back. Skeletonic solids, such as the rhombicuboctahedron, were one of the first solids drawn to demonstrate perspective by being overlaid on top of each other. Additionally, the work also discusses the use of perspective by painters such as Piero della FrancescaMelozzo da Forlì, and Marco Palmezzano.

It is in De Divina Proportione that the golden ratio is defined as the divine proportion. Pacioli also details the use of the golden ratio as the mathematical definition of beauty when applied to the human face.

“The Ancients, having taken into consideration the rigorous construction of the human body, elaborated all their works, as especially their holy temples, according to these proportions; for they found here the two principal figures without which no project is possible: the perfection of the circle, the principle of all regular bodies, and the equilateral square.” from De Divina Proportione (1509)

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