John Sims “MathArt Brain” Arts & Communications
Luca Pacioli "Without mathematics there is no art."
THE GOLDEN MEANNature • The Golden Mean, 1.61803398874989…, represented by the Greek letter phi, is a naturally occurring number, like pi, that repeatedly occurs in various relationships. Like pi, it is an irrational number. Unlike pi, it clearly and regularly appears in the growth patterns of many living things, like the spiral formed by a seashell or the curve of a fern.
THE GOLDEN MEANArt • The Greeks discovered they could create a feeling of natural order, as well as structural integrity, in their works. Artists since have used it for the same reason, to create a feeling of natural order in their works. It is thought by many people to describe the most aesthetically pleasing rectangle.
Golden Rectangle: Modern artists use it, and even the ancient Greeks used it to develop the facade of the Parthenon.
Golden Mean • The Fibonacci Series and the Golden Mean are intimately connected. The Fibonacci Series numbers increase at a rate equal to (actually, oscillating round) the Golden mean.
A rectangle whose sides are related by phi (such as 13 x 8) is said to be a Golden Rectangle. It has the interesting property that, if you create a new rectangle by swinging the long side around one of its ends outward from the rectangle, to create a new long side, (in combination with the short side), then that new rectangle is also a golden rectangle. In the case of our 13 x 8 rectangle, the new rectangle will be 21 x 13. We see that this is the same thing that's going on in the Fibonacci Series.
The Fibonacci Sequence: If you dissect a work like Perugino's Madonna Enthroned with Child and the Saints John the Baptist and Sebastian you will notice that the saints are set into rectangles which reflect a .618034 ratio of the total width of the work, measuring from each side inward.
At left, Edward Burne Jones, who created "The Golden Stairs" at left, also meticulously planned the smallest of details using the golden section. Golden sections appear in the stairs and the ring of the trumpet carried by the fourth woman from the top. Can you find more examples?
This self-portrait by Rembrandt (1606-1669)... is an example of triangular composition. A perpendicular line from the apex of the triangle to the base cut the base in golden section.
Leonardo DaVinci used phi when examining artwork for the human body. The famous painting the "Mona Lisa" shows phi, as does a wide variety of artwork throughout time.
Da VinciDrawing studies of the human face is an expression of the Golden Ratio of the Golden Mean
Human beauty is based on the Divine ProportionThe blue line defines a perfect square of the pupils and outside corners of the mouth. The golden section of these four blue lines defines the nose, the tip of the nose, the inside of the nostrils, the two rises of the upper lip and the inner points of the ear. The blue line also defines the distance from the upper lip to the bottom of the chin.The yellow line, a golden section of the blue line, defines the width of the nose, the distance between the eyes and eye brows and the distance from the pupils to the tip of the nose.The green line, a golden section of the yellow line defines the width of the eye, the distance at the pupil from the eye lash to the eye brow and the distance between the nostrils.The magenta line, a golden section of the green line, defines the distance from the upper lip to the bottom of the nose and several dimensions of the eye.
Salvador DaliFlamboyant and controversial Spanish surrealist painter who employed mathematics in some of his work.
Bathsheba GrossmanI'm an artist exploring how math, science and sculpture meet..