Jessica Crabtree

The Golden Ratio is a mathematical relationship in which the ratio of the larger portion to the smaller is the same as the larger portion to the whole. While the number itself is irrational and goes on indefinitely, it is usually rounded to 1.618.

As in many other cases, underlying mathematical patterns in a structure or design often result in an aesthetically pleasing visual form. The mathematical properties of this proportion have fascinated scholars as long as mathematics has been around. They can be observed in the designs of Egyptian pyramids and in Greek monuments (naturally the Greeks were fascinated with it and today it is represented numerically by a letter of their alphabet).

It was all the rage during the Renaissance, as studies like mathematics were being rediscovered with new zest, and humankind’s natural instinct to find patterns in the world went into overdrive. Renaissance men like da Vinci saw mathematical ratios everywhere – from to the proportions of the human body – and incorporated them into their art and architecture. In fact we get the term “divine ratio” from a friend of his, a monk and scholar named Luca Pacioli, who felt he had found God’s formula for ultimate beauty.

Even before the Renaissance, the medieval mathematician Fibonacci (drawing off of Eastern scholars) uncovered a sequence of numbers that follows this very same ratio. Ever since then, scientists have found more and more ways that this ratio is ingrained in the behaviors of the natural world. The Fibonacci spiral, as an example, is visible in everything from the arrangements of flower petals to the strands of our DNA.

Photo from MathematiciansPictures.com.

Whatever our motives in uncovering the patterns that exist in nature – the fact remains that we find them irresistible. Consciously or not, artists constantly borrow from the patterns that make up the natural world. Every time we create art, we recreate nature ourselves on a very small scale – as if by reproducing it we are somehow able to master it. It’s ironic that Renaissance man tried so hard to find divine patterns in himself to prove that he was a superior part of nature. Nature is so very big and we are really such a small part of it. That begs the question, Is art a product of man or of nature? Is nature the art or the artist?

“Art is the imposing of a pattern on experience, and our aesthetic enjoyment is recognition of the pattern.” (Alfred Whitehead North)

ThinkQuest: The Fibonacci Series – more on Fibonacci sequences, da Vinci, and patterns in art

Mathematicians Pictures – lots of interesting posters related to math patterns in art, architecture, etc.

Wikipedia: The Golden Ratio

Space photo from FabulousFibonacci.com.

May 21, 1471: Birth of German Renaissance artist Albrecht Durer

Left: Self-Portrait, Oil on lime panel (1500)

Durer is most famous for his signature work – the ubiquitous “Praying Hands.” The story has it that they are the hands of his brother, who gave up his chance at an art career in order to provide for Albrecht’s training. Praying Hands, brush drawing on blue primed paper (c. 1508)

Whether or not the story is apocryphal, Durer did go on to become possibly the most influential artist of the Northern Renaissance. Durer’s style is characterized by painstaking attention to detail and a focused, dramatic approach to composition. His fascinating portfolio betrays him as a man with an open mind and a curious nature.

He was a prolific artist, and unlike his Italian contemporary Leonardo da Vinci, left behind an incredibly diverse collection of artwork in a wide range of mediums and subjects. Well over a thousand of his paintings, drawings, and etchings have survived to the present day.

Left: Portrait of a Young Venetian Woman,
Oil on elm panel (1505)

Right:
Head Study of a Man Aged 93, Brush drawing on primed paper (1521)

Like da Vinci, however, his most significant accomplishment lay in his ability as a draftsman. Living in Germany in the wake of the printing revolution, he used the crafts of woodcutting and engraving to capitalize on the potential of art reproduction as an industry, making him one the most widely published and esteemed artists of the Renaissance.

Web Gallery of Art – Online Museum Database: Albrecht Durer Biography and Gallery

Below: Wing of a Roller, watercolor/gouache on vellum (1512)
Right: Two Squirrels (1492)
Below right: Young Hare, watercolor and gouache (1502)

April 15, 1452: Birth of Leonardo da Vinci

Leonardo was born near Florence, Italy and spent his career in various Italian city-states during the height of the Renaissance. He is the archetype of the “renaissance man” – inventor, engineer, architect, botanist, anatomist, mathematician, philosopher, musician, sculptor, and artist. His reputation has eclipsed even such contemporaries as Michelangelo and Raphael. And in recent times his legend has undergone something of a renaissance (no pun intended) thanks to Dan Brown.

Out of all his achievements, Leonardo is best remembered as a painter. The Mona Lisa and the Last Supper are still cultural icons and arguably the most famous paintings in the world.

His work largely contributed to the development of modern painting, especially portraiture. Ironically, few of his paintings have survived (not much over a dozen) and many of these are not entirely original due to the practice of sub-contracting work to talented apprentices who exchanged acknowledgment for experience under a master’s guidance.

The bulk of Leonardo’s artistic work consists of his extensive drawings of many subjects, ranging from character studies to anatomy to landscapes.

Leonardo: Master Draftsman – Interactive exhibit from the Metropolitan Museum of Art

Quotes:

“A good painter is to paint two main things, men and the working of man’s mind.”

“Art is never finished, only abandoned.”

“Every now and then go away, have a little relaxation, for when you come back to your work your judgment will be surer. Go some distance away because then the work appears smaller and more of it can be taken in at a glance and a lack of harmony and proportion is more readily seen.”

“The noblest pleasure is the joy of understanding.”