Several Circles (1926) by Wassily Kandinsky and the Golden Rectangle

Successive Golden Rectangles dividing a Golden Rectangle into squares (Several Circles by Wassily Kandinsky).

Wassily Kandinsky (16 December 1866 - 13 December 1944) was a Russian painter, printmaker and art theorist. One of the most famous 20th-century artists, he is credited with painting the first modern abstract works.

Geometric abstract art is a form of abstract art based on the use of geometric forms sometimes, though not always, placed in non-illusionistic space and combined into non-objective (non-representational) compositions

Wassily Kandinsky. Several Circles. 1926. Oil on canvas. 140 x 140 cm. The Solomon R. Guggebheim Museum, New York, NY, USA.

A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618. A distinctive feature of this shape is that when a square section is removed, the remainder is another golden rectangle, that is, with the same proportions as the first. Square removal can be repeated infinitely, which leads to an approximation of the golden or Fibonacci spiral.

The Circular Logic of the Universe
By NATALIE ANGIER. Published: December 7, 2009. Source: The New York Times

CIRCLING my way not long ago through the Wassily Kandinsky show now on display in the suitably spiral setting of the Guggenheim Museum, I came to one of the Russian master’s most illustrious, if misleadingly named, paintings: “Several Circles.” 

Those “several” circles, I saw, were more like three dozen, and every one of them seemed to be rising from the canvas, buoyed by the shrewdly exuberant juxtapositioning of their different colors, sizes and apparent translucencies. I learned that, at around the time Kandinsky painted the work, in 1926, he had begun collecting scientific encyclopedias and journals; and as I stared at the canvas, a big, stupid smile plastered on my face, I thought of yeast cells budding, or a haloed blue sun and its candied satellite crew, or life itself escaping the careless primordial stew.

I also learned of Kandinsky’s growing love affair with the circle. The circle, he wrote, is “the most modest form, but asserts itself unconditionally.” It is “simultaneously stable and unstable,” “loud and soft,” “a single tension that carries countless tensions within it.” Kandinsky loved the circle so much that it finally supplanted in his visual imagination the primacy long claimed by an emblem of his Russian boyhood, the horse.

Quirkily enough, the artist’s life followed a circular form: He was born in December 1866, and he died the same month in 1944. This being December, I’d like to honor Kandinsky through his favorite geometry, by celebrating the circle and giving a cheer for the sphere. Life as we know it must be lived in the round, and the natural world abounds in circular objects at every scale we can scan. Let a heavenly body get big enough for gravity to weigh in, and you will have yourself a ball. Stars are giant, usually symmetrical balls of radiant gas, while the definition of both a planet like Jupiter and a plutoid like Pluto is a celestial object orbiting a star that is itself massive enough to be largely round.

On a more down-to-earth level, eyeballs live up to their name by being as round as marbles, and, like Jonathan Swift’s ditty about fleas upon fleas, those soulful orbs are inscribed with circular irises that in turn are pierced by circular pupils. Or think of the curved human breast and its bull’s-eye areola and nipple.

Our eggs and those of many other species are not egg-shaped at all but spherical, and when you see human eggs under a microscope they look like tranquil suns with Kandinsky coronas behind them. Raindrops start life in the clouds not with the pear-shaped contours of a cartoon teardrop, but as liquid globes, aggregates of water molecules that have condensed around specks of dust or salt and then mutually clung themselves into the rounded path of least resistance. Only as the raindrops fall do they lose their symmetry, their bottoms often flattening out while their tops stay rounded, a shape some have likened to a hamburger bun.

Sometimes roundness is purely a matter of physics. “The shape of any object represents the balance of two opposing forces,” explained Larry S. Liebovitch of the Center for Complex Systems and Brain Sciences at Florida Atlantic University. “You get things that are round when those forces are isotropic, that is, felt equally in all directions.”

In a star, gravity is pulling the mass of gas inward toward a central point, while pressure is pushing the gas outward, and the two competing forces reach a dynamic détente — “simultaneously stable and unstable,” you might say — in the form of a sphere. For a planet like Earth, gravity tugs the mostly molten rock in toward the core, but the rocks and their hostile electrons push back with equal vehemence. Plutoids are also sufficiently massive for gravity to overcome the stubbornness of rock and smooth out their personal lumps, although they may not be the gravitationally dominant bodies in their neighborhood
In precipitating clouds, water droplets are exceptionally sticky, as the lightly positive end of one water molecule seeks the lightly negative end of another. But, again, mutually hostile electrons put a limit on molecular intimacy, and the compromise conformation is shaped like a ball. “A sphere is the most compact way for an object to form itself,” said Denis Dutton, an evolutionary theorist at the University of Canterbury in New Zealand.

A sphere is also tough. For a given surface area, it’s stronger than virtually any other shape. If you want to make a secure container using the least amount of material, Dr. Liebovitch said, make that container round. “That’s why, when you cook a frankfurter, it always splits in the long direction,” he said, rather than along its circumference. The curved part has the tensile strength of a sphere, the long axis that of a rectangle: no contest. Read more at NYT.com
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