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Saturday / April 10.
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Infinite Beauty Of Pi


First calculated 4,000 years ago, π represents the ratio of a circle’s circumference to its diameter. You learned it as 3.14, which is why today some take the chance to bask in the brilliance and beauty of the mathematical constant, while others try to tear it down.

But Pi’s ubiquity goes beyond math. The number crops up in the natural world, too. It appears everywhere there’s a circle, of course, such as the disk of the sun, the spiral of the DNA double helix, the pupil of the eye, the concentric rings that travel outward from splashes in ponds. Pi also appears in the physics that describes waves, such as ripples of light and sound. It even enters into the equation that defines how precisely we can know the state of the universe, known as Heisenberg’s uncertainty principle.

Albert Einstein was the first to explain this fascinating fact. He used fluid dynamics and chaos theory to show that rivers tend to bend into loops. The slightest curve in a river will generate faster currents on the outer side of the curve, which will cause erosion and a sharper bend. This process will gradually tighten the loop, until chaos causes the river to suddenly double back on itself, at which point it will begin forming a loop in the other direction.

Math and art may appear, superficially, like two disparate fields, but they’ve been in conversation for millennia. One recent example of the synergistic possibilities between the two comes from Canadian scientists Christian Ilies Vasile and Martin Kryzwinski, the stunning images show the number Pi, the ratio of a circle’s circumference to its diameter, which is approximately equal to 3.14159.

Krzywinski started publishing his pi art in 2013, beginning with this visualization:

Each digit of pi is represented by a dot of a different color: 3 is orange, 1 is red, 4 is yellow, and so on. Krzywinski then folded these colored dots, each of which represents a different digit (“1” or “4”), into a spiral. Going from the center of the circle outward, here is the first 13,689 digits of pi:

Krzywinski also created a series of circular representations of pi, where the numbers are connected across the circle with a chord. 

The image below follows the same process, except now, when a number is repeated (for example a “1,” followed by another “1”), Krzywinski and Vasile place a dot at the outer edge of the circle.

Bremer’s graphics follow pi as it “walks” out 100, 1,000, 10,000, 100,000 and finally 1 million digits.