Happy Pi Day! What the number is actually used for

Pi is used to determine the area of a circle. Pi's importance, however, extends far beyond that simple calculation. It stars in a number of other, larger mathematical equations, including Euler's identity and the Fourier transform, both of which have had a tremendous impact on the fields of science, technology, and engineering. The snappy symbol π, derived from the Greek alphabet, was introduced by Welsh mathematician William Jones in the early 18th century.

Pi is an essential element of the Fourier transform, developed in 1822 by French mathematician Jean-Baptiste-Joseph Fourier to measure the movement of heat waves. The equation continues to inform the design of modern heating systems. Scientists at the University of Maryland recently created a self-powered thermo-regulation fabric, which instinctively warms the body, vetting the material's effectiveness with a Fourier-transform IR spectrometer.

Pi can be used to measure one of the most basic components of human life—DNA. The ladder-like structure of DNA contains a mind-boggling amount of genetic information, typically measuring 1.8 meters long. Amazingly, this string manages to wrap itself into a tiny, 10-micron sphere—approximately 1.8 pi of its original length.

What proportion of the American population has brown eyes? Owns their home? Can speak a foreign language? All of these questions can be answered with the help of the Greek letter π (pi), commonly used by statisticians when calculating population proportions.

In 1926, Albert Einstein noted that rivers often travel in loops, which are similar to circles. As with all things that curve or bend, pi appears to inform the length of meandering rivers, known as sinuosity. In 1996, Hans-Henrik Stolum built on Einstein's observations, determining that the sinuosity of the average river trends toward 3.14, or pi.

In 1859, British writer and theorist John Taylor realized that the perimeter of the Great Pyramid at Giza, when divided by its height, equals 2pi. Like their ancient Egyptian predecessors, modern architects and engineers also rely on pi when calculating curved elements, such as pillars and pipes.

Vibrations—including those created by earthquakes—travel in waves, and can, therefore, be measured by the Fourier transform. Engineers and architects can consult data gleaned from Fourier Transform infrared microspectroscopy to design buildings capable of withstanding the potentially disastrous effects of shifting tectonic plates.

The drudgery associated with household chores is decidedly less onerous thanks to modern electrical appliances—all of which owe their existence to pi. Pi is critical for the computation of electrical currents and their accompanying wave patterns. The larger the wave pattern, the bigger the wire needed to contain the power coursing through it.

Whether you're knocking it out of the park, dunking it through a hoop, or slamming it cross court, a ball is essentially a simple sphere. As with the manufacture of any spherical object, its surface area, which determines the amount and cost of the materials necessary for production, is calculated using pi.

It took a supercomputer to calculate pi to a jaw-dropping 22 trillion digits, yet without pi, which is used to calculate the area of microchips, computers never would have existed. Engineers also rely on pi to determine the size and shape of a computer, as well as necessary air flow.

Pi may be squared, but cakes, generally speaking, tend to be round. When calculating the amount of frosting needed to cover a round cake, bakers must first determine its surface area by multiplying the height of the cake by its circumference—which is simply pi multiplied by the diameter.

Pi plays an important role in astronomy, particularly when calculating the distance between stars. In order to accomplish this, research scientists at NASA employ spherical trigonometry—a geometry that takes place in a sphere, rather than a plane, and therefore requires pi.

How did the leopard get its spots? Or the Zebra its stripes? The answer to both of these questions—or, more specifically, to the question how these patterns are distributed—would appear to be pi. English mathematician Alan Turing first theorized that pi is the constant that determines the various patterns presented by living creatures while still in an embryonic state—a process known as morphogenesis.

Biologist Gerald Pollack studies the love lives of crickets. With the help of a loudspeaker and a spherical treadmill, Pollack tracks the journey made by crickets toward a projected mating call. The accuracy with which the crickets move toward the sound is measured in terms of pi.

Up until the invention of quartz in 1927, the pendulum clock was the most precise time measuring device known to man. The square root of the gravitational constant, which underpins the theory behind a swinging pendulum, is roughly 3.1305, or pi. The definition of a meter was originally derived from the movement of a pendulum, which took a single second to swing in either direction.

When you tune into your favorite track, you can thank pi. Sound, like heat, travels in waves and therefore can be measured using the Fourier transform equation. Fourier analysis breaks down MP3 files into easily digestible frequencies, which are then filtered through the ears and are subsequently synthesized by the brain.

Molecular chemist Chandrajit Bajaj researches molecular recognition models for drug designs. Molecules, spherical by nature, require the use of pi to calculate both surface area and volume.

NASA routinely relies on pi for a variety of out-of-this-world calculations. Chief among these is a technique known as a “pi transfer,” which alters a spacecraft's orbit. The Cassini Orbiter utilized pi transfers to “flip” the spacecraft to the opposite side of Saturn during its 13-year exploration of the planet.

The science of crystallography, which beams x-rays at semi-transparent solids in order to determine their molecular patterns, is also indebted to pi, as expressed in the Fourier transform, and has been instrumental in scientific advances in chemistry and medicine. Fourier-transform spectroscopy has recently been employed in skin tissue research.

The infinite possibilities inherent in pi have inspired a number of contemporary artists, including astronomer and digital artist Aaron Javier Juarez. Bioinformatics expert Martin Krzywinski, astronomer Nadieh Bremer, and mathematician Francisco J. Aragón Artacho have all turned the science of pi into an art form.

Esoteric filmmaker Darren Aronofsky also pays homage to pi with his eponymous 1998 meta-thriller about a mathematical genius obsessed with unlocking the mysteries of the universe. The film also spawned Clint Mansell's electronic title song, “πr²."