Pi: The Transcendental Number
Pi (commonly shortened as 3.14159, or π) is the ratio of a circle's circumference to its diameter. Its value can be expressed as a mathematical series that produces an infinitely long number.
As such, Pi is 'irrational', which means that the digits never end or repeat in any known way. This mysterious mathematical quirk has been recognised by humans for millennia, and the symbol has now become well represented in popular culture.
The famed astrophysicist Carl Sagan's science fiction work 'Contact' proposed that radio transmissions carrying prime or transcendental numbers would be the best patterns to broadcast across interstellar distances in the search for extra-terrestrial intelligence.
Certain astronomical objects like Pulsar Neutron Stars are known to send out precise and rhythmic radio signals, which at one time caused much premature excitement before they became better understood as natural phenomena. There is, however, no star which would emit radio pulses in a sequence as complex as Pi. Amid vast stellar expanses filled with spikes of static and confused electromagnetic noise, this elegant pattern could only come from an 'artificial' source.
As Sagan's character Ellie Arroway puts it , upon the Very Large Array's discovery of such a signal emanating from the Vega star system; "Mathematics is the only truly universal language. It's no coincidence that they’re primes - it may be a beacon. Some kind of announcement to get our attention."
Science fiction aside, Pi remains a source of fascination due to its ubiquitous presence throughout the world of physics. Among many other applications, it is crucial to the calculation of circular or elliptical planetary orbits; satellite speeds, geometries, path vectors and decay rates - the Newtonian clockwork of the universe.
Pedantic or curious readers with mathematic questions about the transcendentality of Pi can click here to see NASA's explanation, which covers the topic far more thoroughly than I ever could. Or, to see more mathematically inspired artwork, take a look at The Golden Ratio. Thanks for reading, folks :-)