What distinguishes pi from all other numbers is its
connection to cycles. For those of us interested in the applications of
mathematics to the real world, this makes pi indispensable. Whenever we
think about rhythms—processes that repeat periodically, with a fixed
tempo, like a pulsing heart or a planet orbiting the sun—we inevitably
encounter pi. There it is in the formula for a Fourier series: That series is an all-encompassing representation of any process, x(t), that repeats every T
units of time. The building blocks of the formula are pi and the sine
and cosine functions from trigonometry. Through the Fourier series, pi
appears in the math that describes the gentle breathing of a baby and
the circadian rhythms of sleep and wakefulness that govern our bodies.
When structural engineers need to design buildings to withstand
earthquakes, pi always shows up in their calculations. Pi is inescapable
because cycles are the temporal cousins of circles; they are to time as
circles are to space. Pi is at the heart of both.
For
this reason, pi is intimately associated with waves, from the ebb and
flow of the ocean’s tides to the electromagnetic waves that let us
communicate wirelessly. At a deeper level, pi appears in both the
statement of Heisenberg’s uncertainty principle and the Schrödinger wave
equation, which capture the fundamental behavior of atoms and subatomic
particles. In short, pi is woven into our descriptions of the innermost
workings of the universe.
Even though I don't understand all that, I know it is really cool.
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