No number can claim more fame than pi. But
why, exactly?
Defined as the ratio of the circumference of
a circle to its diameter, pi, or in symbol
form, π, seems a simple enough concept.
But it turns out to be an "irrational number,"
meaning its exact value is inherently
unknowable. Computer scientists have
calculated billions of digits of pi, starting
with 3.14159265358979323…, but because
no recognizable pattern emerges in the
succession of its digits, we could continue
calculating the next digit, and the next, and
the next, for millennia, and we'd still have no
idea which digit might emerge next. The
digits of pi continue their senseless
procession all the way to infinity .
Ancient mathematicians apparently found
the concept of irrationality completely
maddening. It struck them as an affront to
the omniscience of God, for how could the
Almighty know everything if numbers exist
that are inherently unknowable?
Whether or not humans and gods grasp the
irrational number, pi seems to crop up
everywhere, even in places that have no
ostensible connection to circles. For
example, among a collection of random
whole numbers, the probability that any two
numbers have no common factor — that they
are "relatively prime" — is equal to 6/π .
Strange, no?
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.
Finally, pi emerges in the shapes of rivers. A
river's windiness is determined by its
"meandering ratio," or the ratio of the river's
actual length to the distance from its source
to its mouth as the crow flies. Rivers that
flow straight from source to mouth have
small meandering ratios, while ones that
lollygag along the way have high ones. Turns
out, the average meandering ratio of rivers
approaches — you guessed it — pi.
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.
Because the length of a near-circular loop is like the circumference of a circle, while the straight-line distance from one bend to the next is diameter-like, it makes sense that the ratio of these lengths would be pi-like.
The definite value of this number is still a mystery.... The only fact everyone is sure of is that it's approximate value is 3.142
Source : livescience