A Slice of 𝜋

This character that looks suspiciously like a picnic table is the Greek letter pi. Like e (see Easy as 1, 2, e), 𝜋 is a very significant mathematical constant.

Here is 𝜋 to a hundred decimal places for your pleasure:

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679

The definition of 𝜋 is rather simple. 𝜋 is the ratio of a circle’s diameter to its circumference, and this ratio never changes, no matter how large or how small the circle is.

Therefore, a formula can be developed that connects a circle’s radius and its circumference (the radius is used instead of the diameter because it has more scientific significance):

C = 2𝜋r

Another formula can be developed that determines the area of a circle from its radius:

A = 𝜋r²

As you can see, everything related to circles revolves (pardon the pun) around 𝜋. Like e, 𝜋 is an irrational number (it has an infinite number of decimal places), and it is also transcendental (it cannot be expressed as the solution of a polynomial equation).

𝜋 pops up in a lot places. Anything remotely related to circles uses 𝜋, and as a result there is a unit of angle that uses 𝜋, called the radian. Radians are used more often in science than degrees due to multiple benefits it has. In short, it is the angle subtended by an arc of length equal to the circle’s radius, and is about 57.3°.

In addition, 𝜋 appears in various probability and statistical equations, such as the normal distribution, and even Heisenberg’s uncertainty principle, which governs how precisely we can measure anything in the Universe.

And finally, 𝜋 is notorious for being subject to the memorisation of many decimal places, a practice called piphilogy. To date the recognised world record holder can memorise 70,000 digits of 𝜋.

Have a go yourself. This page which lists 𝜋 to a million decimal places: http://www.piday.org/million/. It’s even significant enough to have it’s own day – 𝜋 day is 14th March. You can figure out why.

Yanhao