Wednesday, March 14, 2012

My Favorite Number: π

Why π is My Favorite Number

The number π describes a beautiful relationship between a circle's circumference, area, and radius.

The π is irrational, which means the decimal expansion goes without end.

π ≈ 3.14159265358979323846... (this is from memory). Mathematicians from ancient Greece on forward have worked on obtaining more digits of π. I think the current count is a trillion decimal places.

The gamma of 1/2 is the square root of π.

π is involved in the normal distribution function: f(x) = e^(-2x)/√ (2 π)

Unlike pie, enjoying π doesn't make anyone fat. Furthermore, unlike pie, π has no calories.

The (basic) sine and cosine functions have a period of 2 π radians. (360°)

The number π is involved in infinite series. For example:
π /4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - 1/11 + 1/13 - 1/15 + 1/17 - 1/19 + 1/21...

or π = 4 Σ ((-1)^n / (2n + 1), n = 0 to infinity)

This series converges slowly - at 10,000 terms I only get 3 decimal points (3.14169264367).

I was born on March 14 - and π = 3.14 to two decimal places.

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