Pi Explained in 5 Minutes

Pi Explained in 5 Minutes

I suppose that thousands of years ago someone drew a circle in the sand and admired its shape. After all, this was the inspiration for the wheel.

They probably wondered if there was anything special about the shape. So they measured the two most obvious features.. the circumference c and the diameter d. Of course, these numbers are different for different circles, but the ratio of the measurements c/d is the same for all circles!

This must have come as an amazing surprise, and so this ratio became an important number in ancient mathematics and sometime along the way became known as pi and denoted by the Greek letter π.

For thousands of years pi was thought to be a fraction and only relatively recently was it proved to be irrational. Swiss scientist Johann Heinrich Lambert proved this in 1761, several thousand years after pi was first discovered!

So pi can never be written as a fraction, meaning pi can never be written as pi=a/b where a and b are integers. Of course it can be approximated by a fraction, 22/7 being the most famous approximation.

In decimal notation pi=3.14159265359... and the decimal places go on forever. They appear to be random.

But perhaps the biggest surprise was this. Modern mathematicians started to see pi show up in areas of math that had nothing to do with circles. This makes pi even more amazing, and perhaps a bit mysterious.

For example, here's pi written as an infinite series using only the odd integers 1,3,5,7,9,..

pi/4=(1/1)-(1/3)+(1/5)-(1/7)+(1/9)-(1/11)..

The other obvious feature of a circle, its area, is also determined by pi..

area=pi*(r)^2 where r is the radius r=d/2

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Content written and posted by Ken Abbott abbottsystems@gmail.com