- On 2011-01-29
- By Edugain
The Magic of "Pi"
Let's start with the circle - can there be a more simple shape. Just take any point, and map out all the other points on a plane that are at some fixed distance from it. And you get a circle.
The word itself is from the Greek for circle - kirkos (Oddly enough, the word "circus" comes from the same root). Of course, our ancestors were familiar with the circle much before they had any language. In nature, they could see the moon, and the sun. When they cut a tree, they could see that the trunk had a circular cross-section. They invented the wheel – so they knew about the shape. And they believed it to be a symbol of perfection.
So there you have it - a simple shape, nothing seemingly complicated about it. A point. Another set of points that are equidistant from it. What could be simpler?
Ah, but in this seeming simplicity lie some wonderful things. Let's just take one of them - the number "pi".
What is pi, you ask. Well, it's just the ratio of the circle's circumference to it-s diameter. This ratio is the same for all circles - no matter how large or how small.
So what is the value of this number?
This is where the story starts to get strange. When you were in 3rd grade, you were probably told that the value of this number, this “pi” is 3 (which makes sense, you really didn’t know much about decimal numbers at that point). Then in grade 4 or so, when you got used to fractions and decimals, you were probably told to use the value 22/7 or 3.14 for this value to solve problems.
Here's the funny part - although we can define what this number is (remember - ratio of the circumference to diameter of any circle) we can't tell the exact value of the number. Sure, we know that goes something like "3.1415926535,,,," but there is no precise value. The part after the decimal point never ends. It goes on and on into infinity, and the numbers don't repeat. What this means is, unlike a fraction like 1/3, which is also infinite (0.333333…) we can’t get a repeating pattern that lets us predict what, for example, the billionth digit after the decimal is (for 1/3, the billionth, or trillionth digit after the decimal point is always going to be 3?). It must be said that mathematicians recently have come up with some clever tricks that let you compute the value of any digit of the value of pi very fast (and without knowing any of the previous digits), but that involves rather advanced mathematics, and we won't go into that here.
Another fascinating fact about pi is that it can be proven (some very clever German mathematicians showed this in the 19th century) that you can never get an equation with a finite number of operations on integers to give you the value of "pi".
Mathematicians have been trying to find the value of pi for over 4000 years. By 1900 BC, Egyptian and Babylonian mathematicians knew the value to within 1%. Indian mathematicians also knew a very good approximation - the Shatapatha Brahmana , a 6th century BC work from India, gave the value as 339/108. Of course, today we know the value to trillions of digits.
More strangeness - "pi" appears everywhere in physics, maths and engineering. Even in places that seemingly have no connection to the circle. For example, if you were to try to compute the average height of all the people in the country, the formula for that would have a "pi" in it. In advanced physics, some of Einsteins equations trying to describe the nature of the universe have "pi", as does Heisenberg's equation governing the behavior of really small particles. Strange isn't it? And all the more reason to learn maths. The secrets of the world around can only be understood through mathematics.
And yes, dont forget to celebrate National PI day (March 14, at 1:59. (3/14 1:59))