I think nature’s imagination is so much greater than man’s. She’s never gonna let us relax.

Richard Feynman.

Above quotation by famous physicist explains what keeps the scientists and mathematicians wondering.

There are certain quantities that can’t be expressed by numbers. Let’s discuss further.

Lets talk about Pi. You must have studied the Pi in your mathematics high school. Matematically we denote it as a division of perimeter of a circle by its diametre.

If you were to take a thread and put it in a circular shape, the value to pi would be length of the thread divided by the circle’s diameter(dotted line).

The dotted line is the diametre. Golden circle is the thread we are experimenting with.

Mathematcians call pi an irrational number. i.e. it can’t be expressed as a division of 2 simple numbers. e.g. we can write 5 as 5 divided by 1 or 10 divided by 2. Or even 15 divided by 3. However, one can’t write Pi as a division of 2 numbers.

Wait! But we just mentioned pi as a division of perimeter by diametre. Well, that’s just an approximation. You ask how?

Ok. If you were to find out the length of the string and the diameter, you would be relying upon a physical scale to measure the length. Each scale that we use will give a different measurement. Of course, you must understand that we are talking about exact measurements.

So what exactly are we talking about? That one can’t measure anything with perfect precision?

Yes. That’s what the point is. When you look at a circle through a microscope, you will find out that not all the points on the circle are at equal distance from the center. A circle, a triangle or any geometrical figure is a mere abstract imagination. When put into real life, it won’t be possible to create one that is exactly what it is supposed to be. Therefore we have to take help of approximations.

To put it in other words, you will never be able to create a perfect circle using a string. Or even a perfect square. Mathematical formulas have been derived for ideal geometric figures.

Now coming back to pi.

So what is a pi? For approximation,it is still equal to perimeter divided by the diameter. But we must also remember that its actual value can never be found out. Therefore it is used as it is. When mathmatcians work on calculations and there is a pi that comes in, they keep it as it is without using its approximated value. By the way its approximately value is 22/7.

Another way to put it is that there are certain quantities which can not be expressed by our numbers. For that we start using symbols like pi!

Alright, last question..

What is the use of this pi?

Answer- lets assume you are in a dark room with 1 candle that you could light. When you light the candle, you find out that the maximum distance from the candle at which you are able to read the book is 5 meters. Now you want to place chairs around the candle. To find out how many chairs you can put, you will find out the perimeter of a circle with diameter as 2×5.

The above calculation will also use the value of pi as 22/7. Finally, you will not get a perfect answer. However, it will certainly give you a working solution.

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