Ohhh its really a long time since my last post. Not that I was busy. But somehow didnt make it. Basically much time gone in project frustration and debugging. Nikhil (my proj partner) and I had lot of tensed moments and restarts. Finally everything is over now and I am back here.
Talking about school math, there are really some concepts from school level math which I haven’t understood completely yet. May be the way we are taught at schools is responsible for that or may be I really never tried to get to depth of things.
Few days before I got confused between Rational and Irrational numbers. The only thing I remembered was definition of Rational numbers. i.e.
number which can be represented in the form p/q
where p,q are integers, q != 0.
Basically why this kind of classification is needed. And if above formula is true our well known number PI = 22/7 should be a Rational number. But facts are opposite and PI is not a Rational number.
Ummm if someone asks me what according to me should be the definition of Rational number I will simply say, number whose position on number line is known is Rational number. Book writers really make it difficult for those little school children to understand.
We can represent 1, 2, 3... 1/2, 1/3... 2.4, 3.56, all such numbers can be represented on number line. Obviously next question will be then which is the number we can’t represent??? Answer is simple number which we don’t know we can represent. Here I was wondering how it is possible that we don’t know the number. Anything we write we have name for it. (one = 1, one point one = 1.1...)
Now lets go back to our today’s guest of honour PI. Really its the number we don’t know and still it is involved in almost everything we use, see and think of. For introduction lets have a look on story of PI.
In an ancient world some great mathematician was trying to calculate perimeter of circle. For square it's easy to calculate: for side 'x' it is 4x. But what about circle, how can we calculate circumference of the circle given its diameter. A very basic and correct way to do this is take a string make a circle of desired diameter with string and then measure the length of string to get the circumference, and mathematician did the same thing. For some readings he took he observed that circumference of the circle is directly proportional to diameter. He calculated the ratio for each reading and APPROXIMATED that value by taking average Which today we say is PI.
As it is approximated value, no one knows what is the accurate value of PI. We just can go closer and closer to that value but can never get it completely. So, actually from this explanation it is clear that 22/7 is not the correct value of PI but just the approximation. Irrational numbers are mysterious of all in the number line. Its like a god, who is said to be everywhere but we can never see him but faith in his powers keeps world running. Irrationals are everywhere and we cant reach them but they have occupied most of our Physics' laws and keep our civilization live.
That’s all for today folks!!!! Enjoy math!!! Respect the unseen and unknown!!!!
