“Clue for the solution lies in the problem itself”- roared Prof. P.P.Raman to a student when the latter was unable to answer a question. Raman Sir, as we used to call him, is a Retd. Headmaster who used to take tuitions for High School Mathematics & English. Even though in his 80’s, believe me, he roars like a lion when any of his students commits a mistake.
Till I was in the 8th grade, I was just an average student in Maths. Even though Maths was my favourite subject, I could score only average marks in it. When I was in the 9th grade, I joined Raman Sir’s coaching class. And that was definitely one of the best decisions of my life. The way he used to teach us was something out of this world. Let me share with you what I learnt from Raman Sir & Geometry.
Geometry can be compared with our life. In Geometry, there are problems; in our lives also there are problems. Geometry drives most of us nuts, so does our lives. Some of us hate Geometry and leave a problem half way without wanting to think a bit more which could provide us the solution. Instead we give the excuse, the general excuse of any student, “The problem was too hard” or “It wasn’t from the text book” or “Even the top ranker couldn’t solve it”, etc. That’s what we do with our lives too. When we are unable to find a solution for any problem even after scratching our head or hitting it against the wall, we presume, “This is the greatest problem of my life, and it can’t be solved”.
Well, Geometry proves this wrong. Let me try to explain how.
Any problem in Geometry is divided into 4 parts:
2. To Prove,
3. Construction, and
4. Solution or the Proof.
“Given” is some data that is provided to us. “To Prove” – is what we’ve to finally derive at or prove out of what is given to us. And how we do that is the “Solution”. Sometimes it cannot be directly derived from the given data. So, we’ve to do some “Construction” part, which gives a mould to the “given” facts. Then, using our logic and a little bit of thinking, we’ve to proceed further to arrive at the solution.
Firstly, we should study the problem. Think, how can we tackle this one? What’s the given information and what can we bring out of it? Imagine the “given” facts as our strengths, a gift from God. We can’t increase it nor can we decrease it. And if we think that what we’ve got is less, we’ll spend our time worrying upon it and that won’t give anything for our “solution”. Instead, if we think, for any problem (whether in Geometry or in life), there’s a solution. And usually there is more than one. All that’s required is a little bit of thinking in the right way using our strengths. And Bingo! We get the “solution”.
Each one of us may arrive at a different solution to the same problem. That’s not because, some of us are more intelligent than others. No! It’s because, all of us think differently. Let’s come back to Geometry. Suppose 10 different clues are given and we’ve to prove some certain thing. I may think that the first 6 points could be more useful for the solution, and my friend may think, the last 6. Both of us are successful in solving the problem. I could have proceeded with the last 6 points to derive the solution, but I didn’t. That’s because I though, the last 4 in the given facts are not strong enough. My friend also did the same mistake.
What we often forget is, we all have got the same strengths. But, we focus on some and leave the rest. When some other person comes up in his life using those strengths (which we ignored), we think, “Ah! What a brilliant man!. He’s a genius! Only if I would have got his brains…” and on & on & on. But the sad part is, we forget the fact that, it is in us too. Only thing is that we didn’t realize it, or try to realize it.
Both in our life & in Geometry –
1. What’s “given” to us cannot be changed.
2. What’s to be proved or solved cannot be changed.
What can be changed is our attitude towards the problem. It is this attitude which makes our solution different from others. And for the rest of them, they don’t arrive at a solution. These people may argue that there’s no solution for the problem. Well, there’s a general rule in Geometry – “For any given problem, there exists a solution. If we get a problem with no solution then, either we didn’t think in the right way or, the problem is wrong. That means, there was no ‘problem’ at all”.
So, my dear friends, whenever we come across any problem, firstly let us think whether it is really a problem or not. And if it is a problem, all we’ve to do is to think in the right manner with the right attitude.
Geometry, or for that matter, any subject can be interesting if & only if we know how to play with the subject. Just like a flute when given in the hands of a boy who’s handling it for the first time. Initially, the air he blows in may come out as noise. Why? Because, his fingering is not correct. Once he realizes this and learns to play flute from a Guru, the flute is just a toy in his hands. He once again blows the same air into the flute. But, this time his fingering is correct. Now, what comes out is enchanting music. That’s it! All of us need nothing, but a Guru. Things become easier after that.
If we look at life as a lump of problems, then we are going to die with the same feeling. So, in order to live a NO PROBLEM life, first KNOW our problem. Once we KNOW our problem, then there’s NO problem! So, let “KNOW problem, NO problem” be our ‘problem mantra’.