Wednesday, April 14, 2010

The Road Not Taken

Some times it feels like its all done with life, exhausted, boring and becoming old. When everything was in our hands (only once though), with lots of dreams and ambition- love for stars in the sky, respect for science (god ...this is out of order now ...can't help), looking at everything with surprise and bit of confusion, thirst for building things, desire for breaking things, brains attentive to words...of wonder and of magic and to the slightest illusion.

Did you ever think what a trisection of an angle has to do with your quant skills? I remember a page of a book on failures of mathematics in geometry ( the book however was lost- I cried whole of the day for the irreplaceable loss that happened to me then). It says no angle can be trisected by a compass and a ruler. I struggled for countless days and nights for breaking the rule. Giving it up I posed my problem ( I felt as if it's like Clay Institute problems of millenium) to one of my teachers. He's a tall, dark eyed intelligent and quite interesting man. For me he was a genius at math. It’s not worth mentioning but I have to - I was his favorite student. At the sight of the problem he asked for a bit of time to think about it. I was waiting eagerly for the solution what he poses. He was my competitor for the moment. To my surprise he came up with his solution. He called it n - section of any angle. I couldn't just believe how he did it in a day on what I was struggling for many days. I was dying to move home and check its credibility. I tried a few ways to (mis)prove it- I wasn't in any mood to accept it (Einstein felt like dual nature should never exist). And my take on it - IT’S WRONG. I became excited and if I had to declare it false, the RIGHT had to be shown. That night an idea came to me about a special property of centroid dividing the median in 2:1 ratio. I thought this‘s the right property to be used - as the only possible trisection ever can be done is this. I tried different ways how this can be done. I took 60 deg for trisecting ( the book aforesaid proves 60 deg can't be trisected). With some arbitrary radius I had drawn an equilateral triangle on those two rays. I thought then I'd construct an isosceles triangle on the third side I had drawn previously. With an arbitrary radius I constructed it. Then I had to get somehow the centroid. Had drawn a line from bottom vertex to the right most side of the isoscles. Centroid was found. Joined the vertex of angle to that centroid. Without waiting for a moment, I ran and searched for a protractor and measured the angle this line made with base. It was perfect 20 deg. Hooray!!! I did it. The pride in me rose up and placed me at the elites. The day I could never forget. Next day I moved to my class. My math teacher came to me and told me that the proof he gave was wrong. Then I explained MY METHOD OF TRISECTION.

Google out today.. you’ll find articles saying not to try trisecting any angle as its impossible. A tenth grader did it. GALOIS THEORY proves it's impossible.

Man... I was like with wings on shoulders. He was surprised at my proof and even went on to declare a prize of 500 bucks for my achievement. I didn't get the prize though … but enjoyed those moments a LOT. Soon I discovered my method applies only to trisect 60 deg. No problem ...this was good enough. I made a poster on that and my teacher trained a few 9th graders to explain that model. I heard from them and the poster acknowledges - PROVED BY CHARAN. You understand my feelings.

There are a few instances more I would put up later. Gone are the days of fun and love to find new things- being original, challenging even greatest theories and persons. Now it’s more of a dumb life- nothing more than surfing and wasting time. If ever have a chance I would love to take up mathematics - Not for certifs. but only to enjoy it.

I dedicate this post to my beloved mathematics teacher Bhanu Prakash for his serious commitment to educate and support his students for breaking frontiers of unoriginal and conservative education system that prevails in our society.