Day 1: 6th Jan 2013
Everyone in our room woke up around 6 am. Srivatsav, the boy of 11th standard, asked me to give him a hand in folding his bedsheet. I was taken aback when I saw him struggling to fold the bedsheet which was a bit bigger than the normal size. I showed him how he could fold it. However he still seemed to find it difficult.
After the shower, I got into a small conversation with Mr. Karmarkar and told him about Mr. Nair’s poem that I penned down the earlier day. He immediately recited a small poetry on fraction-addition in Marathi. I quickly penned down the beautiful composition which I was sure would come handy for a Maharashtrian kid. It was a surprise for me to have met the second mathematician-poet in such a short while.
Soon we headed for the canteen to have breakfast, following which; we proceeded to the lecture hall. The hall was full with around 200 delegates comprising equally of teachers and students. After the inaugural ceremony, the first session was Prof. Bhatnagar Memorial Lecture on ‘Applied Mathematics in solving problems in Aerodynamics’. Honestly speaking, I could follow only what was explained in the first ten minutes. After that was beyond my learning capacity. Yet it was a revelation for me to see so much of applied Mathematics in engineering.
What I understood was that aerodynamics dealt with the study of motion of air (or fluid) past bodies. For example, kite, boomerang, bird, aero plane, missile, etc. The speaker, Mr. Venkateshan Bhaskaran, said that basically the study of motion of flying objects involves four parts:
• The structure of the flying object
• The propulsion of the object
• Avionics – the mechanics involved in the flying object
• Aerodynamics – again divided into two sections:
o Given the shape of the body, what are the forces that will be faced by it, or
o What should be the structure of the body which has to be constructed to be carried in the given force?
He explained how different kinds of wings of aero planes were invented and that we have thousands of designs of such wings. One just has to choose the right body to achieve his purpose of getting the optimum utilization of resources. He said that airlines have tough competition and research going on in their field so that they can choose the most effective design on the aircraft to suit their needs which will incur minimum costs as compared to their competitors. He explained various differential equations and other topics from calculus. The only few symbols that looked somewhat friendly to me in those equations were 0, +, = and π. But I thought, had we been taught the applications of calculus in college while we were learning to solve the equations, it would have given altogether a different meaning and approach for Mathematics. In college, we just solved equations without knowing the least where and how it’s going to be useful. But there was so much of use of calculus in applied Mathematics of engineering, aero dynamics, etc.
The second session was about π. As soon as I heard it, I was very happy because π happened to be one of my favourite topics. But my heart was saddened because the speaker didn’t talk about π in the way I understood it. He explained π using calculus. Yet, I wasn’t totally disheartened because he showed a series by ancient Indian Mathematician Madhavacharya, known as the Madhava-series which said:
1 – 1/3 + 11/5 – 1/7 + … + ((-1)^n)/2n+1 = π/4
As we learn in school that π comes in calculations related to circular shapes, here is a series given by a Mathematician who lived somewhere in the 13th or 14th Cent. CE, where he expresses the value of π/4 in the form of a series and without a circle!! So, π can exist even outside a circle!!
The presenter, Prof. Pandurangan, said that the above formula could be proved using Gregory-Leibnitz series (~1670 CE) which says:
π/4 = z – (z^3)/3 + (z^5)/5 – (z^7)/7 + ….
We just have to take the value of z as 1 in the above series.
It gave me immense joy when I learnt that this was proved by Madhava, an Indian mathematician three or four centuries before the mathematicians in the West discovered it.
The session was followed by lunch break. I took a short nap in my room after the lunch and went back to the lecture hall to attend the remaining sessions. On my way I saw a display of books for sale. And all of them were on Mathematics. Books have always been my weakness. I chose 6 books which dealt with magic squares, a book on Pi, e & i, and few other topics.
A teacher was presenting on a software called Geogebra which could be used to give more visual clarity in clearing concepts mainly in geometry. Constructions could be made very quickly using this software. Everyone enjoyed the presentation because the teacher made it really precise and clear. The next teacher presented upon ‘Exploring & Visualising Mathematics through Graphic Calculators’. She too did a great job in explaining. There is something called as a Graphic Calculator available in the market. In it we can draw graphs and plot the points, draw curves, and do almost anything with graphs. This gives the student an immediate picture of what an equation 4x + 3y = 24 would mean. A graphic calculator can also be downloaded from the internet. Her point was that if we are able to show the children the graphs of functions visually, then they would be able to understand the functions better than what they seem to understand merely in terms of x and y.
I didn’t quite enjoy the next two presentations by two teachers who almost emphasized that everything should be electronic and using technology. In their explanations they almost left no space for a teacher to think and set a question paper. Even that was suggested to be prepared from using a software. However, certain points were good and acceptable to me.
The following session was presentations by students. The students were divided into two classrooms and the audience could choose whichever classroom they wanted. I chose Classroom 1. The presentation skills of children in the classroom where I went into, were average even though they spoke of very nice concepts. It seems they were trained on the concepts more and less on presentation skills. Nevertheless, the kids did a great job on the stage. I was told that the students in Classroom 2 had done excellent presentations. My roommate, Shrivatsav, had his presentation in Classroom 2 of which I wasn’t aware and I missed it. His presentation was on methods to solve complex problems in simple ways using logic and observation.
I came to my room after the students’ session and didn’t go for the cultural programme that was arranged. I chose to take a quick nap for 20 minutes and started going through the notes I prepared and working on something. Soon it was time for dinner and I came back to the room immediately after dinner. I asked Shrivatsav how his presentation was and he said that it was good. I asked him what he feels about Calculus (which most of the students are scared of.) He said, “It’s easy. I like it.” I was surprised. This was the same boy who found Calculus a lot easier than folding his bedsheet. I had never imagined that easy and difficult things could be so relative!
At night I saw that Varada was sitting on his bed, feeling sleepy but not wanting to sleep. I had seen him playing with a Rubik’s cube all the while. The cube was almost worn out. I could imagine how many lakhs of times he must have rolled his fingers on it to get it into that state. Suddenly I observed that the cube was perfectly arranged with single colours on all sides. I asked him if he actually did that. He smiled and replied, “Yes.” “How much time do you usually take to complete it?” I asked. He said, “Less than a minute.” I said, “WHAT? What is your record time?” “37 seconds” was his reply. I had seen the genius in his eyes the very moment I saw him the first day. But he was not happy when he said this answer. He said, “That’s not a good timing. I’m still the second in my class. There’s a boy who does it in 25 seconds in my class.” I was like ‘WOW’ because I never knew that record timings were so fast. He said that the world record timing is of a man who could do any cube in 5 seconds (however badly they are jumbled.) Then I watched him arrange a cube. He held the cube very firmly in his hands and moved the cube with his index and ring fingers of both hands. Yes, he used just one finger to get the rotations done. That saved a lot time of his as compared to beginners who use one the whole of their palms to rotate the cube. Of course, he did that through practice. So I asked him how much time he took to achieve this skill. I was thinking that he would say some time with respect to years or many months. He said, “One and a half months back I started training myself. And I practiced for 3-4 hours a day. I somehow wanted to crack it. Cracking the whole cube took me two full days. The rest of the time was spent in studying the algorithms and formulae for getting it done faster.” This was a new class for me. I never knew such things like algorithm and formulae existed for solving a Rubik’s cube. He continued, “There’s a lady who has given many formulae for solving different situations in Rubik’s puzzle. The number of formulae goes beyond 150 or 250. The formulae go something like this – Right-inverted, Up, Right, Right, Up-inverted….” He went on saying such words. He said, in a particular situation, we have to think which formula to choose. If we are able to do that correctly then we can solve a cube in less than 30 seconds. “But have you by-hearted all the formulae?” I asked. He replied, “No. I prefer to do it using algorithms and pattern-observation. I had my friends who guided me to get out of some situations where I would get stuck up sometimes in a puzzle. And I was passionate about this to such an extent that I couldn’t get myself out of it.” And I could see that in him. All the while he was talking to me, he would solve the cubes and he would be hardly looking at it. I was imagining the capacity of a human brain and how much of it we were actually utilizing!
We retired to bed by 11:30 pm.
…to be continued in the following post https://vinayrnair.wordpress.com/2013/01/09/experiences-at-national-conference-of-amti-2013-day-2