Irrational But Well Rounded!

3.141592653589793238462643383279502884197169399375105820974944592307816406286 ….digits after digits arrayed effortlessly in his mind as this student recited the first two hundred and fifty five digits of π to the precision of a computing Machine as the rest of the school watched with a gasp! Whether the rest of them can memorize first five digits or hundred, they get the idea- this mysterious number can go on for ever, never ending, never repeating. This particular student won the π- digit memorization contest that our school proudly conducts every year as part of the π -day celebrations!

Each year, we celebrate π – day a little differently. In the past, we ate apple pie, doodled with circles, played bingo with problems that involves pi or just decorated the room representing the non terminating feature of this number. This year, it falls on a Saturday-and since we are racing to make up school days we missed due to snow, I was not planning to do anything special in my class. But students were quick to remind me today that Saturday is March 14th and wanted to celebrate it! They welcome any distractions wholeheartedly!

In a rare coincidence, it is also Albert Einstein’s birthday. π – Day is hence a tribute to the great scientist! As a high school teacher, I am also aware of a group of students anxiously waiting for this auspicious moment when MIT releases their irrational but well thought out college admission decisions every year. There is a pang of anxiety surrounding this date with certain section of the senior class here in Boston and around the country.

Coming back to the irrational nature of this number, the very existence of it as the ratio of the most symmetric geometric figure's circumference to its diameter has intrigued human mind from early on. How did this number come to exist? Who used it first? What is the context? Answers can be found in this great book: ” pi- the biography of world's most mysterious number”. Rereading this book after few years is my past time this weekend

Written for the general audience without much tedious mathematical processes, this book is an attempt to understand π and its beautiful aspects. The book is divided into six parts- what is π, history of π, calculating value of π, π enthusiasts, π Curiosities, applications of π and π paradox. I was fascinated by how the number evolved into today's form.

The first chapter explains in detail one of the greatest challenges the ancient mathematicians faced – trying to measure a circular figure in terms of a straight line.  The problem they experienced was that the circular arcs and straight line could not find a common measure; there were always something left over when trying to compare these types of measurements. The various approximation of the value of in ancient times was the attempt to find out what is left out from a circular measure to the straight line measure.

One of such early attempts was from Egyptians who tried to make a square with the same area as that of a circle. In Rhind Papyrus, a mathematical handbook from early Egyptians, there is reference to this construction which has fascinated the mathematicians for generations until finally they came up with a proof that it is an impossible construction. If we begin with a circle of radius d/2 and a square with side length 8d/9, we can see that Egyptians were reasonably close to the approximated value of. Babylonians approximated the value of to 3.125 in an attempt to find the ratio of the perimeter of a regular hexagon with the circumference of its inscribed circle.  It was Archimedes who is credited with calculating first most accurately. The symbol π, which is the sixteenth letter in Greek alphabets, was used in 1706 for the first time to represent the ratio of the circumference to the diameter of the circle by an English Mathematician.

The book also deliberates π’s appearance in unexpected places, like in Euler’s identity where it join its distant cousin e to form one of the most beautiful mathematical equations (e^(iπ)+ 1 = 0) or in harmonic series or where, at times it almost appears in places like that of square root of 10 or cube root of 30 or square root of 2+ square root of 3 (the values of these expressions being close to that of π). They are fun to read and experience the wonder where things that are seemingly unrelated fit as pieces of jigsaw puzzle.

Now, there are supercomputers that can approximate the value of π to millions and millions of decimal places. While just reciting or memorizing the digits in this number to some random decimal places don’t mean much in the long run, it is a chance for young children to come face to face with what a non terminating non repeating decimal number might look like and to appreciate the beauty of mathematics in their own ways! Just like Egyptians and Babylonians thousands of years ago, this mysterious number, its disguise in a well round figure with an irrational behavior, will continue to fascinate the mathematicians to come!

Life in these united states.....

Recently an Indian grandfather, who was visiting his son and family in Madison, a small town in Alabama was manhandled by a cruel police officer. Mr Patel, who was left partially paralyzed and needed multiple surgeries, was taking a morning walk in the neighborhood when a police officer approached him. Mr. Patel's mistake- he didn't know English and failed to understand the question or instructions that was given to him. In a video that has gone viral ever since, Mr. Patel is shown repeatedly saying “no English” and this police officer instructing him in English “do not move, if you move I will put you down- do you understand?"He must have been so out of mind to think that a person who doesn't know the language can understand the instruction he is giving in English. The police officer was later suspended and is facing a possible termination.

The atrocious stories of police officers mishandling the situation is abundant, in some cases costing life to the people involved. Is it the lack of training they receive?  lack of empathy? Racism still prevalent and police officers are not immune to it? Or is it that the police that control a gun laden population needs to be brutal to keep things under control? After all, they risk their life to be in the street. All these incidents that I read and hear in the media is slightly against what I have experienced in my fifteen years of stay here.

First time, it was through a 911 call. It was my first month in this country- not long enough for me to learn about emergency calls. Lying on the sofa, I dialed 01191 which is the international code and then the country code for India. I stopped half way through as my son interrupted me, dialed again only to miss it, and dialed one more time before I finally got the line through. It was Vishu, a festival day in Kerala, I was talking to my mother in law.

Two minutes into the conversation, I saw a police officer peeping into my room. He asked if I am okay. Confused, I nodded but continued talking as I walked up and down the room about the presence of police in the house. When I glanced through the door, I saw my husband trying to explain something. I saw him leading these officers to the door and waving while I continued talking oblivious to what is happening. Entering the room, the furious husband snatched the phone from me and told his mom that I called these police officers. It took a while for me to comprehend- by mistake I have dialed 911 and these officers were responding to that call. Then I vaguely remembered that I was getting a phone call which I never cared to take as I was conversing with the folks in India. They wouldn't leave when Vinod informed them there is nothing wrong and we didn't need help. They insisted they see other people in the house and made sure everything is okay before leaving.

Even though it is one of those embarrassing incidents in my life, I derived enormous strength from the feeling of security knowing that I would get help in a phone call within minutes. There were times I lived alone with my son when he was still a child. For someone who was extremely fearful of dark and experienced an overprotective childhood in a joint family, living alone in a foreign country is made possible because deep inside, I knew my safety is only a 911 call away. Whenever I sleep alone, I have my phone beside my pillow- just in case if I need to make that call. I feel protected and safe in a way I never would have if I was staying alone in India.

Years later, as I hurried into my car to get to work one fine morning, I noticed my car was unlocked. I had the habit of forgetting to lock it at times, but in safe Winchester neighborhood, breaking in the car was unthinkable. In a panic I realized that some one has gone through my stuffs and the GPS is missing. I was late to work and was a testing proctor for that day, so I drove away distressed. My parents were visiting me at that time, I saw panic in their eyes too. I thought of reporting it to police once I settle down with the testing. However after an hour my father informed me that a police officer came home and knocked on the door to ask if we lost something. They caught a teenager who was breaking in cars in the neighborhood and confiscated many things including our GPS. We were asked to wait for the investigation and the closure of the case against the boy. In couple of weeks, we got a call to collect my GPS. As I walked into the police station with my husband, I was anxious, but was politely received and was handed the GPS and made me sign some papers.

The role of the police of a state is to protect its citizens. There are a lot of good police officers out there who relentlessly put their life in danger and protect the people. And then there are few like the one in Alabama who will exert their power over a fragile old man. But it is soothing to know that they are few and far between.