Infinity, Founder's Issue 2012

INFINITY FOUNDER’S EDITION 2012 ISSUE NO. 11

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A Tribute to O.P. Malhotra

Mr Vishal pays a humble tribute to the legend that was OPM

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Tejit Pabari analyses the application of Mathematics in the rapid game of table tennis

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Beauty of Maths in Origami

Pranjalya discusses the application of Mathematics in the beautiful art of Origami

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Functioning of a Calculator

Udbhav analyses the inner working of the innocent-looking Calculator

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G.I.M.P.S.

Shivam talks about the functioning of the Great Internet Mersenne Prime Search

The Olympic Torch Design

Devesh discusses 'The Olympic Flame - A Modern Legend'

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Mathematics in Table Tennis

The Unnoticed Beautiful Mind

Ujjwal talks about the beautiful mind that never made it to the screens

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Cell Phones Deciphered

Shrey examines the application of Mathematics in the now indispensable cell-phone

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Anirudh examines the application of Mathematics in the dynamic sport of basketall

Pythagorean Triplets

Harsh Vardhan discusses the divisibility of the ever-so-common Pythagorean triplets

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Mathematics in Basketball

Mathematics in Daily Life

Abhinav discusses the application of Mathematics in our daily life

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Mathematics in Hockey

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Laila Majnu

Professor Sandip presents the mathematical modelling of a love affair: the Laila Majnu story with a twist

Chinmay analyses the application of Mathematics in our national sport

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Parth will intrigue you with some puzzles and mathematical patterns in daily life

Mathematics in Shooting

Rudra analyses the application of Mathematics in the precise sport of shooting

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Puzzled...

Behind the Scenes

Editorial

Last term the 'Infinity' focused on the legendary Ramanujan, his miraculous life and tremendous achievements. This time the focus has shifted to more current events and inquisitive findings of the application of mathematics.

The key focus this time is the application of mathematics in sports. The excitement, the hard work, the unpredictability are a few of its many aspects that make it attractive to a vast majority of people almost everywhere on the planet. The recently concluded London Olympics portrayed the global nature of sports with a record breaking 204 nations participating in the event. We have made a humble attempt to express and explain sports in mathematical terms. The junior members of the board have tried investigating the application of mathematics in a diverse range of sports, from the national sport, hockey, to shooting which is presently riding high on popularity in the country thanks to the awe-inspiring performances of Gagan Narang and Abhinav Bindra on the global stage.

Mathematics cannot be alienated from the other sciences and will always have to be accompanied

by Physics in the investigation of dynamic events

such as sports. However keeping the focus of the magazine in sight we have tried analysing it from the mathematical perspective as far as possible.

As Bertrand Russel once said 'mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture.' Pranjalya Shukla, inspired by Russel, decided to investigate the application of mathematics in a similar form of art, origami, where intricate figures are 'sculpted' out of paper.

Udbhav Agarwal on the other hand has examined something at the other end of the spectrum, a calculator. He has attempted to explain how the little and innocent looking machine manages to compute gargantuan problems in a matter of seconds.

Albert Einstein once said ‘Gravitation cannot be held responsible for people falling in love. How on earth can you explain in terms of chemistry and physics so important a biological phenomenon as first love? Put your hand on a stove for a minute and it seems like an hour. Sit with that special girl for an hour and it seems like a minute. That's relativity.’ Einstein tried his hand at explaining love but tried doing so in terms of physics, chemistry and biology apparently forgetting all about the 'Queen of Science', Mathematics. Sandip Banerjee , a professor in the department of Mathematics at IIT Roorkee, has done what Einstein could not.

Banerjee has used the quintessential Laila Majnu story to not only explain love but also predict its possible consequences in simple mathematical terms!

As I pen my last few words ever as Editor-in-Chief for the 'Infinity' I reflect back and look at what the publication has given me over the years. Hours of pondering and probing into the past made me realize what exactly it was that the publication, rightfully living up to its name, gave me. It gave me the ability, the freedom and the power to imagine.

I, on my behalf, would like to leave you free to turn the pages and amaze your mind with a message, let your imagination flow- to infinity and beyond...

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A Tribute to O.P. Malhotra -Vishal Singh Narain Ex-260/HA, Batch of ‘84 OPM - an abbreviation for a legend, a genius, an institution, a teacher and above all a gentle loving person.

and individually sort out the problems of that particular boy. He also encouraged all of us to approach him at any time, at school or at his house, for extra lessons and help. I must confess that I did take him up on his offer on more than one occasion, not only for the extra lessons but also for the goodies we'd be served at his gracious home. Individual lessons with him at his home constitute some of my best memories of him.

I had the good fortune and luck to be taught Maths by OPM from B Form through to SC Form, a good solid uninterrupted 4 years. So while one could argue that's a long enough time to get to know a person well enough, I spent those 4 years being in complete awe of OPM, a person who was a giant among men.

Since the maths text books we used were all written by him, he didn't really need to refer to them at all. He knew the printed contents of each page from memory. He'd start by just mentioning the chapter, the page it was on, the topic it covered and off he'd go expounding on the profound (at least to us) theorems and algorithms, while we valiantly tried to keep up. But, in spite of the fact that he, a genius, was disseminating his knowledge to a bunch of novices (such as we were), he was surprisingly patient with us and also fully aware of the strengths and weaknesses of each of his students.

OPM an abbreviation for a legend, a genius, an institution, a teacher and above all a gentle loving person.

He'd know instinctively when one of us was struggling and take extra pains to walk up to him

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We had the option of dropping Maths after ICSE, and not being a student of particularly sharp mathematical intellect, I was looking forward to doing just that. True to his dedication to his students, Mr. Malhotra kept a sharp lookout for his students. On learning that I'd opted out of Maths in S Form, he called me to his house and advised me against dropping Maths from my subjects. I remember that day as clearly as if it was just yesterday. I walked straight back from his house to the school office and changed my options to include Maths. The next day I found out that I was in OPM's maths class.

OPM would occasionally officiate as the Headmaster in the absence of Mr. Ramchandani.

As luck would have it, I landed up with a YC in the Autumn Term of my S Form. YC's needed to be collected from and returned to the HM in his office during break time i.e. the time between the 4th and 5th classes. The HM was out and OPM was officiating on his behalf. I thought I'd get a mouthful from him and went apprehensively to collect my YC. To my immense relief (and surprise), OPM didn't say a word, just handed me my YC and that's it. I still wasn't out of the woods

Inifinity | Founder’s Issue 2012

though as the 5th school was OPM's Maths class. I thought I was going to go from the frying pan (which I'd survived) into the fire. The class went off without a hitch. No mention or reference was made to my YC, and I wasn't made to feel condemned at all. YC had to be returned after a week by which time the HM still hadn't returned. So off I went to hand it back to OPM. You can imagine my relief when he took the YC back and sent me back without a word. I would like to believe that it was his genuine affection for me which ensured that the whole exercise was conducted by him to ensure the least discomfort for me. Such was the man.

Sadly, I failed to keep in touch with him after leaving school. It is one of my great regrets. In Feb. 2009, almost 25 years after leaving school, I met again with Prabha, his daughter who is also my batchmate, who updated me with the latest on Mr. Malhotra. I learnt that he was not keeping particularly well and was on oxygen most of the time, but was still very active in his academic pursuits and regularly updated and edited all his

text books. It was also my desire to get my two sons to meet him and take his blessings.

But, in spite of the fact that he, a genius, was disseminating his knowledge to a bunch of novices (such as we were), he was surprisingly patient with us and also fully aware of the strengths and weaknesses of each of his students.

I planned with Prabha to meet with him on one my visits to Dehradun. Regretfully, that meeting never happened. Mr. Malhotra, OPM to most, passed away in June 2012 leaving behind a legacy for all, his family, students and friends, to be proud of.

Mathematics in Daily Life -Abhinav Kejriwal 'The universe is a grand book which cannot be read until one first learns to comprehend the language and become familiar with the characters of which it is composed. It is written in the language of mathematics.' -Galileo Galilee.

Many a time, people do question how mathematics will help them later. It is often considered as a tedious subject hard to understand most of the times. Well, to come to think of it, at some or the other point, we all do wonder how could such intricate Mathematics prove to be of any help in the future? But after this article I have realized that Mathematics is not just a subject mentioned in our time-table but in fact it is an important tool used in everyday life.

Mathematics is a universal language shared among all individuals all over the world, irrespective of their culture, religion, or gender. From poor to rich,

each one uses it, directly or indirectly, wherever they may go and everything that they may use. It is present everywhere. Living a life without it would be no less than null and void. Mathematics acts as a problem solver that helps us gain an aptitude for critical thinking and develops reasoning skills that assists us in all spheres of life. At a more advanced level, math builds up an analytical slant of mind aiding in improved organization of ideas and appropriate application of thoughts.

Everyone uses Math. I use it to calculate the amount of time it would take to finish off my projects. A housewife uses Mathematics to budget her expenses, needs and spending. We also use it whenever we are going to buy a car, following a recipe, decorating our home, gardening, sewing, and go shopping or even while walking. It is also a part of many games, hobbies and sports, business,

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industry as well as science. People use math every day. When we make our own decisions like whether to open the umbrella or not, we apply rules of probabilities, utility theories, Bayes rule etc, in order to do that. Ever thrown a ball? It involves math principles like geometry, inertia, spatial calculations, and so on. Even a nomad in the desert needs math to count his number of goats. Aristotle rightly said, “There are things which seem incredible to most men who have not studied mathematics”.

Nonetheless, to know in detail, we would need to classify math into its categories of application.

Algebra - We all use it without even realizing it. For instance, when we go shopping, in order to know how many 2 dollar candy bars one can get out of 10 dollars that one has, he uses simple equation in a blink of eye i.e. 2x=10. Now this is what we don't realize but we just use it. Another instance, while walking when we take a 90 degrees turn, we prefer to walk along the hypotenuse to get to a short cut.

Again making use of Mathematics.

Statistics: This is used by researchers, scientists and even us. Scientists use them to help find a kind of data, for example in order to record how many elephants from a herd would defend themselves from predators while what percentage would run away, requires stats. Researchers use them to advertise their products in order to create consumer purchase. The price of which then depends on the demand at that point in time. It is because of these statistics that we consumers pay a certain amount of money to buy a certain product. So it affects our daily life as well.

Trigonometry - Trigonometry is used in various fields. For instance, it is used to find the height of towers and mountains or in navigation purposes where the distance of the shore from a point in the sea needs to be calculated. Today we know about weather forecast and the height of tides, all because of trigonometry. Every time we listen to a radio, watch TV, or use a computer, the sine and cosine functions become fundamental to describe

the theory of sound and light waves. Every time one changes the TV channel, we should be thankful that someone has learned how to identify such trigonometric problems that we all are tortured with.

Geometry - This comes in handy in our very own houses. In order to find the floor area to lay the carpets or tiles, you do need geometry. And not to go too far, to even reupholster a piece of furniture, the amount of fabric needed is calculated by nothing but the surface area of the furniture. So we can’t deny the importance of mathematics in any field.

Stocks and Shares : When it comes to the market of shares and stock, mathematics finds wide usage as a share is nothing but a premium (above par), at par or at discount (below par) according to its market value which is greater than, equal to or less than the face value. The brokers who deal in selling and purchase of these items are often paid at their brokerage amount and for one to earn profits in the share market, a lot of mathematics is again used.

Banking: Banking basically involves a lot of transactions which is nothing but mathematics. It is nothing but that system of trading in money which entails upholding deposits and making funds readily available for borrowers. Banks are also involved in mutual funds, stocks options, bonds, derivatives, and so on whose calculations are quite mathematical. Insurance companies use probability in math to calculate the risk.

To be frank, all those funny Greek letters, or the sine, cosine and the tangent must now make sense and hold importance to us as they shall stay with us later in life. All in all, mathematics is so involved with us in our everyday routine that we simply do not realize its value. Yes, it's correct to say that one realizes the value of something only when it is taken away from him. Truly, Mathematics is the gate and key of the sciences. “Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world.” - Roger Bacon.

MATHEMATICS M - Mental A - Action T - Through H- Hard-work E - Especially to M - Maintain

A - Activeness T - Tolerance I - Impulse C - Character S - Skill - Chandan Singh Ghugtyal & Anjan Chaudhary

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Pythagorean Triplets -Harsh Vardhan Singh For students of mathematics, the Pythagorean Theorem is but an essential to understanding 2 2 geometry. It is represented by the formula a + b = c2. This implies that the square of the hypotenuse of a triangle is equal to the sum of squares of the adjacent sides. Any given set of values for any two sides of a right angled triangle is such that the value of the third side can be determined without any calculation other than the theorem. These sets of values are known as Pythagorean triplets. As the name suggests it consists of three numerical values, each denoting a particular side of the given right angled triangle. A very fundamental example is that of the values 3, 4 and 5. Suppose the values of any two sides of a right angled triangle are given as 3 and 4, the third side is 5, as easily determined by the theorem. Continuing on that idea, this article will talk about a fantastic observation that can be observed Pythagorean triplets.

Euclid, a great Greek mathematician gave the formula for generating Pythagorean triplets from any arbitrary pair of positive integers 'm' and 'n' with 'm' being greater than 'n'. The formula for sides A, B and C (depending on the various angles of the triangle) states as follows:

A = m2 - n2 B = 2mn C = m2 + n2 Limitations to the formula are that the HCF of the given numbers should be one. Obtaining a few Pythagorean triplets shows us that each generated triplet will have one number among them divisible by three. And one amongst them though not necessarily a dissimilar one will be divisible by four. Not very surprisingly another one and once again not necessarily a different one will be divisible by five. A proof to establish the same is as follows: We know that the group '3, 4 and 5' is the first triplet. Let us take the numbers in the triplet to be 2 2 2 2 m - n , 2mn and m + n . As stated above, one of the numbers in Pythagorean Triplets is divisible by 3. If either 3 divides m or 3 divides n, we have nothing more to prove. Now we need to prove that m=±1 2 and n=±1. It is certain that m =1(modulus 3) and 2 2 2 n =1(modulus 3). Hence m - n =0(modulus 3).

Four should be the divisor of one of the numbers in the Pythagorean Triplets. We can say that if either m or n is even then 2mn is equal to zero (modulus 4). The case to prove is when both m and n are odd 2 2 numbers. Then m - n = 0(modulus 4) because the square of an odd number is of form (4t+1).

Lastly at least one of the three numbers should be divisible by 5. If m and n are divisible by 5, we have nothing to prove. Now the case to consider is m=±1(modulus 5) or m=±2(modulus 5).The same holds true for n. Two situations are seen as a consequence. Either both m2 and n2 are 1 or 4 modulus 5.If they are equal modulus 5, then m2 - n2 = 2 2 0(modulus 5). Otherwise, m + n will be equal to 0(modulus 5).

Thus, we can observe that the apparently clichéd Pythagorean Theorem is actually much more intricate than what we perceive and has a lot more applicable potential.

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Cell Phones Deciphered -Shrey Aryan Mathematics has always been an integral part of our lives, from the very fundamentals to some of the most intricate things. However, we still sometimes fail to realize the importance that it carries and consequently resign to superstition and fate. Furthermore, the average human fails to understand that many of the factors that make their life easy are actually a consequence of some very complicated ideas. One such idea, the formula 'x =√( -1)’, is one of the many mathematical ideas which has perplexed mathematicians for decades in the past. The first time these numbers were noticed was when Heron (one of the mathematician whose formulae are used to take out the area of a given triangle) tried to determine the volume of a truncated pyramid and came up with the solution ‘√((81)-(144))' which would result to √(-63), something which obviously baffled his limited knowledge. Heron put down √63 in place of the complexity.

To understand the use of imaginary numbers in a cell phone we must first understand the functioning of the device.

Later it was Leonard Euler who worked with these numbers and termed them as Imaginary Numbers, denoted by the symbol ‘i’. Many mathematicians failed to notice the beauty behind the application of these numbers, so they tried avoiding them, just like Heron. Later on, as the modern period of technology came in where science governed a large chunk of human life, regrettably a majority of the people became oblivious to the most basic thing that goes into the making of these grand devices and gadgets.

The cell Phone is an integral part of a modern day human being's life. To understand the use of imaginary numbers in a cell phone we must first understand the functioning of the device. The basic devices within an average cell phone are a

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battery, an antenna, a speaker, a microphone, an LCD screen and a keyboard. The real use of imaginary numbers is in the voice conversion to a high pitch frequency. Also the behavior is calculated by formulae in terms of i. Pi (π), one of the most common symbol in mathematics when multiplied to i raised to the power of e (which is a mathematical constant and the base of a natural logarithm). The equation appears to be like this e^(πi) = -1 .

Some of the most important aspects of our modern day technology are integrated circuits, which process data at an unbelievable speed. We know that these circuits comprise electrons, hence it became tough to predict the movement which was fortunately possible by Schrödinger's equation, which is:

Earlier it had been proved by Euler that an equation involving this formula could be used to represent oscillating behaviour therefore the problem faced earlier could be easily solved.

Now with the equation at hand, integrated circuits were created and consequently so were cell phones, not to forget the fact that even computers and other devices came into existence because of this breakthrough.

Some of the most important aspects of our modern day technology are integrated circuits, which process data at an unbelievable speed.

Subsequently, despite the complexities that it brings with its applications and understanding, we now know how important it has become as a factor of our progress.

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The Unnoticed Beautiful Mind -Ujjwal Dahuja Who would crack a century old conundrum, refuse to be awarded the Fields Medal and then go on to put down a million dollar reward? Grigori Perelman, Russia's so called 'reclusive' mathematician who was able to prove the Poincare's conjecture did just that when he turned down the Fields Medal (equivalent to a Nobel in the field of mathematics) and a sum of one million dollars that was kept as reward money for the one who could prove the century old problem.

The Poincare conjecture, in elementary terms, is a problem in topology that involves the characterization of the three dimensional sphere, which is the hyper sphere that bounds the unit ball in fourdimensional space. An abstract mathematical problem that requires a great deal of imagination, the Poincare conjecture was about to be deemed as one of the unsolved problems in mathematics until Grigori Perlman posted online a terse solution to the Poincare Conjecture. This solution, which has been termed by the journal Science as the “Scientific Breakthrough of the Year”, is more than just a boring proof in pure mathematics. The proof is very closely linked with the complicated processes in the theory of creation and is thus also sometimes referred to as the Formula of the Universe. Some mathematicians even believe that the solution of the Poincare Conjecture contains within itself the subject matter needed to determine the shape of the Universe. When asked by a journalist why he had rejected the Fields Medal and the million dollars, Perelman replied, "I've learned to compute hollowness. Me and my colleagues are studying the mechanisms that fill social and economic hollowness. Hollowness is everywhere, it can be computed, and this opens large opportunities. I know how to control the universe. Why would I run after a million, tell me?"

Perelman's attitude has caused a lot of uproar in the mathematical community. While some believe that Perelman, though a genius, is extremely arrogant, others hold the belief that his eccentricity comes as part of his being a genius. But then,

Perelman has his own reasons too. Since the time he declined to receive the Fields Medal because he felt he was “isolated from the mathematical community”, journalists have been flocking to him and not letting him have the space that he requires to continue work. While some journalists have gone on to call Perelman 'reclusive', others have focused more on his habits of not cutting his nails and hair rather than focusing on the man's mathematical genius itself. On top of that, Perelman believes that the mathematical community lacks the ethical conduct conducive for creativity because on two occasions his work had been downplayed for no apparent reason.

The Poincare conjecture, in elementary terms, is a problem in topology that involves the characterization of the three dimensional sphere, which is the hyper sphere that bounds the unit ball in four-dimensional space.

In fact, it is even rumored that Perelman, distraught with the way the mathematical community has responded to his proving the Poincare conjecture, is now considering leaving the world of mathematics completely. What a loss would that be to the mathematical community! Will the world with all its commonplace workings, not let a genius prosper simply because he has his idiosyncrasies? Masha Gessen, in her book “The Perfect Rigor” which is based on Perelman and mathematics in communist Russia elegantly lays out in a metaphor what I believe is at the core of understanding this “obscure” mathematician.

The more Perelman talked about his disappointment with the mathematical establishment, the more his acquaintances decorated his stories.

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The Olympic Torch Design -Devesh Sharma

The creator of man, Prometheus, is said to have gifted man with fire, an element encompassed by sacred qualities. In fact, the Greeks of the ancient era were so enthralled by these convictions that they even used to focus the sun's rays via mirrors in order to keep flames perpetually burning outside their temples. Other traditions such as torch relays, although not a part of the Olympics, were also followed. Even to date, the Olympic flame is lit outside the façade of the ruins of the Temple of Hera in Olympia, Greece, using something called the skaphia, which is thought to be the ancestor of present day parabolic mirrors.

This flame is said to symbolize the everlasting relationship between the Ancient Olympics and the Modern Olympic.

This year, competing with a staggering 599 other contenders and hoping to survive the intense legacy of the Olympic Torch were the winners Edward Barber and Jay Osgerby. The internationally acclaimed duo were to work from their Shoreditch base, along with the engineering firm Tecosim from Basildon, and The Premier Group, a

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manufacturing giant well known for its extensive exertions in the aerospace and automotive industries.

Undoubtedly, the London 2012 Olympics Torch showcases pretty much the epitome of British design and engineering dexterity. Let us now take a look at the more remarkable details of this feat.

The 8,000 holes that can be found all around the Torch represent and connect the 8,000 inspirational stories of the 8,000 Olympic Relay Torchbearers, and how they serve their respective communities. The holes not only provide a poignant figuration, but are also responsible for the efficacious functioning of the Torch. The large number of holes also allows for the quick and essential dissipation of accumulated heat, that prevents the direct conduction of the heat down the handle. They also provide an extremely lightweight design, taking into consideration the fact that a number of proposed Torchbearers were aged between 12 and 24. Also the adequate length of the Torch grants a good vision over crowds to people even when held by the younger Torchbearers. Interestingly this seemingly iconoclastic design has also been proven to give a better grip to the Torchbearer.

The 8,000 holes that can be found all around the Torch represent and connect the 8,000 inspirational stories of the 8,000 Olympic Relay Torchbearers, and how they serve their respective communities.

The Torch might appear outwardly fundamental at first, but is actually a product of six distinct components. Amongst those components is an

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elegant burner system within the sleek structure that is responsible for keeping the flame alive.

The burner system has been engineered to keep the flame alive for a minimum of 10 minutes, providing sufficient time for a 300m run that is expected from each of the Torchbearers. The 8000 holes also provide a lucidity that lets viewers view the burner system keeping the Flame alive right at the heart of the Torch.

Reviewers say that the ‘magic number of this year's Olympic Torch is the number three'. I couldn't accede more. The triangular form of the Torch provides further buttresses the already magnificent parallels that the entire Olympic 2012 theme provide. Firstly, the Olympic council values three essential rudiments, i.e. respect, excellence, and friendship. Secondly, the Torch swathes the three dimensions of the Olympic motto, i.e. faster, higher, and stronger. The third parallel that the Torch's triangular shape draws is more clairvoyant than the others, i.e. the fact that the London Olympics 2012 would be the third of its kind, the other two being 1908 and 1948.

Lastly, the London 2012 Olympic association also based its administration on three principles, i.e. sport, education and culture.

The golden finish of the Torch gives it the ability to

withstand over a 1000°c of heat generated by the flame, other than providing an aesthetic value, and symbolizing the race to win in the Olympics.

There are more remarkable statistics that engineers managed to achieve in the Torch, statistics that are proof of the fact that the Torch can withstand the harshest of both British and Greek climates. The Flame has been engineered to work below freezing levels up to 40°c, at 95% humidity, against 50mm/h rain and snow, against winds of around 35mph and gusts of up to 45mph, with 50mm/h rain and snow, at a height of 4500 feet, and even at an angle of up to 45 degrees from the horizontal. A fundamental question regarding the aftermath of the Torch if dropped by a clumsy Torchbearer has also arisen. The engineers reassured that the Torch could be dropped from a height of up to 3 meters without being dented or harmed in any way.

The Olympic Torch is a symbol of unity that brings together international athletes at a time of tensions. The statistical wonders that constitute this masterpiece are all remarkable in their own way. I would like to conclude by once again applauding the masterminds Edward Barber and Jay Osgerby for producing such a mathematical yet emblematic article for the world to admire.

Mathematics in Hockey -Chinmay Sharma Hockey is a game that has been played in varying forms and in different cultures for over 4,000 years, simply because the striking of a ball with a stick either towards a goal or away from an opponent is a universal sporting concept. The main objective of hockey is to direct a hard ball using a stick into the opponent’s goalpost. The ball can be advanced up the field against the opposing team by a player dribbling the ball, which includes any use of the stick to keep the ball under control while the player moves down the field, by passing the ball or by driving the ball ahead and running after it.

This year has undoubtedly been a great year for the sport, especially after the recently concluded

London Olympics, which was a major success.

Although the bustling excitement is over now, the fantastic performances of the excellent athletes who took part in the Olympics this year cannot be forgotten. The men's hockey turned out to be a very big event, with the glorious German team claiming the gold medal after a terrific performance.

Although not always realized, mathematics plays a very important role in all sports. The connection between mathematics and sports can be explained using physics, calculus, and geometry. Have you ever wondered why a particular player is able to impact the outcome of a game whenever he or she

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is playing? For example, have you ever wondered why some field hockey players deliver perfect and accurate passes each time, almost always at the desired angle?

Whether discussing a player's statistics, a coach's formula for drafting certain players, or even a judge's score for a particular athlete, mathematical application is essential. Even concepts such as the chances of a particular athlete or team winning are mathematical in nature. One can always note the connection and importance of maths, especially shapes and angles, in both field and ice hockey.

Some examples where you can see mathematics primarily being used are 'cutting off the angle', 'passing the puck', 'power play situations' and 'face-offs'.

A field hockey goalpost is 7 feet high and 12 feet wide while an ice hockey goal is 4 feet high and 6 feet wide. When a player comes in on the goalie, he sees open areas of the net where he can shoot the ball and score a goal. However, if the goalkeeper comes out of the goal post and charges towards the shooter, he limits the shooter's ability to find an open area of the net. This is called cutting off the angle on the shooter by the goalkeepers. Now, instead of seeing 30% to 40% of the opening of the net, the shooter only sees about 10% open area when the goalie comes out. This makes it harder for the opponent to score a goal.

In team games like field and ice hockey, the most important is the pass. Passes can be made anywhere on the field at a range of angles, 45 degrees, 90 degrees, 135 degrees, and 180 degrees. When a player passes the puck or ball to his teammate, he would want the ball or puck to hit the stick's blade at the time, when his teammate accelerates. To do this consistently, the player must calculate the speed of his teammate and his position when the pass arrives. While doing this, he does have to do a little mathematics, but not with a calculator or pencil and paper, but simply with his brains. Each type of pass has its own speciality and need. The 45 degree pass must have a great deal of force because it is often done when the receiver is running by the player who has possession of the ball. The 90 degree pass must also be quick to the open receiver. The even better passes are the 135 and 180 degree passes because they allow little time for interception by the opposing team and

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have the greatest accuracy when executed properly. An accurate pass may result in a scoring opportunity for his team, while a poor pass may cost his team the possession of the puck, and may give the opposite team a scoring opportunity.

In ice hockey, when referees call penalties, a team usually gains a numerical advantage over its opponent, which is called a power play. The teams regularly play with five skaters and a goalie throughout the game, but after a penalty, the offending team will only have four skaters and its goalie on the ice. The team with the numerical superiority will try to use this ratio to its advantage by getting the puck to an uncovered player for an unpreventable shot on goal.

As has been said by Stephen King 'Talent is cheaper than table salt.

What separates the talented individual from the successful one is a lot of hard work.'

In ice hockey, a face off is when the official drops the puck between two opposing players standing one stick length apart, with their stick blades flat on the ice. This usually happens when the play is being resumed after it had been stopped for certain other reasons. Before players use their sticks in an attempt to gain possession, they have to figure out how fast the official will drop the puck, where it will land and how fast they will have to move their stick to gain possession of the puck. The faster a player calculates these movements, the better chances he has to gain possession of the puck.

As has been said by Stephen King, 'Talent is cheaper than table salt. What separates the talented individual from the successful one is a lot of hard work.' One important aspect for any successful sports-person is hard work. Hard work with application of science and mathematics can achieve superior results. The application of mathematics and science in sports is becoming more and more important in achieving consistency in performance and also in understanding the strengths and weaknesses of both opponents and one's own team.

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Mathematics in Shooting -Rudra Srivastava The excitement caused by the recent London Olympics has been great and though the bustle has relatively subsided, the world community has great expectations from the 2016 Olympics. Sports have undoubtedly been a widespread interest within all kinds of communities with the Olympics being at the forefront.

However, the simple question here is- 'Why does a sportsman with mathematical knowledge fare better than the others?'

This article shall, however, attempt to answer that only within the scope of shooting. A sportsman with mathematical knowledge is not only more judicious and analytical but has the ability to play in the 'right manner'. In case of a shooter, if the person is experienced in the field of ballistics and approximations along with the calculation of elevation and wind changes he will most likely earn a better score than other shooters who lack these skills. India has had many great shooters and a majority of them have been mathematically experienced leading to their success in the sport.

Now I shall like to address certain issues concerning the basic and foremost uses of mathematics in shooting for those who are inexperienced and lack adequate knowledge in the field. These examples might also concern physics since mathematics and physics are indeed interdependent.

The first and foremost mathematical application is range estimation with the help of a Mildot Reticle Scope. The distance from a target can be estimated with accuracy by determining how many angular mils a known target or object subtends. The angular mils are determined using the Mildot Reticle. To determine the distance or range of a target of known size at an unknown distance, a formula can

be applied: Where D is the range to the target or object in meters, S is the size of the target or object in centimeters (known width or height of the target), and Mil is the number of Mildots. They are numerous other formulae that are used for range estimation on the application of various factors but require much more advanced understanding of the subject. Trignometry has a lot to do with these formulae.

Ballistics is the science of mechanics that deals with the flight, behaviour, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance. Ballistics too involves mathematics to a great extent. Here it would be appropriate to mention the ballistic coefficient. The ballistic coefficient is simply a measure of how well a projectile behaves in air. It is necessary for shooters to know what type of bullet behaves well in the air in different conditions in order to strike the target.

To put it simply, the magnitude of the ballistic coefficient is directly proportional to the efficiency of the bullet in air. The formula that has been put together is:

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C = SD/i = w/id Where C is the ballistic coefficient, SD is the sectional density (weight of the bullet divided by the square of its diameter), i is the form factor (number comparing the shape of a bullet being tested to the shape of a standard bullet), w is the weight of bullet, and d is the diameter of the bullet.

The calculation of elevation is another area where mathematics plays an important role. Suppose we fire a shot at 500 yards and one observes it strike 17 inches low. By how much do we adjust the elevation? The following is a formula for determining the scope correction or change in elevation; Minutes of Angle scope correction (MOA) = Change correction in inches/ total distance; In this case, the MOA scope correction will be 17/5.00, or simply 3.5 MOA Adjustments are mostly in" MOA", for most scopes and one click of adjustment is ¼ MOA to allow adjustments to be more precise. Thus 3 ½ MOA will be equal to 14 clicks of change in elevation.

Formulas for the other two factors can also be derived from the above formula.

Another important example is that of a bullet's trajectory fired at a target and gauging the bullet

drop. The Rifleman's rule accurately describes bullet drop when fired uphill or downhill and is based upon rules of differential calculus. In fact most shooting and projectile motion formulas and calculations are based upon differential calculus, or simply any other form of calculus, and even trigonometry.

A rifleman's rule of thumb makes a rifleman accurately fire a rifle that is suitable for horizontal targets at uphill or downhill targets. The horizontal range set for engaging a target either uphill or downhill is known as the slant range. For a bullet to strike a target at a slant range (Rs), the incline being α, the adjustment to the horizontal target must be Rh = Rs cos(α) .

When one thinks about it, one cannot even imagine a world without mathematics where the result of its absence might have led to non-existence of sports. In the dimensions of a soccer and hockey field, in the manufacturing of a gun, and even in a simple basketball shot mathematics has found an important usage. In conclusion, shooting, amongst many other sports, depends on the mathematical knowledge of the shooters, without which let alone accuracy, precision too would not have been achievable.

Mathematics in Basketball -Anirudh Batra Basketball is a sport played by two teams of five players each on a court of 94 feet from end to end and 50 feet from side to side. The primary aim is to shoot a ball to make it pass through a basket which is placed at a height of 10 meters above the ground, like a perpendicular on a flat base. For accuracy, factors such as a convenient angle for the shot depending on the height of the player, the length of the arm, the extension of the muscles, and the curve of the wrists play a key role. How can it possibly be even remotely linked to Mathematics?

To start with, Mathematics is a subject which finds application in the most unpredictable of places. In light of that statement, it is a compulsion for

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something as mechanical and athletic as basketball, to be theoretically driven by mathematics.

Let us take a look at the basics of shooting a basket.

There are three basics involved in this particular process- the impulse, the angle and most importantly the position of the arms. For instance if we take a shot from the free throw line at an angle of 45 degrees or greater it will result in a successful one. To add more power your elbow should be as close as possible to your face so that the ball follows a straight line towards the basket and extend your hand as far as possible to involve a greater force. The concept is simple; imagine the loop to be a destination, the ball to be the object, and the aim

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being to set the object in projectile motion such that when the curve is arching downwards it passes through the basket.

According to Newton any object which is a semisphere will react with the amount of force applied to it. In case of a long pass you need to apply a proportionate amount of force to the ball.

Geometry, another important part of mathematics, can be applied in 'rebounding '. A basketball that is dropped in the basket at a 70 to 90 degree angle from above, simply speaking has a larger diameter target to drop through than a ball approaching the hoop from a 30 to 50 degree inclination. Geometry can also be applied in defen-

sive strategy.

If geometry is further applied in multiple defense strategies it would be far easier to get the ball. The main feature which has to be focused on a man to man defense strategy is the defender's leg angle, keeping in mind the dictum, the more folded one's legs are the faster one will be.

To conclude, one might say that if one does do the math then who would play the game? The answer is simple - willingly or unwillingly, the game is designed around math. The angle at which the shot is taken, the motion in which the ball is set, for each action, certain knowledge about the math is imperative and shall always be so.

Mathematics in Table Tennis -Tejit Pabari Table Tennis is a sport in which two or four players hit back and forth a hollow, light ball with special rubber coated rackets. The game takes place on a hard table divided by a net. The game of table tennis is mostly based on math and physics.

Anyone who has ever played table tennis should know that, since accuracy and speed are essentially the most pivotal aspects of the sport.

There are a handful of formulae that are applied in table tennis. Sir Isaac Newton derived these formulae in his work “Philosophae Naturalis Principia Mathematica”. It accurately explains how objects move, from colossal objects to those about 1000th of an mm.

The formulae put forward by Newton areP=W÷t W = Fs F = ma a = (v - u)÷t T = rF Where P is power, W is work done, t is the time spent, F is the force applied, s is the displacement, m is the mass of the body, a is the acceleration on the body, v is the final velocity, u is the initial velocity, T is the torque generated, and r is the radius of the object. The application of these

formulae is very interesting.

P = W÷t (Power = work ÷ time)In order to gain power in your shots, you have to do more work or take less time in your shots. To increase the work the second equation must be used.

W = Fs (Work = force × displacement)If the amount of force applied is increased then the work will increase. The work can also be increased by increasing the displacement which is not possible as the size of the table remains the same. In order to increase the force the third equation must be used.

F = ma (Force = mass × acceleration)The third equation requires the mass or the acceleration of the ball to be increased in order to increase the force. Increasing the mass of the ball is impossible. Therefore to increase the acceleration (the only option left) we need to apply the fourth equation. a = (v - u) ÷t (Acceleration = (final velocity-initial velocity) ÷time)If you want to maximize the acceleration of a body you must minimize the initial velocity (which is not possible as it depends on how fast the ball is hit by

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your opponent) or maximize the final velocity for which you will have to hit hard. Also the initial velocity is added as when the ball is coming towards you its value is negative (retardation)!

Therefore it is actually added to your velocity! The time remains fixed. So if you hit hard the acceleration will increase which will increase your force, which will increase your work, which in turn will increase the power of your shots.

The further you back away from the table the more time you will have to prepare yourself to hit a shot.

This demonstrates that the harder you hit the ball the more power it has. After leaving the racket the ball is influenced by three factors: gravity, air resistance and spin. In case of top spin, gravity and spin work together to give a slightly larger arc than normal. In a back spin gravity and spin work against each other so the ball first curves and then drops down as gravity decreases. Air resistance is also a vital factor like gravity and spin. It increases or decreases by the square of the given speed. This means that if we double the speed of the ball there will be an increase in the resistance and vice versa.

In case of fast counter play, an average speed would be 12.5m/second. In case of top spinning the force of the ball is at the right angles to the speed and the ball.

Counter hitting is one of the most important aspects of table tennis and math plays a role in that too! If you assume that the two players pick the ball at a distance of about 20-25cms, then the ball would reach an average speed of about 1214m/sec. therefore you can roughly calculate in your mind the speed if distance is know. Applying some other angle formulae you can know where exactly the ball would come in a counter hit.

The serve is of great importance in table tennis.

Because the serve must bounce at both the halves of the table, the upward and downward movement will be around 34-35cms. The time limit from bounce to bounce will be same for the short and long service. However in case of short serve we must add the time it takes for the racket to touch the ball. Therefore the total time for a short serve will be around 0.6 seconds while for long and fast

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serve it will be 0.4 seconds.

When the ball and racket make contact, the ball will be at 85% of the incoming speed (other factors such as force not applied). For an attacking player the rubber's task is to preserve the speed as best as it can and also give a good chance for the player to spin. The material and quality of the racket can also change the bounce and friction.

The effect which occurs between the table and the ball is because of the bounce and spin. There is also a loss of energy. As a result the bounce doesn't reach its full height. It'll only be 70% of the normal.

In case of a top spin the ball acquires forward energy and this is converted to increase the forward movement of the ball. Therefore the bounce will be less and the forward will be more.

The further you back away from the table the more time you will have to prepare yourself to hit a shot. However, logically speaking, it also gives more time to the opponent. Both benefit from the fact that the ball loses speed over distances. It gives more time to react and therefore a good sensible player can beat you easily. Nevertheless there are several advantages in playing closer to the table: The angle of play, speed and time increases.

The knowledge of angles helps players in determining the best possible position and its advantages.

The knowledge of angles helps players in determining the best possible position and its advantages. Why angles? Because the player must be able to return incoming shots from any angle available to the opponent and move to a position where his/her right shoulder is on the center line.

So when playing from FH to BH corner the opponent's diagonals gives the most advantage return angle. In doubles the same geometry applies the only difference is that the one who take the ball doesn't have to return it.

Table tennis undoubtedly has a large involvement of mathematics in it. We can observe that the great speed that the sport is played at requires an unmatched level of dexterity and understanding of the mathematics involved.

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Beauty of Maths in Origami -Pranjalya Shukla Though origami is nowadays synonymous with Japan, it was started in 200 AD in China when paper was first produced as a cheap alternative for silk. This art was earlier known as “Zhezhi” in China and was brought to Japan by Chinese Buddhist monks. Origami took off in Japan from that time onwards and became a popular activity for children for many centuries. The basic rule of origami is that one is restricted to using only one square sheet of paper and can make an origami model by just folding it and not using tape, glue or scissors. It is a skill which transforms a flat sheet of paper into 3-D models and these 3-D models can be transformed back into the same 2-D sheets.

For an art as old as paper itself, origami has taken a long time to reach its status. But till now, mathematicians and origami experts are exploring new avenues every day.

Origami influences our life in really simple ways and appears in folded napkins at the restaurants, in household decor, in jewelry items and in the way the air-bags in the cars are folded and kept. Many concepts of Euclidean geometry are manifested in the creases and the valleys of the unfolded square of the origami model. Euclid was a Greek mathematician and is referred to as the ‘father of Geometry'. He knew that by using a straight edge and a compass, it was possible to construct a large number of geometric figures, like quadrilaterals and circles. The basic operations to make the same were termed as ‘Euclidean Functions'. However, these axioms were not referred to until origami

was introduced. Just as Euclid had devised axioms for earlier origami, the modern mathematicians Humaiki Huzita and Koshiro Hatori devised different set of axioms to describe origami geometry the “Huzita Hatori ” axioms.

Origami influences our life in really simple ways and appears in folded napkins at the restaurants, in household decor, in jewellery items and in the way the air-bags in the cars are folded and kept.

For an art as old as paper itself, origami has taken a long time to reach its present status. But till now, mathematicians and origami experts are exploring new avenues every day. These days mathematician are using origami in different ways. Its creases on the flattened surfaces are now applied to areas such as graph theory, combinations, optimization problems, fractals, topology and supercomputing. Some exciting theorems

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recently discovered are: i) Maekawa's Theorem: the difference between the number of mountain creases and the number of valley creases in a flat vertex is always 2. ii) Kawasaki's Theorem: the sum of every other angle about a flat vertex in a flat fold is always 180 degrees.

For an art as old as paper itself, origami has taken a long time to reach its status. This art shall go on expanding as new theorems will be discovered and new doors will open. After all, all it requires is a sheet of paper.

Functioning of a Calculator -Udbhav Agarwal “Most human beings have an almost infinite capacity for taking things for granted.�

And yes, Aldous Huxley has been right always. If thought about it then given an opportunity man shall and always will take the easy way out. It is a simple theory, popularly framed as 'abstraction', that man would care only and only for the information which is necessary while the background information shall for all means and purposes be left behind. And so is the case with a calculator, a device so common in our lives, that all we know about it is how to switch it on, press the keys and get the answer! But, have you wondered, what goes on beneath the keys? Never, I suppose. And for that very reason, read on, as what follows is the story of the calculator.

Before we go further, there are certain terms/parts about/of a calculator which need to be understood.

Another warning before we proceed - the information is true only and only for electronic calculators, and not our calculators in the computer which, by the way, run on programmes. Like any other device, a calculator obviously has a power source, and it also has a keypad; but it is the processor chip (the green plate with various grooves and spikes) which matters the most.

One of the first components of a processor chip is

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the scanning unit. When a key is pressed an electrical signal is sent, and the scanning unit, as the name suggest, scans the keypad for these very signals.

The encoder unit converts, the hence picked signals converted into the binary code, it either gets sorted into a X register or a Y register. The X and Y registers are 'number stores', where the scanned signal, or the digit, is stored temporarily.

In that time frame, calculation can be carried out on those numbers.

To cut a long story short, when we enter a number, it gets scanned by the scanning unit and gets converted into a binary number in the encoder unit.

While the calculator is doing the calculations the functions required are stored in the Flag Register.

Permanent Memory or Read-Only Memory, is the seat of in-built functions. The instructions, hence given in there, cannot be erased from a calculator.

In most of the calculators, one also gets the option of storing answers, or digits; these numbers are stored in User Memory or Random Access

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Memory. The most important and crucial part of a calculator is the arithmetic logic unit (ALU). The ALU executes all arithmetic and logical instructions, and gives the result in the form of a binary code, which is then converted back to the desired result by a decoder unit.

What is baffling is the fact that such a complex process is employed in such a basic calculator. If the method is to be followed, then in graphic-display calculators (GDC) where equations are solved as a whole, so many registers would have been required.

To cut a long story short, when we enter a number, it gets scanned by the scanning unit and gets converted into a binary number in the encoder unit.

After this it reaches the X Register, where it can be manipulated by using functions present in the Flag Register. Meanwhile, the Flag Register has already extracted the functions from the permanent memory, and executed them using ALU. The answer given out can be stored in the User Memory, after it has been converted back to numerical form using the Encoder Unit. And hence we solve 2+2 on a calculator. ~ Let us take an example of 25*5. As one presses the four keys( the keys for 2, 5, multiplication symbol, and five again) the following is the sequence of events which take place: ~ When 2 5 is entered, the scanning unit reads it as 25 and after passing through the encoding unit it reaches the X Register. ~ As the * key is pressed, the multiplication function is also sent to the Flag Register in its encoded form. ~ As the second number 5 is entered, the encoded number 25 is pushed to the Y register, while 5 enters the X Register, passing through the Encoder Unit on the way. ~ Now, when we enter the '=' sign, a message sent

by the Flag register to the permanent memory, tells the latter, “Multiplication needs to be done�. ~ The contents of the X and Y register are then loaded into the ALU, where instructions are executed, using the functions from permanent memory. ~ The answer calculated is sent back to the X register to the decoder unit and then flashed on the display panel.

Further calculations are carried in the same manner

. The answer goes to the X Register and as the operation and the second number is typed it gets pushed to the Y Register, only to be operated on once again. Therefore we usually see that in plain calculators the whole question, supposing 2+3+4 , is not solved as a whole, rather 2+3 is first solved and then 5+4 is solved.

What is baffling is the fact that such a complex process is employed in such a basic calculator. If the method is to be followed, then in graphic-display calculators (GDC) where equations are solved as a whole, so many registers would have been required.

But once again, a calculator is just another thing on the table, which makes life easier. That is all that there is. Press some keys and the answer flashes. It is magic... till you know what happens.

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G.I.M.P.S. -Shivam Goyal Prime numbers seem to be quite fascinating, simply because no prime formula has been discovered till date. Many scientists have dedicated their lives to crack this code, but no one has been successful.

Many have invented some formulae, which work in only a few cases. One of them is that one should multiply prime numbers in order and subtract one from it. That is (2*3*5)-1= 30-1= 29 which is a prime number. This goes on till a specific number and then it doesn't work. Many worldwide groups and organizations have been formed to try to get as close as possible. One of them is G.I.M.P.S (Great Internet Mersenne Prime Search). G.I.M.P.S is a project consisting of volunteers who try to find out the biggest Mersenne prime number. A Mersenne number is a number which is 2n -1, where n may not necessarily be a prime number. This project was

founded by George Woltman, a graduate from Massachusetts Institute of Technology. It was founded in the year 1997. The volunteers who are involved in this project do not need to perform complex mathematical calculations but just need to sign up, whereas the rest is done by his computer. The project has till date found 13 Mersenne prime numbers. The largest prime number till date is 243,112,609 -1 (or M43, 112,609) which was discovered on 23 August 2008 by Edson Smith at the University of California, Los Angeles (UCLA)'s Mathematics Department. He got awarded $100,000, although it was whereas his computer deserved the award not him. No one knows whether the formula for prime numbers will be discovered or not, but certainly it will remain a mysterious concept in mathematics.

Laila Majnu -Sandip Banerjee Department of Mathematics, IIT Roorkee Mathematical modeling is the application of mathematics to describe real world problems and investigating important questions that arise from it. Using mathematical tools, the real world problem is translated to a mathematical problem, which mimics the real world problem. A solution to the mathematical problem is obtained, which is interpreted in the language of real world problem to make predictions about the real world.

What I am going to discuss now is a mathematical modeling of love affairs. I call it the Laila Majnu story with a twist. We consider a system of first order linear differential equations of the form

Here, M(t) represents Majnu's love for Laila at time t and L(t) represents Laila's love for Majnu at time t.

The constants a and c gives the the impact of the individual's own feeling on himself/herself. If a, c > 0 but less than 1, then initial feeling dampens over time.

Using mathematical tools, the real world problem is translated to a mathematical problem, which mimics the real world problem.

But, if a, c >1, then initial feeling intensifies over time. The constants b and e give the impact of the

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individual's feeling affecting the others. If b>0, then Majnu gets excited by Laila's love and discouraged by her hate for him, whereas, if b<0, then Majnu gets excited by Laila's hate and loses interest in Laila's love for him.

We consider a case when a = 0, b = 1, c = 1 and e = 1.

This means Majnuâ&#x20AC;&#x2122;s own feeling do not impact his

The graph says that over time their love turns into hate (as the graph goes below zero) and then their love knows no bounds. However, Laila's love dampens a little due to lack of response from Majnu.

Similarly, various cases can be considered and different interesting dynamics may emerge.

feelings for Laila but gets excited by Laila's love and discouraged by her hate. On the other hand, Laila has perfect love for Majnu but loses interest if Majnu shows love. Let us now solve the differential equation and observe the graph for the dynamics of this complex nature of a love affair.

Reference: Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering, Steven H. Strogatz.

Puzzled...

-Parth Khanna 1) A cube has 6 faces and 8 corners. On each corner there is a circle. Write numbers from 1-8 in such a way that the sum of the four numbers on each face is 18.

3) Add a 3X3 grid in a calendar. Take out the lowest number in the grid and add 8 to it and multiply the result by 9. The product would be the sum of the total digits inside the grid.

2) Interesting pattern: 2 2 2 1 = 1, 1+3=4=2 , 4+5=9=3 , 2 2 9+7=16=4 , 16+9=25=5 and so on.

Keep on adding a successive odd number to the previous square of the number to find out the square of the next number.

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Behind the Scenes Editor-in-Chief: Aditya Vikram Gupta Aditya has opted for the Commerce stream in ISC with Mathematics being one of his stronger subjects.

Apart from Mathematics, his interest lies in Economics as well, relating to which he is a member and Boy-in-Charge of the Business Club. Aditya serves on the board of a number of other publications and has been actively involved in MUNs as well. A respectable publicspeaker, he is the LAMDA boy-in-Charge. Aditya also works actively for the Stage Committee and the Archives, being the Boy-in-Charge of both.

Swimming is his main strength on the sports front and he is the School Swimming Captain. Aditya joined the Board in his 10th grade and has since contributed adding quality to the magazine.

Chief-of-Production: Aviral Gupta Aviral is studying Science under the ISC programme along with Psychology, which makes his combination an interesting one.

Aviral is the Head of Science Society. Social service is his main forte in school where Aviral has worked extensively and is presently the School Social Service Secretary. Aviral is a talented musician and dancer and has performed on several occasions. Aviral loves playing squash and does athletics. Eccentric to his subject combination, Aviral is a keen photographer. Aviral has been on the Board since his 10th grade, and has been instrumental in the graphical enhancement of the magazine and making it a reader-friendly magazine. All credits for the graphics editing of the magazine go entirely to him.

Senior Editor: Shivam Goyal Shivam is studying the IB Diploma and amongst others his subjects include both Mathematics Higher Level and Physics Higher Level. Mathematics and Physics are the two subjects that Shivam says 'excite' him and also the two that he wishes to pursue later on.

Astronomy and Aeromodelling are the two extracurriculars that Shivam has worked actively in.

Shivam is also the Boy-in-Charge of the Aeromodelling STA. Shivam has been on the Board since his 10th grade and in this issue has discussed an interesting and unique topic - Great Internet Mersenne Prime Search.

Senior Editor: Ujjwal Dahuja Ujjwal is studying the IB Diploma and amongst others his subjects include Mathematics Higher Level and Further Mathematics, with Ujjwal being one of the few students in India to have taken the subject.

Ujjwal also has a professed love for chess and is also the School Chess Captain. On the co-curricular front Ujjwal is both an avid debater and 'MUNner', and has participated in numerous MUNs and debates.

Athletics and cricket are his main interests in the sports arena. Ujjwal has been on the board since his 10th grade and in this issue has focused on 'a beautiful mind that never made it to the screen.'

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Editorial Board Editor-in-Chief Aditya Vikram Gupta Chief-of-Production Aviral Gupta Senior Editors Shivam Goyal, Ujjwal Dahuja Associate Editors Devesh Sharma, Udbhav Agarwal Senior Correspondents Abhinav Kejriwal, Pranjalya Shukla, Siddharth Suri Junior Correspondent Shrey Aryan Faculty Advisors Anjan Chaudhary, Chandan Singh Ghugtyal, Mona Khanna Special Thanks Purnima Dutta, Stuti Kuthiala Contributors Anirudh Batra, Sabhya Katya, Harsh Vardhan Singh, Tejit Pabari, Parth Khanna Photo Credits Orijeet Chatterjee

“Ultimately, I am certain about one thing — mathematics is extremely beautiful. Only a few can truly appreciate it. Beauty is not in the eye of the beholder. Beauty is in the mind of the beholder.

Mathematics is a sophisticated toy you can play around with until reaching total intellectual satiation. It is unbelievably perfect and this is why I feel it is not the universal language. The world is an interesting but imperfect place and needs something to balance it.

So let’s dream in mathematics and wake up in the real world.”

-Gergana Bounova, Bulgaria

Mathematics Department, The Doon School, Dehradun - 248001.

Website: www.doonschool.com © Copyright: The Doon School, Dehradun 2012 All the information is correct at the time of going to press.

The school reserves the right to make any amendments.