Experience Mathematics #4 -- Division by zero!

Both Koonal Sharda (Class VI, DPS, Mathura Road) and Sarthak Parikh (Class VIII, Sardar Patel) gave the correct solutions with good explanations. What is creditable is that students are expected to answer these questions only when they reach Class XI. However, they say that Gauss found these patterns when he was only 10 years old! But anyway, well done.

Assuming the pattern that you observed continues forever—and it does—the sum $O$ of the first $n$ odd numbers is given by the formula: $O=1+3+…+2n-1=n^2$. This fact can be proved using Mathematical Induction. Adding $n$ is the same thing as adding $1$ $n$ times. So we obtain: $E=2+4+…+2n=n^2 +n$. From this it is easy to find the sum of the first $n$ numbers. We divide each term by $2$ to get $$1+2+3+…+n=(n^2 +n)/2 = n(n+1)/2.$$

Once again Sarthak asked some deep questions on which today’s experiments are based. He asked: What meaning can be given to division by 0?

At the outset, let me say that division by 0 is not allowed.

The reason is the confusion caused by the following argument: We know that $0=0.$ This implies that $0$ times $1$ is equal to $0 $ times $2$. So $0 \times  1 = 0 \times 2$.  Now canceling $0$ from both sides (by dividing both sides with $0$) we obtain $1=2$, which clearly is false. And there is a theorem in mathematics that says that a false proposition implies any proposition. Which implies that Santa Claus exists. And also implies that Santa Claus does not exist.
Now you can see why mathematicians have very sensibly banned division by $0$.

However, this does not mean that mathematicians do not try to give division by $0$ some meaning. Try the following (you may need a calculator or a computer for some of these experiments):
1. Make a table of the function $y=1/x$. In the first column place numbers very close to $0$ that are positive. For example $0.1, 0.01, 0.001, \dots, 0.0000000001$. In the second column, replace $x $ in $1/x$ by this number and see what values come out for y. For example, when we replace $x$ by $.01$, we get $y=100. $ Describe the results of your experiments.

2. Now replace $x$ by negative numbers that come closer and closer to $0$ and find out what value $ y$ takes. Describe the results of your experiments.

3. Try the above with the function $y=x^2/x$. Does the value come closer and closer to a number? 

Describe the results of your experiments.

We say a function (depending on the variable $x$) approaches the limit $+\inf$  (read plus infinity) when $x$ approaches a number $a$ from the left, if given any large number $M$ (any large number you can think of), we can find a number a little smaller than $a$, so that the corresponding value of the function becomes larger than $M$. (The ‘left’ refers to the number being to the left of $a$ on the number line.) Similarly, we can define the limit approaching from the right, and the limit approaching minus infinity.
Intuitively, it is easier to understand the limit of a function if it approaches a number $q$, when $x$ approaches a number $a$. We replace $x$ by numbers close to $a$, and find the value of the function. If the value comes close to a number $q$, the limit is $q$. Try the following experiments and get a feel for the definition.

4. Multiply $(1-x)$ in turn by $(1+x),$ $(1+x+x^2),$ $(1+x^2+x^3)$ and simplify. Can you generalize the pattern?

5. What is the limit of $(1-x^2)/(1-x),$ $(1-x^3)/(1-x),$ $\dots$, $(1-x^n)/(1-x),$ as $x$ approaches $1$. (Hint: Replace $x$ by numbers close to $1$, like $1, 1.1, 0.9, 1.01, 0.99, 1.001, 0.999,$ $\dots,$ and guess the answer in each case.)

Experience Mathematics # 3 -- The sum of the first n odd numbers

Akarsh Gupta (Class VII, A.P.J., Noida), Sarthak Parikh (Class VIII, Sardar Patel) and Richa Sharma (Class IX, Swami Vivekananda Sarvodaya School) all gave excellent explanations/solutions to the questions asked in the previous column. The answers (very briefly) are:

Q1. The numbers that have $0, 2, 4, 6, 8$ in the last digit are divisible by $2$.

Q2. The numbers that have $0$ or $5$ in the last digit are divisible by $2$.

Q3. If the sum of the digits of a number is $9$ or a multiple of $9$, then that number is divisible by $9$.

Q4. If the sum of the digits of a number is a multiple of $3$ then that number is divisible by $3$.

Sarthak Parikh also asked an interesting question. Sarthak asked: How many lines of symmetry does a parallelogram have? What about the square? Rhombus? Rectangle? Octagon? Cut these shapes out of paper and label the vertices. Experiment by drawing various lines, and flipping the shape. If you get back the same shape (but with different labels) you have discovered a line of symmetry. For example, a square with vertices labeled ABCD, you may get a square labeled BACD (see the top two squares in the picture). If you notice, by flipping across a line you have rotated the square by 180 degree. You should also try to find other rotational symmetries. When you rotate a square ABCD clockwise by 90 degrees, you get the square DABC (bottom square in the picture). After doing some experiments, perhaps you would like to answer Sarthak’s query?

Here is another activity involving squares—the squares of natural numbers.
Complete the following table. For n going from 1 to 20 write the square of n in the second column, and the sum of the first n odd numbers in the third column. The odd numbers are (1, 3, 5, …).

Sum of first $n$ odd numbers
$1+3= 4$


Make a picture showing the pattern above. (Hint: see the picture below)

  1. Find a formula for the sum $O$ of the first $n$ odd numbers: $O = 1+3+5+7+\cdots +(2n-1).$
  2. Use the formula for $O$ to find a formula for the sum $E$ of the first $n$ even numbers: $E=2+4+\cdots+2n .$
  3. Use the formula for $E$ to find a formula for the sum of the first $n$ natural numbers. 

Check your work by putting $n=1, 2, 3, 4, 5$ for each formula you find.

Experience Mathematics # 2 - Divisibility

Among all the students who tried to answer the questions presented last week, Anirudh Matange (Class VI, Ahlcons School) gave the best explanations. The answers are: 

Q1. The Commutative Law for multiplication. 

Q2. The Prime Numbers $(2, 3, 5, 7, 11, 13, 17, 19)$ give rise to only two rectangles: 

Q3. The largest number of rectangles arise from $12, 18,$ and $20.$ 

Q4. The rectangles with side $2$ can be formed by the Even Numbers: $2, 4, 6, \dots, 20.$ 

Q5. All the Multiples of $3$ (namely: $3, 6, \dots, 18$) can form rectangles with side $3.$ 

Here is another mathematical activity on the concept of divisibility. When a number $n$ divides a number $m$ evenly, we say that $m$ is divisible by $n$, or that $n$ is a factor of $m$. There are a number of tests that determine whether a given number is divisible by $2, 3, 5,$ or $9.$ By doing the following experiments, you can discover these tests for yourself. 

1. Consider the numbers: $2030, 4201, 89782, 129083, 124, 5435, 67656, 9087, 8888, 90919.$ For each number, you have to tell the last digit when the given number is multiplied by $2$. 

2. For each of the numbers in Activity 1, you have to tell the last digit when the given number is multiplied by $5$. 

3. Make a table with 2 columns. In the first column, place the multiples of $9$ less than $100$ ($9, 18, 27, 36,\dots , 81, 90$). In the second column, note the sum of their digits. 

4. Make a table with two columns. In the first column, put any $10$ multiples of $3$ less than $100$—such as $12, 15, 63, 51$—that are not all multiples of $9$. In the second column, note the sum of their digits. 

Now use your experiments and guess the answer of the following: 

Q1. Which of the following numbers is divisible by $2$: $100000, 1201, 2342, 9083, 2124, 21245, 1906, 6757, 1978, 9879.$ 

Q2. Which of the following numbers is divisible by $5$: $100000, 1201, 2342, 9083, 2124, 21245, 1906, 6757, 1978, 9879.$ 

Q3. What is the rule for checking whether a number is divisible by $9$? 

Q4. Which of the following numbers is divisible by $3$: $101010, 1201, 20112, 2124, 21223, 1906, 6757, 1978, 9879, 1080.$ 

Bright students should verify, and then prove that their guesses are correct. But the proofs, while easy, are not covered in school syllabi. For the moment, it is enough to know the tests of divisibility without knowing why they work.

Experience Mathematics # 1 -- Mathematical activities


Children learn by doing. By doing these activities, they will experience interesting mathematical ideas. They will also gain experience in thinking mathematically. This will help them understand concepts easily, and better their performance in exams.
It is also very important to remember that the encouragement of parents and grandparents motivates a child a lot. Praise them when they show their intelligence by doing mathematical activities successfully. This will make the children work hard to become better at mathematics.
Why do children find mathematics difficult? The most important reason is that they find mathematics removed from their daily existence. However, it is not too difficult to give mathematical experiences to children. In this column, we will give an activity for children. It is a good idea for parents to help the child with the activity, if the child is studying in class I-V. For older children, show them this column and challenge them to explain the answers of the questions below.

This activity requires 20 round pegs. The round pieces of a Carrom Board set will do nicely. You may also use 20 buttons of the same size. 

Pick a number—say 15. Take 15 pegs and make as many rectangles as you can out of them. Each time you are able to make a rectangle, reproduce the rectangle in a drawing book and note the dimensions. (You can use dots to make rectangular arrays.) For example, using 15 pegs, you can draw the following rectangles. 

Repeat this activity for each number from 1 to 20. Now try to answer the following questions:
  1. When you rotate a rectangle by 90 degrees, you get another rectangle with the same number of dots. What is this law called? 
  2. List the numbers that give rise to only 2 rectangles? 
  3. Which number (or numbers) lead to the largest number of rectangles? 
  4. What are the dimensions of all the rectangles with one side consisting of 2 dots? 
  5. What are the dimensions of all the rectangles with one side consisting of 3 dots? 
It is not necessary that you will be able to answer all the questions. But it is important to try hard. In the next column, we will give explanations of the mathematics underlying this activity.

Horowitz and Sahni - Book Review of a book on Computer Algorithms

Here is a book review I wrote for the Journal of Indian Education. Here is a link. I read it again after nearly 10 years and find myself agreeing with it. Especially, the one about how teachers should act...

There is a quote by Bill Gates in it, but I cannot find the link to his article that I have referred in the article.

From the Diary of a Netizen

My day began at my daddy’s tea stall at 6 am and the big guard gave me fifty paisa as a tip. I bought a chocolate toffee from the corner shop on the other side of the orange office building.


The children from the school near my house laughed at me because my shorts were torn. I hid behind the wall and aimed a stone at the boys, and ran into my house.


I am nine years old. I don’t go to school because I have to help my father and elder brother run the tea and cigarette stall. Today I was able to give change—to someone buying cigarettes—without asking my brother or father. You don’t have to go to school to be able to do arithmetic, I guess.


While playing cricket, our new ball went over the top of the wall, right into the manicured garden of the office complex. A tall auntie with a long sharp nose wearing a saree gave it back.


Today a strange man came and distributed packets full of a pink liquid. My old man drank one too many, fought with a friend, and got a black eye in the bargain. The man promised to bring something for my mother and me next time. My brother told me that he is a politician.


Today three people came and made a hole in the wall of the orange building. They have put a computer there. Guddi, Raju and I went to see what we can do with it. It’s a little TV screen with pictures on it. They showed us a little black square on the side. By moving our fingers on this square we can move an arrow on the screen. It feels like it is made of thick rubber.


My father got drunk and beat up my mother. They fought so loudly that I went away and ate at Bina and Guddu’s house.

Ramu, the big bully in our colony, will never bother us again. Today we made so much fun of him when he slipped and fell into the big pile of cow-dung lying in the middle of the ground. He tried to catch and beat us up but we ran away.


We moved our cricket playing so that the ball does not break the TV screen. Renu Aunty came to ask whether we like the computer. Raju said he liked to play games on it. Guddi did not say anything.


My mother hung clothes to dry and my shirt flew over the roof. She held up my two-year old sister so she could clamber up the asbestos roof to bring back my shirt. She nearly fell down but mommy caught her in time.


Today I somehow shut down the computer. An uncle from inside re-started it. We closed it again and asked the guard to re-start the computer. I showed everyone how it could be done. For some reason, Vivek Uncle was in a smiling mood that day.


There are many aunties and uncles in this office building. They all come in Maruti cars, and hang around the front of the building drinking coffee or tea. The guard told me they have a machine which can make tea.


Sanju Bhaiyya, who lives near my house and goes to work, made a picture in the computer. He knows a lot about the computer. But all I wanted to do was to play with Mickey Mouse. In the evening some older people came and asked us to show them how to play with the computer. But they left soon after, because they could not understand anything.


My mother’s sister came over from the village, with my mausa and Tejali. They will live with us until they find a room for themselves. My father and mausaji had to sleep outside in the cold.


Something went wrong with the computer last evening and Raju cut the touch pad and spoiled it. Somebody complained to his father who gave him a thrashing. I too cried that night.


Today another politician came in an auto-rickshaw and gave pouches of a red drink to my father and his friends. He gave us children small flags and we ran all the way behind the auto until it turned the corner. My father and his friends laughed and shouted boisterously all night.


Today, an uncle came and took our photograph. He asked Guddi whether she knew how to use the computer. I told him that she is a girl, and not too interested. He asked my name. The next day Raju, Guddi and I were on the front page of a newspaper. Vivek Uncle and Renu Aunty were very excited, but Guddi thought her hair was not looking too good.

Vivek uncle put a page in Hindi on the computer. It had stuff written in Hindi, but no pictures. I closed it and went back to playing the Tarzan game on Mickey’s site. We found some Hindi film songs on the internet and some movies.

Today was the market day of the week. A naked beggar snaked his way through the crowded bazaar. I saw the Aunty with the long nose drive her Esteem through the crowd, trying to avoid the crawling beggar on the road.


Some foreigners came to see us and talk to us. They were shown round by an uncle wearing a suit. I showed them how I wrote my name in English on the computer. They were quite surprised.


Ran into some uniformly dressed schoolchildren again. This time their jokes did not bother me much.

The characters and events mentioned above are a creation of the author’s imagination.

However, they have been inspired by conversations with colleagues conducting an experiment in Minimally Invasive Education, at a slum adjoining the NIIT Corporate office, in Kalkaji, New Delhi. Children who live in this slum were given access to an Internet Kiosk. This experiment received wide media exposure, following the front page headline: Rajender Ban Gaya Netizen (by Parul Chandra, The Times Of India, May 12, 1999).

One Size Fits All

// Just found this article I wrote for Linkage long back, with some colleagues in NIIT.

One Size Fits All


Gaurav Bhatnagar, Ritu Dangwal, Renu Gupta, N.N. Ramanathan, Himanshu Tayal

Refer as: Gaurav Bhatnagar, Ritu Dangwal, Renu Gupta, N.N. Ramanathan, Himanshu Tayal , One Size Fits All, Linkage, Volume 6.2, Summer 1998

The Cognitive Engineering Forum (CEF) is a small group in NIIT, searching for ways to make intelligent anthropomorphic interfaces. Currently we are working on the design and construction of an emerging cognitive agent. In the last CEF meeting, the authors were trying to design an algorithm for an emerging learning system, that not only appears to have some chaotic human ability, but is also a strategic learning system.

This kind of system is not new to the R&D labs. The program Fluke, now being tested in many CEG centers as an electronic classmate for NIITians, is a good example of the emerging randomized architecture that we wish to build upon. Fluke is an advanced anthropomorphic system, much, much better than the program Eliza (e.g. see the web-site: http://www.ed.ac.uk/~humphrys/eliza.html).

The basic algorithm that we developed turned out to have other applications also. The first implementation of the emerging randomized paradigm, or ERP for short, turned out to have applications in other areas of the lab too. Before going on to the details of the program itself, we will spend some time in looking at the other applications of ERP.

For example, the infant learning multimedia software developed at the R&D lab is an interesting new concept, creating a multimedia learning software for children just born, or about to do so. This software is targeted strategically at new parents, and their new children, and is not the result of corporate randomized management, as it first appears to be. Tests on a three year old child has shown that it aids in the teaching of important motor skills, that are absolutely essential in the IT professional of tomorrow. For example, the youngest known child in the universe who can handle an input device named after the small mammal called "mouse" is a graduate of the infant learning software called MGR.

Another example is of a product developed in the R&D lab of NIIT is the advanced cognitive perception system (code named psycho-mouse). The basic idea is that the chaotic human engineering, especially that of the brain, still sends some recognizable signals, that can be used as an input device for the computer. The feasibility of improving the device to handle intelligent NetCentric perception is being studied. If developed, this device could have an interesting consequence: Email writers will not be able to hide behind the networks, and their thoughts will be bared for all to see.

Finally, the application that is closest to those of us who have an interest in improving humanity for generations to come by means of fundamental research. A random response from the ERP can set our minds thinking for titles of new papers to be written, and further researches in its emerging transformational ability can help us fill in the details. Indeed we almost did that in this paper, except that we changed the title. This title was chosen after the strategic learning methodology of ERP was identified.

This is partly true because of the nature of the human brain itself. We will not go into the theory of how it happens. Suffice it to say that Margaret Boden, of "Creativity" fame has said it all. As Lewis Carroll did not say: When in doubt, trot out Boden. This last statement is false.

I think by now you (the reader) would be really raring to get your hands, or other advanced learning resources, on the program. The basic idea is simple; we will leave the implementation to you.

Choose one word from each of the columns appearing in Table 1.







Table 1

Type it in a suitable text editor, or a typesetting package like MS-Word, and add a few words so the sentence formed appears to make sense. Now try very hard to interpret this sentence. You will find that it is not difficult to make some sense, or at-least some nonsense, out of it. This is due to the properties of the mind, covered in any philosophy of computer science book. If this doesn't work, you probably need to see a computer scientist or a robotist, and re-take the Turing test.

How To Have Smarter Parents

by Tejasi Bhatnagar

In your neighborhood bookstore, or at a nearby web-site, you will find many books concerning parenting: A New Life, Bringing Baby Home, Baby's First Year, and so on. However, there are no documents at all about How to Train New Parents, Calming Mommy and Daddy when they are Freaking, Don't Let Them Sleep, etc. Since I was born so recently, I decided to keep notes of the event, and a few days after. Of course, your parents will be different, your grandparents will be different, their friends will be their own, so much of what I say will not apply to you. But, I took notes anyway.

First, some notation. New users of any computer software are often referred to as newbies (pronounced: new-bees). I call my new parents newpies, pronounced new-pees. Other unfamiliar words may be found in the Lingo Section.
The Birth Itself
Dr. Moorma told my parents that I was due on November 26, 1995, with an expected error of a fortnight. She also warned them to be ready a month in advance, which advice they disregarded completely. As an example of the lax attitude of many parents, let me reproduce a conversation between my parents on October 26 (or it could have been a day or two earlier) before The Birth:
Priti (mom): Gaurav, When will you get a pager, so I can call you in an emergency.
Gaurav (dad): Yeah, OK, soon.
Guess what. At 1:00 p.m., Thursday, October 26 1995, my mom was in Labor. She was in her office. Toiling in the fields, so to speak.

Its not that I had not warned them. A few days ago, mom had spent four hours cleaning up her office. She just felt the urge to clean up: a classic example of what is called the nesting instinct. She told my dad, and they laughed it away. Mom said: "Why would I clean my office." Now you know.

Back to 1:00 p.m. Oct 26. Mom's water broke, and for a while there, she just lost it. I calmed her down, and she called Dad in his office. Completely a waste of time, and I could have told her that, since I knew he was in class, teaching. Luckily, I kept her calm and suggested she send e-mail to some of the desi junta in OSU, and look for Auntie Jennifer in the next room. In less than an hour, Uncle John K. and Auntie Jennifer took her to the hospital. (Tip: Don't let Uncle John give you a ride in his car, even if he buys you lunch.) Meanwhile, what of the desi junta?

It can be said, that at any given time, at least one Indian in the Math Department is playing on the computer. It was Prabhav Tau who saw mom's message, and proceeded to put Radha Mausi and Manav Chacha into a panic. To make a long story short, they found Dad, and everyone went to the hospital, all except Manav Chacha, who proceeded to show Dad's next class what Logarithms are all about.

After mom got comfortable in her hospital gown, the resident Doc said that labor has started, and that I was to be born soon after. That is, soon after Mom and me had gone through enough pain, and Dad had to watch and help. That's no triviality, mind you. Karan Chacha went yellow, and then green, when he came to visit mom, even though he saw her through only 2 contractions. After several hours of intense pain, mom took an epidural, and had a restful couple of hours. That was when my work started, and at 3:59 a.m. on Oct 27, 1995, I was out, and my newpies were born.

The First Hour
As I came out, the first person I saw looked like a green Darth Vader: In fact that was Dr. Wagner, who performed the delivery. Then I saw some blinding lights, and surmised that it must be Dad, taking pictures. I was a bit worried on how he will react when he sees me, since I was covered in some disgusting white goo, but Dad thought I was just beautiful, and so did mom. I was with them for just afew seconds, before a couple of nurses took me away. I was early, you see, and they had to make sure I was OK.

The nurses checked me out as they cleaned me up. My mom was being looked after by the Doctor, and Dad had of course started ignoring mom, and was busy taking pictures and talking to me. After the nurses pronounced me to be 5lb. and 2oz., and furthermore, all of 18'' tall, we both returned to mom, and we bonded.
The Ride Home
Soon after that, I was taken to the nursery, and mom got to nap for a little while. Dad went home to call everyone with the news, and tried to sleep a little bit. He returned in the evening after buying a lot of baby stuff, which he should have bought weeks earlier. I sent him out again to find some cigars. He bought a box of cigars, whose wrappers said "Its a Girl", and some chocolate ones for the wimps. In the evening, lots of Junta arrived, including Sneh Dadi (the one with the fancy haircut), and made a lot of noise.

Since there was so much activity in the room, a funny nurse was sent in to kick everyone out. I suppose she was still under training, for she did a pretty lousy job. Eventually, however, people left, and Iwas back to the nursery. Next morning, we were told to pack up from the hospital, and were back homeonce the newpies had figured out how to install me in the car seat. Vivek Chacha and Vidhi Chachi were there, helping out in the move. They just got lost once in the hospital.

Hunting for Food
It is well known that in the first week, all the female newpie can do is to feed her young. Meanwhile the male of the species cleans up, does the laundry, and hunts for food. In our case, Sneh Dadi cooked rotis which lasted for a week, and some daals which looked like nothing on earth, but tasted great. Besides, there was Latha Mausi, who got some great food, and Auntie Kim, who sent Uncle John (of the Took-Mom-To-Hospital-Fame) with a major dish. In addition, Vidhi Chachi boiled some water and added something which made it look a little yellow. When Uncle Ken looked at it, Dad assured him that it wasn't what he thought it was, but Uncle Ken did not risk a sip anyway.

Food being taken care of was a big relief and now I could concentrate on the most important job of the first week.


How to Have Smarter Parents
In the first week after being born, your newpies are most fragile, and also the most receptive to new stimuli. This is the time to be most careful in their care. This is also the best time to fully educate newpies. So do not let this opportunity pass.
Essentially, your newpies have four senses: Touch, Hearing, Sight, and Smell. There is a fifth sense too, but you can forget that (see Hunting for Food, above). A well thought out Newpie Stimulation Program should work on all these four senses. The program I describe requires very little effort, very few things to buy, and best of all, works for everyone. Here goes:

Sleep: If you stay close to your newpies now, they will be secure for the rest of their lives. One way to give them a feeling of closeness is to sleep only on top of them for the first few days, and then frequently thereafter. This also helps you acquire your Biological Clock, and helps your newpies get used to less sleep. You will spend most of your day sleeping, and newpies will love to watch you sleep.

Paradoxically, newpies do not know what is good for them, and they try to force you to sleep in a bassinet or a crib. Howl loudly each time they will do that, and quieten as soon as they put you to sleep on top of them. If Mom gets too tired, check out Dad. It makes him feel especially big and strong once you sleep on his chest. Right now do your best to encourage those feelings. After a few years you can tell him how short and flabby he really is.

Food: While the newpies' hunger is easily taken care of, thanks to helpful friends and relatives, your own food supply takes some getting used to. Just one suggestion: Keep the radio on a classical music station. They say this helps with your food supply. It seems there have been experiments with cows ...

Diapers: A baby book says, and I quote, "(Baby's poop) has a characteristic aromatic smell and may look like scrambled eggs". Even changing as few as 8-10 diapers a day will fulfill newpies' needs admirably, stimulating all four of their senses. Once you get going, give newpies this treat as many times as you feel like. And they'll come back for more.

Play: When you're not sleeping, eating, or being changed, its time to play. This is the reward newpies get for not getting enough sleep. It also keeps them awake a little longer, but I don't hear them complaining.

Happily Ever After...
After the first week things cool down appreciably, especially if Nani is able to come and help you take care of your newpies. By now, if you have stimulated them enough, newpies will be potty-trained, stay alert for relatively long periods of time, and feel refreshed if they can get even three naps totaling 6 hours of sleep.

From now on life will be much simpler. However, there will be surprises and challenges. By no means is your newpies' education complete: It is a lifelong project. From time to time, there will be crises, and you will feel the need for help in handling your parents. They will not stay newpies for ever, and before you know it, will become middle aged, and ultimately, senile. When the time comes, look for Newpies in Adolescence: The Mid-Life Crisis; They Call me Adolescent, But I Call Them Senile; How to Stay Out All Night (And Get Away With It), and other similar books. They should be available at a nearby web-site, or in your neighborhood bookstore.


Biological Clock: All humans have it. Newborn babies soon acquire it. Newpies lose it.

Chacha/chachi, tau/tai, mausi/mausa: In Hindi, the generic Uncle/Auntie gets split into more precise titles. For example Chacha stands forDad's younger brother, and could be applied to his friends. (Tau for elder.) Chachi would be his wife, thereby helping keep track of Who is married to Whom. Similarly, Mausi is mom's sister, and again could be applied to friends.

Dadi/Baba: Dad's mom/dad, my grandpies. They organized a big bash in my honor; over a 100 people, they tell me. Lots of singing and dancing and fun was had by all.

Desi Junta: Desi means Indian, Junta means crowd. This neatly identifies nationality, and since it is chosen by theIndians themselves, does not offend.

Nani/Nana: Mom's mom/dad, my grandpies. Nani took grandmaternity leave and flew in from India, bringing a suitcase full of goodies. Half of them she made herself, and the rest were gifted by everyone else. Thanks everyone, for sending her over, and thanks KLM, for not losing her luggage.

Roti/Daal: Staple desi food with no frills.

Tejasi: Tejasi means full of Tej, which in turn could be described as a combination of brightness, heat, glow, aura -- you get the idea. Still confused? Ask Dadi, she's the one who found this name.

Some Trivia: I was born on October 27, the birthday of P. R. de Montmort, of the Probl'eme des Rencontres fame. A coincidence? I am also the fourteenth in the third generation from the Yugal Sadan (if you skip 13), approximating pi to 2 decimal places.


The design of Tejasi's name has been made by Punya Mishra, http://www.punyamishra.com. He had made the basic design as a birthday gift for Tejasi's parents, when she was born. He has updated the ambigram as a gift for her, on her 21st birthday! 

Punya's gift is not the only strange one we received. The following was gifted by my friend Michael Schlosser. 

For the cognoscenti, its quite a unique theorem, which converts a multivariable sum into a product, and generalizes a famous result. The product is more "one-variable" than the sum. It appears in: 
Summation theorems for multidimensional basic hypergeometric series by determinant evaluations [Discrete Math. 210 (2000), 151-169].