The Beggar of Hampi, Pride and Pricked Prejudice !

The Hampi Viroopaksha Temple

Being in Bellary and not visiting Hampi is just not possible. Early days in Bellary, I had heard enough about Hampi. Our primary school history lessons too had given us enough reasons to visit Hampi. Finally I did visit Hampi with a group of friends sometime in 1989 winter. Murali, Vishwanath, Jagan, Shadrak, Umesh, Vishwanath Nayak, Azeem, Thara and me were there on that tour.

Our group in Hampi

A lot has been written about Hampi and I can't better any of that. What stands out for me after 23 years is an experience that made the raw youth feel proud about our heritage that day and a lot more wiser for life.

We were going around the famed Viroopaksha temple. There was a bunch of noisy youth a few paces ahead of us. Being doomed to be Doctors, we were less noisy or perhaps relatively so. When we came to the western part of the temple, we were directed to a small dark corner room by some people. We all went there and saw this...

The Pin Hole Camera !

This is the famed pin-hole camera of Hampi where an inverted image of the main tower of the temple is seen on a wall of a small dark room through a hole in the roof of the outer fortress on the western side. As we were marveling at this piece of architectural wonder of almost 750 years history; the loudest of those boys from that group proclaimed loudly in Kannada, "Hey this is all fraud. Someone has drawn this here and that too inverted. How can people fall for such con ! blah blah blah".

There was a sun burned unshaven man appearing to be in his seventies, sitting just outside that room. He had unkempt silver hair, shrunken cheek lined by sharp bony jaws to his face and a frail body. He was clad in worn off saffron robes with an equally weather beaten towel spread on the floor. That must have been white some time in history but looked brownish yellow. He was obviously begging and there were a few coins on his towel.

He suddenly got up pulling his towel in a hurry, scattering his coins all over the place in the process. He didn't seem bothered, but went directly to the young man and called him out to follow him. He crawled to the darker corner of the dark room and asked the youth to hold the other end of the towel so that it was positioned in front of the shadow. All of us could see the shadow of the tower appearing on the towel.

We couldn't see the face of that boisterous boy in the darkness that prevailed in the room. But a lot of darkness must have been driven away from his mind in that beautiful moment. Though I had a camera on me, I couldn't capture the magnificent moment on camera because it all happened in such a hurry and the darkness in the room just didn't allow me to click the event. Alas !

Coming out of the room, the saffron clad man gave a lecture to the youth and his friends. It was as good a lesson to all of us blinded by the arrogance of our modern life. He said, "Oh you the pant and shirt clad city bred youth of today, young men; pause before you proceed to mock anything that you don't know. This is a construction that is almost 1000 years old and has stood the ravages of time like many of those marvels in this great place called 'Haalu Hampi' [Ruined Place]. This was the Vijayanagar empire where gold and diamonds were sold in the road side shops. Over 50 generations of yours must have turned into ashes since this place was constructed. Look at every stone, pillar and idol of this place. They were constructed when there were no machines and cranes and such things. If they managed to construct such a magnificent place at that time, what does it say ? Those people were far more intelligent, wiser, stronger and talented than you, me and all of us. Never again make fun of our heritage. You are a nobody who has done nothing precious yet and will achieve nothing in life if you continue with this attitude. God bless you with better sense in future !"

I could see the pride in the eyes of the senior gentleman and the pricked prejudice on the sheepish face of the youth. And was I having goosebumps ? I still get them thinking of that day. Ever since, I have made it a rule not to mock anything that I don't know or understand. Questioning anything is fine, including the concept of God. No progress can be made if we believe everything without questioning. But before you sit on judgement, make sure you are qualified enough to do so and you know the truth. Else, it is better to be cautious. The world is a lot more intelligent and wiser than a single human being can normally aspire to be !




Dr. Punned-it

Squaring up 25 !

After squaring up numbers ending with 5, me and my daughter have moved onto squaring numbers ending with 25. We proceed exactly the same way we did with 5, but with a larger number. That is all.

We will begin with same equation of (a + b)2= a2 + 2ab + b2.

Here b = 25.

Now the equation gets simplified like this:  

a2 + (2 x a x 25) + 625

That is further simplified into: 

 a2 + (50a) + 625. 

Now we will leave out 625 to be added at the end.

a2 + (50a) is further simplified as:

a (a + 50)

Here 'a' is any number that ends with 00, like 100, 200, 300 and so on. We have 625 at the end of the number. 

a (a + 50) is a round figure that will end with at least '000' because we are multiplying 100 x 150 or 200 x 250 and so on. Leaving out the 'three zeros' we will further simplify the equation a (a + 50).

We will take the two zeros [00] from 'a' and arrive at a simpler number 'n'. We will remove the third zero [0] from the [a + 50]. We remove these three zeros [000] because we have 625 at the end of the answer and hence we are simplifying the multiplication leaving out the '0's.

That means: 150 becomes 15, 250 becomes 25, 350 becomes 35 and so on.

So what we have is following simplified equation:

n (n5) - *n5* here is NOT a product here, but we just write n and place 5 next to it to derive the number. So if 'n' is 7, n5 is 75.

Now the n (n5) product is placed before 625 and we have the whole square.

Like: n25 whole squared = n(n5) followed by 625 

Some examples: 

For Whole square of 125: 1 x 15 = 15. Whole square: 15625

For Whole square of 225: 2 x 25 = 50. Whole square: 50625

For Whole square of 425: 4 x 45 = 180. Whole square: 180625

For Whole square of 725: 7 x 75 = 525. Whole square: 525625

For Whole square of 1025: 10 x 105 = 1050. Whole square: 1050625

For Whole square of 1325: 13 x 135 = 1755. Whole square: 1755625

This is quicker, accurate and time saving way of doing Arithmetic for school kids. This again can be worked out without a paper and pencil, if we know our simple multiplication well.

 

Dr. Punned-it

Music Sense !

This is a real incident from my life. I had earlier posted it on Facebook as a note. Since notes on Facebook are prone to get lost, I am securing this on my blog. If anyone finds this offensive, this is not meant to be so. I apologize to the characters if they happen to read this and recognize themselves here. Only the fun element has to be imbibed from this. No malice intended !

Early 90s, Medical College Bellary. The boys and girls were preparing for the college day celebrations. We used to spend most of our free time in the room given to us behind the Microbiology department. We had a talented Violinist named Anil. He was practicing hard for the upcoming event.

I was waiting for my turn to rehearse my song with the Orchestra. At that moment one of our senior boys who was part of the organizing committee came calling to make sure everything was going smoothly. Looking at Anil concentrating on his violin, our man asked him some questions. I was witness to the entire conversation.

The original Kannada exchange was hilarious beyond words. Hope the fun is not completely lost in translation. We will call the senior GS for convenience. Here we go with the dialogue.

GS: Hello Anil, great, how is everything going ? Your guitar is superb...
Anil [looking upset]: Hey, this is not guitar...
GS: Oho, so this is Piteelu, right ? [Probably, he meant Fiddle, a colloquial form of violin]
Anil: No man...
GS: Right right, Tambourine, I know, I know...
Anil [looking frustrated]: This is NOT Tambourine...
GS [Not ready to give up]: So this must be Mandolin...
Anil: [Exasperated]: Hey GS, this isn't any Mandolin or Gindolin...
GS [Nonchalantly]: Ho, what is there man, some instrument with strings. It can be 'Rudra Veena' also...

I wasn't able to control my giggles by now. GS saw that and asked, "Hey Shenoy, what are you going to do ?". I said, "I will be singing 'Chupaana Bhi Nahin aata' from Baazigar". GS gave me a free advice, "That is a bore song. You sing 'Kaali Kaali Aankhen oooo oooo oooo' instead". I nodded saying, "Well, let me try..."

GS turned to Anil and said, "Well you can give music for that song with your 'Sarangi' and we will rock the function". Anil was by now completely demoralized and said, "See GS, this is not any Sarangi or Firangi, why can't you let me tell you the name of this ?"

GS left with a parting shot, "Hey come on man, what difference will it make even if it is a Tabla ? Haven't you heard William Wordsworth saying 'what is there in a name' ? Finally it is a music instrument that makes a lot of noise. I have that much music sense. Now excuse me and I have a thousand things to do. You carry on with your Bongo"


Dr. Punned-it

Solving the 9th Wonder !

Multiplying any number ending with 9 is a big 'scare crow' for kids in primary school. It becomes virtually a non-issue if we approach it as a process of addition and subtraction rather than multiplication. Once again unfortunately, people shut their minds even before we count from 1 - 9.

My daughter used to do the same till I made her use a method that has eradicated the fear of multiplication from her mind. She now enjoys doing it in the mind and she is always correct. But she still hasn't exorcised the 'Ghost' from her mind and wants to check if her answer is correct. She will be confident with time.

So what do we do ?

Simple. Let us take the simplest of numbers ending from 9, that is 19. Most kids would know the multiplication table by heart. But is that necessary ? I have never found that necessary. I approach it as adding 19 as many times as I am supposed to multiply. So 38, 57, 76 and there goes the table.

Often kids get stuck on reaching 7, 8 and 9. That is where the realization comes that it actually is easier to add and delete than do a table. I do it this way.

19 is 1 less than 20. 

We all can have multiples of 20 easily because 20 is nothing but 2 x 10. 

So just check this method. 

I do 20 x 9 = 180. 

When it comes to 19 x 9, that means it actually is one 9 less than 20 x 9. 

So just delete 9 from 180. 

That means 19 x 9 = 171. 

That is it !

Let us move to larger numbers.

Let us take 89 x 7. 

What I do is 90 x 7 = 630. 

We know 89 x 7 is one less times 7.

So just delete 7 and that means 623.

Let us take another example of 99 x 8. 

100 x 8 = 800. 

Minus 8 means the answer is 792. 

The riddle solved, in the mind. 

No paper, no pencil and in no time. And of course no tension !

Dr. Punned-it

High Fives to Mathematics !

Continuing with my Maths posts, let me deal with one more easy way to Maths. We all love 'Five', may be because we have 'five' fingers and 'five' toes in each of our limbs; well mostly. But '5' is a lot more useful in Mathematics. It is a wonderful number that makes Maths lot more easier, fun and even entertaining.

I asked my daughter, "Do you know the easy way to obtain whole squares of numbers ending with 5 ? Like say, 25, 35, 45 or even 115 and so on ?" I knew she doesn't and hence went on to explain. This isn't anything new again, but somehow not many Maths teachers follow this and I don't know why !

Let me first show how we do it and then explain how it actually happens. We have to remember all numbers ending with 5 will end with 25 when squared. The 25 will remain constant. We just have to look at the first number. Let us say 'u' and multiply that with (u+1) and the product has to be written before 25 and we have a whole square. 

u x (u + 1) before 25

For example: 

Let us take 25: u here is 2. Hence: 2 X 3 = 6. The whole square of 25 is 625.

Let us take 35: u here is 3. Hence: 3 x 4 = 12. The whole square of 35 is 1225.

Let us take 45: u here is 4. Hence: 4 x 5 = 20. The whole square of 45 is 2025.

Let us take 55: u here is 5. Hence: 5 x 6 = 30. The whole square of 55 is 3025.

This will go on and on. Now let us see how this actually happens. Once we know that, we will never have a problem with 'Five' !

-> Let us begin with 55. What is the easiest way to square a big number ? 

-> We have already dealt with that in (a + b)2= a2 + 2ab + b2.

-> When we deal with any number ending from 5, we know the 'b' in the equation and that is 5. 

-> So the equation gets simplified as follows.

* a2 + (2 x a x 5) + 25.

-> That is further simplified into

* a2 + 10 x a + 25

-> Now what are we left with ?

* a2 + 10a + 25 

Now let us keep the 25 away for the time being because we are going to add it at the end. Thus we have

* a2 + 10a

This is further simplified into

* a (a +10)

-> In reality 'a' is a round figure here like 10, 20, 30, 40, 50, so on to 90, 100, 110 and more. Multiplying a round figure with a round figure [a x (a + 10)] always yields a multiple of 100 with 00 at the end. We just have to ignore those zeros for the sake of ease and speed. Thus the 00 goes with 25 as just 25.

So we have to remove the '0's from [a] and [a + 10] to get the smaller simpler numbers.

-> Thus we have: 

*a / 10 and [a + 10] / 10

Thus the equation becomes: 

* (a / 10) x (a + 10) / 10 = (a / 10) x (a / 10 + 1)

-> [a / 10] here is the simplified small number after removing the 'Zero'. 

So we will name it [u] for convenience. So the equation becomes simpler:

* u x (u + 1) with the 00 going with 25. 

Now we just put the product of u x (u + 1) before 25 and we have the whole square.

Let us take 145: u here is 14. Hence: 14 x 15 = 210. The whole square of 145 is 21025 !

Simply put, what are we doing ?

Take the number before 5 and multiply that with the one more than the same number and put the product before 25. We are home !

Hope I have made it simpler for those who like to make things easier in life; especially Mathematics !

Dr. Punned-it