# January 14, 2022

## Pythagoras Theorem Made Easy

**Thanks to Prof Gnaneswara Rao’s whatsapp forward**

From FB

Alternate method to compute hypotenuse

to Pythagoras theorem.

The Tamilian land, centuries before the dawn of the common era had built dams and dikes, palaces and great cities during the Sangam era. I was wondering how the great turrets in temples and great highways were built without any knowledge about Pythagoras theorem was made possible. My search did bring some information to the effect that to find the hypotenuse of a right-angle triangle independent of the Pythagoras theorem, which enunciate that sum of the square of both sides of the right angle will be equal to the square of the hypotenuse, of the triangle. It is not a simple task to find the square of a number, but finding the square root of a number is a herculean task. There is no simple formula to find the square root of a number.

To my own surprise and astonishment, I found that an ancient Tamil mathematician/poet Pothayanar, who had lived 800 years before the common era, has given a quatrain of four lines articulating the method of finding the length of the hypotenuse of a right-angle triangle without the need to find the square or the square-root, only using the length of the sides, and simple fraction. Here is the English translation of the quatrain.

Divide the horizontal to eight,

Delete one portion, and add the remaining,

To half of vertical to result you’ve got’

Available would-be hypotenuse of the triangle.

The Tamil poem by poet Pothayanar goes as follows;

ஓடும் நீளம் தனை ஒரேஎட்டுக்

கூறு ஆக்கி கூறிலே ஒன்றைத்

தள்ளி குன்றத்தில் பாதியாய்ச் சேர்த்தால்

வருவது கர்ணம் தானே. – போதையனார்

The advantage of the ancient theorem is that one need not use a square root function which may be a bit cumbersome. But before we jump to conclusion let us see how our new found formula works. Let us take the three sides of the right-angle triangle to be A, B, and C, where C be the hypotenuse. Let us take B to be the horizontal side. If we are to divide into eight parts and takeaway one eight, it would be 7/8A. The half of the vertical side will be 1/2B. Thus, the result should be;

C= 7/8A + 1/2B

Let us give some numbers and try: Say A=8 and B=6

By Pythagoras theorem C equals √ (8×8+6×6) Which is √ (64+ 36) = √100 =10

According to the quatrain; C becomes 7/8A + ½ B

Now 7/8 of A = 7 and ½ of B +3 And they add up to give hypotenuse to be 7=3=10

Now let us try with taking A=28 and B=21 then

By Pythagoras theorem C= √ (21×21+28×28)

C = √ (441+784)

which is =√1225 = 35

According to quatrain; hypotenuse becomes 7/8A + 1/2 B.

7/8 A=7/8 (28) = 24.5 and 1/2B= 1/2 (21) = 10.5

Thus 24.5 + 10.5= 35.

Now let us try with taking A= 12 and B= 5 then

By Pythagoras theorem C= √ (12×12) + (5×5) = (144+ 25) √169 =13.

According to the Tamil quatrain; hypotenuse becomes 7/8A + 1/2B

7/8(12) = 10. 1/2 (5) = 2.5

Thus 10.5 +2.5 =13

Pothayanar must have been a great mathematician, who got lost like fruit hidden in the foliage of the tree. The great discoveries of the Greeks scientists and mathematicians helped the humanity because of the valour with which they conquered then known world. Unfortunately, not only the great intellectuals but also their findings were lost to the world. Let’s in our thought thank him for his discovery.

# July 2, 2021

## Spelling Bee Contest: A Pointless Exercise

Professor B. R. Sant is an eminent scientist, who is much concerned on excellence for the enthusiasts. our readers knew him through his **book** on ‘Towards achieving excellence in Teaching and Learning’. Now, in late eighties, his concern for the same is not slackening. His reaction on the results of the recent spelling bee contest is presented here:

Dear All:

A slightly controversial subject, Thought it may interest you, your family, and your friends. Do try to give a feedback

** U.S. Spelling Bee Contest Does it help NRI children?**

The year-after-year U.S. Spelling Bee Contest (The Hans India, June 30, 2021) reminds me of Agatha Christie late 1950s film “Witness for the prosecution” with famous Sir Charles Laughton and Marlene Dietrich as main casts. A person, a young man, gets close to a rather old but rich widow and convinces her about some technology-breakthrough research that he is doing for which he needs lot of money. The widow is much enamoured and she even writes a major part of her ‘will’ in favour of the young man. Later, the lady is murdered and the young man is a natural suspect,. However, the lawyer feels his client is innocent. As the trial proceeds, the question came about the young man’s important invention. It was around a unique technology to separate yellow from the white of an egg. The trial and arguments were going on and on, till the Judge asked: Was it really “necessary” to separate yellow and the white of an egg? No answer was forthcoming and the case fell through. The question therefore arises: Is an expertise in knowing spellings of all the words necessary, especially words of foreign origin, rare words? We have dictionaries, google searches. Upto some level of school/college, it is alright. Beyond that it is “huge” stress on children who many a times are virtually forced to enter spellation contests. Health in any game, sports, or academic exercises is the most important. Practicing spellation is highly strenuous and it does not help enhancing IQ either. thehansreader@gmail.com Some of the readers may be remembering a detailed news-report a few years ago that appeared about a USA-based young husband-wife literally forcing their 11 year old son to compete in spellation when the boy was begging he is not interested’ he would rather like to study and learn many other subjects of his interest. Parents did not listen. The child broke down on the test date and was later under psychiatric treatment for 5 years. We do not know how many such cases are there in USA among NRI children. No wonder native Americans dont care for trivial contests. whereas we feel proud about our children. All I am trying to say is parents must not force on children their likes and dislikes.

Professor B. R. Sant

Retired CSIR Scientist

Block B, Flat No. 111, Saket Pranaam

Kapra, Hyderabad 500103

Cell 87901 8233

** [PUBLISHED AS IT IS IN THE HANS INDIA, HYDERABAD, 1ST JULY 2021; Regret inability to make a scan copy] **

# October 27, 2013

## Currency is not a writing pad

In India, we have the habit of taking notes on currency notes. If we resort to this, the currency may just have the value of a writing pad or even less. Please read the following information given by Ms. Shridevi Muralidhar:

1st JANUARY 2014 ANY BANK WILL NOT ACCEPT ANYTHING WRITTEN ON NOTE

[cid:image001.jpg@01CEC742.1CAC35A0] [cid:image002.jpg@01CEC742.1CAC35A0]

Please share this message with all your friends & relatives!!!

Guidelines:

Because of writing on Indian currency notes, Indian Govt loses Rs 2,638 crores every year, so please don’t write anything on currency note as they can’t be used for STD transactions e.g. We can’t find written

Notes in ATM.

When will we learn to value & respect our own currency?

**Have you seen a dollar bill or a Pound with anything written on it?**

RBI RULE FROM 1st JANUARY 2014 ANY BANK WILL NOT ACCEPT ANYTHING WRITTEN ON NOTE YOU CAN NOT DEPOSIT THAT NOTE IN BANK..

BY ORDER

R…B….I..

SPREAD THIS NEWS ITS IMPORTANT.

**Our comment: There are practical difficulties in implementing this just with one stroke of pen. But be prepared for such fate before using a currency note as a writing pad!**

# June 26, 2012

## Patrol the Petrol

In a developed country petrol is the need. India is aspiring to be a developed country and petrol is nothing but luxury there. If you want to understand the magnitude of this luxury read the following comments conveyed through an email by Ms. Shridevi Muralidhar.

**New Greetings**:

May your happiness increase like Petrol Price,

May your sorrow fall like Indian Rupee, and

May your joy fill your heart like corruption in India…!!!

………..

Congress is fulfilling its promise, when they said: GDP will rise this year.

The only thing we forgot to ask him its full form:

G= Gas & Gold

D= Diesel & Dollar

P= Petrol & Penny

…………

Pleasure & Pain come at the same price: Rs.80/- for a Beer Bottle OR 1 Litre Petrol.

Decision is yours…झूम लो,या घूम लो.!!!

……….

All Girls’ Dream come True!

All Girls’ Dream Boys will come on horse!

All thanks to the Petrol Price Hike!

…………..

Dear Father-in-Law,

I deeply regret taking a Car in dowry.

Please take your Daughter or Car back…

I cannot afford both.

……………..

Now Tata Nano’s fuel cost will be more than its EMI per month!

…………

Soon, Rupee will be SENIOR CITIZEN (above Rs.60 per US Dollar);

Petrol has already become VERY SENIOR CITIZEN in Bangalore (Rs.81 per litre) !!!

……………….

Finally it has happened…

After decades,

Beer is now cheaper than petrol !!!

Now, there will be new slogan: JUST DRINK; DON’T DRIVE !!!

……..

Expensive petrol will help solve the problem of traffic jams!

…………….

Drink and drive should not be a problem now.

After all, how many will be able to afford alcohol and petrol on the same day?

…………

We have the world’s cheapest car and the world’s costliest petrol.

Sign board at Petrol pump: Buy Petrol worth Rs. 20,000 and get a TATA nano absolutely free.

(scheme forआम आदमीNow he can get car with petrol! )

……………..

Good News!!!

Please forward this to MAXIMUM people you know,शायद किसी को काम आ जाए:

जिसकोpetrol Rs.17/- per litreचाहिए,

वो इसpetrol pumpसे जा कर ले ले:

…

Man at Petrol Pump: Full tankकर दो…

Attendant: Sir, PAN Cardकीcopyदो…

Man: What? Why? How?

Attendant: Sir, it’s a HIGH VALUE TRANSACTION !!!

# May 17, 2012

## Some Fascinating Historical Photos- 1

Thanks to Shridevi Muralidhar here are some really fascinating historical photos:

** 15th August 1947, First News Paper of INDEPENDENT INDIA **

**Original Photo of Jhansi Laxmi Bhai taken by German photographer Hoffman 160 years ago**

Look out for some more fascinating ones coming soon……