Srinivas Ramanujan

Dhruvi had returned from school and was sitting in the garden lost in her thoughts. A while later, her older brother Dhruv came there and was surprised to see her sitting alone.

“What are you thinking about, Dhruvi?” he asked.

“To celebrate National Mathematics Day on December 22, we have been asked to work on a project on Srinivasa Ramanujan. I’m trying to think about what I should write. Bhaiya, since you are doing your PhD in Mathematics, can you help me?” she asked.

“Of course! Don’t worry. I am free tomorrow, it being a Sunday. Keep your questions ready,” said Dhruv.

The next day, Dhruvi took a book and pen, and went into her brother’s room.
“Come in, Dhruvi! Let’s begin.”

“Firstly, tell me some general facts about Shrinivas Ramanujan, his birthplace, his interests, etc.,” requested Dhruvi.

“Srinivasa Ramanujan is one of the greatest mathematicians of India. He was born on December 22, 1887, in Erode in Tamil Nadu. His birthday is celebrated all over India as National Mathematics Day as that was his favourite subject.”

“Noted,” said Dhruvi as she neatly wrote down these details in her notebook. “Now, please tell me about his education.”

Dhruv said, “At the age of 5, he was admitted in a primary school at Kumbakonam in Tamil Nadu. But he never liked other subjects and spent most of his time studying Mathematics. At the age of 10, he secured the highest marks in the entire district and was sent to Town Higher Secondary School. He even received a scholarship to study at Government Arts College, Kumbakonam.”

“Funnily his love for Mathematics was also the biggest obstacle in his education. He loved Math so much that he neglected all other subjects. Even while attending the classes of other subjects, he would always be solving Math sums. The result was that in his class 11 examinations he failed in every subject except Math and because of this, his scholarship was withheld.”

“This increased the difficulties for his family as they were poor. He lived off the charity of friends, filling notebooks with his mathematical discoveries. He also started taking Math tuitions and doing accounting work for the Madras Port Trust.”

“So even though he was a math genius he failed in other subjects!” exclaimed Dhruvi. “What was his contribution to the world of Maths?”

“At the age of 13, he mastered a book on Advanced Trigonometry written by London University’s Professor S L Loney. By that time, he had already discovered theorems on his own. By the age of 14, he had received many merit certificates and awards.”

“When he was 16, he studied G S Carr’s A Synopsis of Elementary Results in Pure and Applied Mathematics in detail. The book was a collection of 5,000 theorems.

He created formulae on his own and his true achievement was that he did so, without any formal training in Mathematics. He was a self-taught mathematician.”

“Bhaiya, can you tell me anything else about him?” asked Dhruvi.

“In 1913, English mathematician, G H Hardy received a strange letter from
an unknown accountant in Madras, India. The ten-page letter contained about 120 theorems, improper integrals, fractions and so much more.”

“Professor Hardy who could not understand them completely, but discussed it with other mathematicians and colleagues, and concluded that Srinivasa Ramanujan was a person of unique mathematical ability. To understand his work thoroughly, he invited Ramanujan to Cambridge for further research. In March 1914, Ramanujan boarded a steamer for England. In 1918, Srinivasa Ramanujan was elected as a Fellow of the Royal Society, an award given to individuals for their contribution in the field of maths and science.”

“Ramanujan stayed in England for five years and did research. On April 26, 1920, he died at the age of 33 due to ailing health.”

“What! He died at such an early age!” exclaimed Dhruvi.

“Unfortunately, he did. Now, will you be able to compile all this information for your project?” asked Dhruv.

“Yes, I will. Thank you very much,” said Dhruvi and went back to her room.
She submitted her project in school the next day.

On December 22, the result of the competition was announced and Dhruvi won first place.

She also learnt many more things about Srinivasa Ramanujan and then discussed these too with Dhruv Bhaiya.

Math in Nature

Mathematics is everywhere around the world. We observe it rarely and enjoy nature instead of understanding the mathematical concept behind it. Below are some examples which exhibit Math in Nature beautifully.


The Italian mathematician Leonardo Pisano Bigollo, born in Pisa was also known as Fibonacci. French historian Guillaume Libri gave the name Fibonacci to Leonardo. Leonardo introduced a unique sequence of numbers that was then named the Fibonacci series or sequence after him. Fibonacci introduced to the world a sequence of numbers, that start with zero and one, and the next number in the series is obtained by the addition of the first two numbers. Zero and one when added gave one. 1 added to 1 gave 2, the fourth number in the series, and then 2 added to 1 gave 3, then 3 added to 2 gave 5 and simply put, adding the last two numbers gave the next one till infinity. So, the series would be 0,1,1,2,3,5,8,13,21,34 and so on. When these numbers are represented in a diagram form, it is called The Golden Ratio.Maths in nature

The Fibonacci sequence became famous because patterns were found in nature that followed this sequence.

Fibonacci Series and the Nautilus Shell

In a particular kind of seashell called the Nautilus shell the size of the spirals in the shell, when measured in proportion to the previous one, follow the Fibonacci sequence. A Greek mathematician, Phidias, developed the golden ratio diagram that illustrates the Fibonacci sequence. When this is superimposed on the shell, we can see the spiral in the shell, grows from smallest at the centre to be bigger as it gets towards the shell’s opening.

The spirals of the shell follow the Fibonacci sequence.

Latin word Nautilus means sailor. It is a marine mollusk (a shellfish) that is found only in the Indo-Pacific waters. They “live among the deep slopes of the coral reefs. The shell structure of the Nautilus has been unchanged more or less, for millions of years. Belonging to the cephalopod family (symmetrical and soft-bodied sea creatures), the shape of the chambers in the shell matches the Fibonacci sequence.



Maths in nature

Fibonacci sequence is found in the way trees grow. Unlike a mess of tangled branches, we see a pattern in the way the number of new branches that sprout from the previous branch. In the diagram, if we consider the trunk as one, then we can see how two branches form, then three, followed by five branches and so on. The number of branches keeps on increasing as long as the tree continues to grow.



Maths in nature

Hurricanes also display the Fibonacci sequence in their formation. When we superimpose the golden ratio diagram over a satellite image of a hurricane, the way the hurricane spirals out again matches the number ratio of the Fibonacci sequence. In this case, a lot of factors make it look like that, the way the wind blows, air temperature, air pressure and so on. It’s just another manner in which mathematics expresses itself in nature.



Maths in nature

Fibonacci sequence is also seen in the way the rose petals are delicately wrapped around each other from the time it’s a rosebud till the time the rose is fully in bloom. No one really knows why this pattern is followed, but it just does. There is order even in chaos.