Chapter 4.4 – Ramanujan
Warming up!
1. Discuss orally in your class.
In what subjects is knowledge of mathematics used, at school level and college / university level ? Name them. Did you know maths is used in music and poetry also? Can you tell how?
Ans: Science, physics, chemistry, economics, accountancy, etc. Poetry- rhymes, rhythm; music- beat, rhythm, etc.
2. Use the letters in the word MATHEMATICIAN to make 4 letter / 5 letter and 6 or more letter words, within a time limit fixed by your teacher.
Ans:
4 letter words:
mice, item, mine, hate, heat, them, team, etc.
5 letter words:
attach, match, meant, etc.
6 letter words:
cinema, anthem, etc.
7 letter words:
thematic, machine, etc.
3. Sentences can be classified into three types – Simple, Complex and Compound.
> A Simple Sentence is one that has only one Subject and one Predicate. It has only one Finite verb.
For example :
(a) She went home.
(b) In the morning, near my school I saw a snake.
> A Complex Sentence consists of one Main Clause and one or more Dependent or Subordinate Clauses.
For example :
(a) She went home, after school was over.
(b) The boys found the book that had been lost.
> A Compound Sentence consists of two or more Independent or Co-ordinate Clauses. They are joined by Co-ordinators.
For example : and, but, so, or, for etc.
(a) He finished his work and he left his office.
(b) He is poor but he is honest.
From lesson 4.2 pick out one example of each of the following.
Simple Sentence :
Ans: Modern techniques are used nowadays for anesthesia.
Complex Sentence :
Ans: Today, if you need to have a heart surgery, you can choose from many fine doctors.
Compound Sentence :
Ans: Over the years now, revolutionary steps have been taken in different types of complicated surgery and these have made such operations successful.
In Between the Lesson!
Q1. What did the manuscript contain?
Ans: The manuscripts contained theorems. Most of them were wild or fantastic looking, one or two were already well known and laid out as if they were original.
Q2. Why could Hardy not enjoy his game?
Ans: Hardy could not enjoy the game because he was puzzled by the Indian manuscript, which he found that early morning.
Q3. What did the two English Mathematicians realise by midnight?
Ans: The two English mathematicians realized by midnight that the manuscripts were written by a natural mathematical genius.
Q4. What were the two drawbacks in Ramanujan’s career?
Ans: There were defects in his education and he had come on the scene too late in the line of mathematical history, to make a contribution on the same scale. These were the two drawbacks in Ramanujan’s career.
Q5. What superstition did Ramanujan’s mother believe in?
Ans: Ramanujan’s mother was usually strict about her religious observance. She did not allow Ramanujan to travel across oceans or seas. His mother had the highest respect for the goddess of Namakkal. One night she dreamed that her son was seated in a big hall among a group of Europeans, and the Goddess of Namakkal had commanded her not to stand in the way of her son fulfilling his life’s purpose. So she allowed her son to travel abroad. These were the superstitions believed by Ramanujan.
Q6. What surprised everyone, one morning?
Ans: One morning, Ramanujan’s mother made a startling announcement. She had a dream the previous night in which she saw her son seated in a big hall among a group of Europeans, and the goddess of Namakkal had commanded her not to stand in the way of her son fulfilling his life’s purpose. She had banned Ramanujan from travelling abroad, but now she agreed to send him after seeing the dream. So everyone was surprised one morning.
Q7. What did Hardy have to teach Ramanujan?
Ans: Hardy had to teach Ramanujan some formal mathematics.
Q8. Why does he call it an unusual experience?
Ans: Ramanujan was self-taught. He was an untrained genius. Ramanujan had not been able to enter Madras (Chennai) University because he could not matriculate in English. He had not received a formal education. He did not know about theorems, proofs, and reasons for mathematical problems, though Ramanujan was a mathematical genius and had a deep insight into the subject. Hardy found it an unusual experience teaching mathematics to someone who had the deepest insight into the subject but who had literally never heard most of it. This was an unusual and singular experience for him.
Q9. Can you work out the sum of cubes in two different ways which equals 1729?
Ans: 1729 is a Ramanujan number, which can be expressed as the sum of the cubes of two numbers. i.e.
1729 = 1728 + 1 = 12³ + 1³
1729 = 1000 + 729 = 10³ + 9³
Q10. What is exceptional about the number 1729?
Ans: The number 1729 is the smallest number expressible as the sum of two cubes in two different ways, which is exceptional about it.
Q11. Name all the famous mathematicians mentioned in this write-up.
Ans: Hardy, Ramanujan, Gauss, Euler and Kapitsa are all the famous mathematicians mentioned in this write up.
ENGLISH WORKSHOP
1. (A) Use the following words / phrases to make sentences of your own.
enthusiasm
Ans: Meaning – strong excitement about something
Sentence – The speech aroused the enthusiasm of the students.
lope off
Ans: Meaning – to move or run
Sentence – The trainer trained the newly brought horse to lope off.
fraud
Ans: Meaning – cheating
Sentence – The frauds in our country are increasing day by day.
clarity
Ans: Meaning – the quality of transparent
Sentence – His books are a pleasure to read because he writes with such clarity and precision.
amiable
Ans: Meaning – good-natured
Sentence – The drink had put him in an amiable mood.
come to terms with
Ans: Meaning – to learn to accept and deal with an unpleasant situation or event
Sentence – Counselling helped her come to terms with her grief.
conveyance
Ans: Meaning – transportation
Sentence – The company relies on trains for the conveyance of goods.
(B) The following words can be used as Nouns as well as Verbs.
(Visit / honour / report / watch / form / surprise.)
Make pairs of sentences of your own, using them as a Noun in one and as a Verb in the other.
For example :
(i) She gave a smile – Noun.
(ii) Babies smile when they see their mother – Verb.
visit
Ans:
Noun: I recently made a visit to my hometown.
Verb: London is one of the most beautiful places to visit.
honour
Ans:
Noun: Noun: Raju is a man of honor in his words.
Verb: It was a simple ceremony to honor the Goddess Durga.
report
Ans:
Noun: Is the news reporter about the murder true?
Verb: Many accident cases have been reported.
watch
Ans:
Noun: There are various beautiful watches in the shop.
Verb: I will watch television after reaching home.
form
Ans:
Noun: It is a form of marriage registration.
Verb: The students form a line for the morning prayer.
surprise
Ans:
Noun: The surprise plan worked successfully.
Verb: I was surprised by the news.
2. Say WHY.
(a) Ramanujan’s letter bored and irritated Hardy, at first.
Ans: Ramanujan’s letter bored and irritated Hardy at first because, when he opened the envelope, he found sheets of paper that were not clean. It was written in halting English and signed by an unknown Indian, asking him to give his opinion of these mathematical discoveries.
(b) Hardy invited Littlewood for a discussion.
Ans: Hardy was puzzled by the Indian manuscript and wondered if it had been written by an unknown mathematician of genius. Thus, he invited Littlewood for a discussion.
(c) Mother agreed to send Ramanujan to England.
Ans: Mother agreed to send Ramanujan to England because the goddess of Namakkal, whom she had respect for, arrived in her dream and commanded her not to stand in the way of her son fulfilling his life’s purpose.
(d) Hardy and Ramanujan could not talk freely with each other.
Ans: Ramanujan was an untrained genius. There was a big difference between Ramanujan’s and Hardy’s education. Ramanujan knew nothing of modern rigor; he did not know what proof was, and Hardy was obliged to teach him some formal mathematics. He was sometimes confused by Hardy’s conversation when it was outside mathematics. Due to all these reasons, Hardy and Ramanujan could not talk freely with each other.
(e) Ramanujan had to be hospitalized.
Ans: Ramanujan had to be hospitalized because he was not well. Later, he died of Tuberculosis.
(f) Ramanujan found the number 1729 very interesting.
Ans: Ramanujan found the number 1729 very interesting as it is the smallest number expressible in two different ways of two cubes.
3. Read the text and enlist the achievements and honours of Ramanujan, received in England.
Ans: Ramanujan’s achievements and honours, received in England:
(i) The Royal Society elected him a Fellow at the age of thirty, which, even for a mathematician, is very young.
(ii) Trinity College elected him a Fellow in the same year.
(iii) Ramanujan was the first Indian to be given either of these distinctions.
4. Voice – Active and Passive
The form of a verb shows whether the doer of an action is in the Subject (Active voice) or the Subject has an action done to it (Passive voice).
For example :
The thief stole the jewels. (Active voice).
The jewels were stolen by the thief. (Passive voice)
Note : While changing from the Active to the Passive voice, the verb form includes be + past participle.
In a sentence, when the doer of an action is significant, we use the Active voice. In the Passive voice the doer of an action may not be mentioned.
For example :
The thief was caught. (by the police)
(A) Underline the verbs in the following sentences and state whether the sentences are in the Active or the Passive voice.
(a) England gave Ramanujan great honours.
Ans: gave – Active voice
(b) A large untidy envelope was decorated with Indian stamps.
Ans: was decorated – Passive voice
(c) The timetable was not altered.
Ans: was not altered – Passive voice
(d) She saw her son in a big hall.
Ans: saw – Active voice
(e) Hardy corrected his statement.
Ans: corrected – Active voice
(f) Ramanujan was brought to England.
Ans: was brought – Passive voice
(B) Change the voice in the following sentences.
(a) Hardy taught Ramanujan.
Ans: Ramanujan was taught by Hardy.
(b) He knew nothing of the modern rigour.
Ans: Nothing was known to him of modern rigour.
(c) Sheets of paper were found in it, by Hardy.
Ans: Hardy found the sheets of paper in it.
(d) Hardy was bored by that manuscript.
Ans: The manuscript bored Hardy.
(e) Trinity supported unorthodox talent.
Ans: The unorthodox talent was supported by Trinity.
(f) He could not break the ban.
Ans: The ban could not be broken by him.
5. Identify whether the following are Simple, Complex and Compound sentences.
(a) When he opened it, he found sheets of paper.
Ans: Complex sentence
(b) He glanced at a letter.
Ans: Simple sentence
(c) Hardy was not only bored but he was also irritated.
Ans: Compound sentence
(d) Ramanujan turned out to be a poor clerk.
Ans: Simple sentence
(e) If Ramanujan had been better educated, he would have been even more wonderful than he was.
Ans: Complex sentence
(f) Ramanujan was self-taught : he knew nothing of the modern rigour.
Ans: Compound sentence
6. Interview Question.
A brilliant student from your school has won a Mathematics Quiz at the National Level.
Frame questions to interview him / her when the school felicitates him / her.
Follow the steps given below.
(1) Greeting
(2) Introduction of the interviewee and achievements
(3) 2 or 3 questions about the growing years
(4) 4 to 6 questions about the achievements
(5) 2 or 3 questions about future plans and prospects
(6) Expression of thanks and good wishes
Ans:
(i) Good morning, Rachana. First of all, let me offer you my congratulations on winning the Mathematics Quiz, and that too, at the National Level. May I ask you a few questions about your achievement?
(ii) Did you have great interest in mathematics in the early years of your childhood?
(iii) How did you develop this interest?
(iv) How long did you prepare yourself before participating in this Quiz?
(v) Who helped you and guided you?
(vi) Who encouraged you or motivated you at that stage?
(vii) How did you feel when you were actually answering the questions?
(viii) What is the next step from here?
(ix) Do you plan to make a career in mathematics?
(x) Any message to others interested in mathematics?
(xi) Thank you, and all the best for your future. Goodbye.
7. Summary
- Read the first three paragraphs on Page 92. (From……… ‘One morning ………….. upto ………… a discussion after hall)
- Re-read the same noting down only the important points.
- Rewrite the important points in your own simple language, in your notebook.
- Make certain that your summary is less than half the length of the original passage.
Ans:
The Manuscript
One morning in 1913, Hardy received an envelope from India. It contained many lines of symbols written in a non-English script. The letter with it, written in halting English and signed by an unknown Indian, wanted Hardy’s opinion on the mathematical discoveries enclosed. These were only some known and unknown theorems, without any proofs. Hardy, bored and irritated, put the manuscript aside and went to play tennis. However, his pleasure in his game was interrupted by the thought of the Indian manuscript with the wild theorems he had left behind. He wondered if the man was a genius. When he returned to his room, he took another look at the script. Then he sent word to Littlewood that they must have a discussion after hall.