Maharashtra Board Textbook Solutions – Standard VIII

Chapter 4.4 – Ramanujan

Warming Up!

1. Discuss orally in your class.

Q. In what subjects is knowledge of mathematics used at school level and college/university level? Did you know that maths is used in music and poetry also? Can you tell how?

Ans: Mathematics is used in Science, Physics, Chemistry, Economics, Accountancy, Engineering, Statistics, and Computer Science.

Yes, mathematics is also used in poetry and music. In poetry, it is used in rhymes, rhythm, meter, and syllable patterns. In music, it is used in beats, rhythm, timing, scales, and patterns.

2. Use the letters in the word MATHEMATICIAN to make 4-letter, 5-letter and 6 or more letter words.

Ans:

4-letter words:

mice, item, mine, hate, heat, them, team, etc.

5-letter words:

match, meant, teach, chain, 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.

From Lesson 4.2, pick out one example of each.

Simple Sentence:
Ans: Modern techniques are used nowadays for anesthesia.

Complex Sentence:
Ans: Today, if you need to have heart surgery, you can choose from many fine doctors.

Compound Sentence:
Ans: Over the years, 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 manuscript contained many theorems. Most of them looked wild or fantastic. One or two were already well known and were presented as if they were original.

Q2. Why could Hardy not enjoy his game?

Ans: Hardy could not enjoy his game because he was puzzled by the Indian manuscript that he had received that morning.

Q3. What did the two English mathematicians realise by midnight?

Ans: By midnight, the two English mathematicians realised that the manuscripts had been written by a natural mathematical genius.

Q4. What were the two drawbacks in Ramanujan’s career?

Ans: The two drawbacks in Ramanujan’s career were defects in his formal education and the fact that he had come too late in the history of mathematics to make contributions on the same scale as earlier mathematicians.

Q5. What superstition did Ramanujan’s mother believe in?

Ans: Ramanujan’s mother was strict about religious observances. She believed that crossing the seas was against religious customs and did not allow him to travel abroad. However, one night she dreamed that her son was seated in a big hall among Europeans, and the Goddess of Namakkal commanded her not to stand in the way of his life’s purpose. After this dream, she allowed him to travel to England.

Q6. What surprised everyone one morning?

Ans: One morning, Ramanujan’s mother announced that she had changed her decision and would allow her son to travel to England after seeing the dream. This surprised everyone.

Q7. What did Hardy have to teach Ramanujan?

Ans: Hardy had to teach Ramanujan formal mathematics, especially proofs and modern mathematical methods.

Q8. Why does Hardy call it an unusual experience?

Ans: Hardy called it an unusual experience because Ramanujan was a self-taught genius who had deep insight into mathematics but lacked formal training in proofs and modern methods.

Q9. Can you work out the sum of cubes in two different ways which equals 1729?

Ans: 1729 = 12³ + 1³
1729 = 10³ + 9³

Q10. What is exceptional about the number 1729?

Ans: The number 1729 is the smallest number that can be expressed as the sum of two cubes in two different ways.

Q11. Name all the famous mathematicians mentioned in this write-up.

Ans: Hardy, Ramanujan, Gauss, Euler and Kapitsa are the famous mathematicians mentioned in this write-up.

ENGLISH WORKSHOP

1. (A) Use the following words / phrases to make sentences of your own.

enthusiasm

Meaning: strong excitement about something
Sentence: The speech aroused great enthusiasm among the students.

lope off

Meaning: to move or run in long steps
Sentence: The horse began to lope off across the field.

fraud

Meaning: cheating
Sentence: Cases of fraud are increasing day by day.

clarity

Meaning: clearness
Sentence: His books are enjoyable because he writes with clarity and precision.

amiable

Meaning: good-natured
Sentence: The new teacher is very amiable and friendly.

come to terms with

Meaning: to learn to accept and deal with a difficult situation
Sentence: She finally came to terms with her loss.

conveyance

Meaning: transportation
Sentence: The company uses trucks for the conveyance of goods.

(B) Use the following words as a Noun and as a Verb.

visit

Noun: I paid a visit to my hometown.
Verb: We plan to visit the museum.

honour

Noun: He received an honour for his bravery.
Verb: We honour our teachers on Teachers’ Day.

report

Noun: The report was submitted yesterday.
Verb: Please report the incident immediately.

watch

Noun: He bought a new watch.
Verb: I watch television in the evening.

form

Noun: Fill in the application form.
Verb: Students form a line every morning.

surprise

Noun: The party was a pleasant surprise.
Verb: The result will surprise everyone.

2. Say Why

(a) Ramanujan’s letter bored and irritated Hardy at first because it was written in halting English and contained unfamiliar mathematical results without proofs.

(b) Hardy invited Littlewood because he wanted to discuss the unusual and remarkable theorems.

(c) Ramanujan’s mother agreed to send him to England after she had a dream in which the Goddess of Namakkal permitted her son to fulfil his life’s purpose.

(d) Hardy and Ramanujan could not talk freely because of differences in their education and background.

(e) Ramanujan had to be hospitalised because he fell seriously ill.

(f) Ramanujan found the number 1729 interesting because it could be expressed as the sum of two cubes in two different ways.

3. Achievements and Honours Received in England

(i) He was elected a Fellow of the Royal Society at the age of thirty.
(ii) He was elected a Fellow of Trinity College in the same year.
(iii) He was the first Indian to receive these distinctions.

4. Voice – Active and Passive

(A) Identify the 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

(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

(a) Hardy taught Ramanujan.
Ans: Ramanujan was taught by Hardy.

(b) He knew nothing of modern rigour.
Ans: Nothing of modern rigour was known to him.

(d) Hardy was bored by that manuscript.
Ans: That manuscript bored Hardy.

(e) Trinity supported unorthodox talent.
Ans: Unorthodox talent was supported by Trinity.

(f) He could not break the ban.
Ans: The ban could not be broken by him.

5. Identify the Type of Sentence

(a) When he opened it, he found sheets of paper.
Ans: Complex sentence

(b) He glanced at a letter.
Ans: Simple 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 modern rigour.
Ans: Compound sentence

6. Interview Questions

(i) Good morning. Congratulations on winning the Mathematics Quiz at the National Level. May I ask you a few questions?
(ii) Did you develop an interest in mathematics during your childhood?
(iii) How did you prepare for this competition?
(iv) Who guided and supported you?
(v) How did you feel while answering the questions?
(vi) What are your future plans?
(vii) Do you wish to pursue mathematics as a career?
(viii) What message would you like to give to other students?
(ix) Thank you, and best wishes for your future.

7. Summary

The Manuscript

In 1913, Hardy received an envelope from India containing many mathematical theorems written by an unknown Indian. The letter requested his opinion. At first, Hardy was bored and irritated and put the manuscript aside. However, he soon became curious about the unusual theorems. He discussed them with Littlewood, and by midnight, they realised that the writer was a mathematical genius.