4.4 Ramanujan
Complete textbook exercise solutions — Maharashtra State Board (Balbharati), Grade Eight English.
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Warming Up!
In what subjects is knowledge of mathematics used, at school level and college / university level? Name them.
At the school level, mathematics is used in subjects like Physics, Chemistry, Geography, and Information Technology. At the college and university level, it is extensively used in Engineering, Architecture, Economics, Accountancy, Statistics, Computer Science, and Astronomy.
Did you know maths is used in music and poetry also? Can you tell how?
Yes, mathematics is highly involved in both music and poetry. In music, math is used to create rhythm, time signatures, beats, and the frequencies of musical notes, which are all based on mathematical ratios. In poetry, math is used to count syllables and arrange them into structured meters (like iambic pentameter) and consistent rhyme schemes.
- 4 letter words: MATH, TENT, CHAT, TEAM, TIME, MEAT, MINT.
- 5 letter words: MATCH, TEACH, CHEAT, CHANT, CHAIN, MANIA.
- 6 or more letter words: ATTACH, ANTHEM, CINEMA, MACHINE, ANIMATE, INTIMATE.
(Sourced from Chapter 4.2 "Revolutionary Steps in Surgery"):
- Simple Sentence: Surgery dates back to as early as 600 BC.
- Complex Sentence: The doctors had to cut open the part of the body that was not healthy.
- Compound Sentence: In those days heart patients were treated with sedatives and they usually did not survive.
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- enthusiasm: The students participated in the science exhibition with great enthusiasm.
- amiable: Our new class teacher is an amiable person who always helps everyone.
- lope off: After finishing his lunch, the tired dog loped off to sleep under the tree.
- fraud: The man was arrested for committing a bank fraud.
- clarity: The professor explained the complex mathematical formula with absolute clarity.
- come to terms with: It took him a long time to come to terms with his failure in the final exams.
- conveyance: My father receives a monthly conveyance allowance from his office to cover travel expenses.
(Visit / honour / report / watch / form / surprise)
- Visit:
Noun: We paid a quick visit to the national museum.
Verb: I will visit my grandparents next week. - Honour:
Noun: It is a great honour to receive this award.
Verb: The principal decided to honour the brave student during the assembly. - Report:
Noun: The weather report predicts heavy rain tomorrow.
Verb: You must report to the school office immediately. - Watch:
Noun: My father gifted me a digital watch on my birthday.
Verb: We will watch the cricket match on television tonight. - Form:
Noun: Please fill out this admission form in blue ink.
Verb: Dark clouds began to form in the sky before the storm. - Surprise:
Noun: The birthday party was a huge surprise for him.
Verb: I plan to surprise my sister with a new bicycle.
(a) Ramanujan's letter bored and irritated Hardy, at first.
Ramanujan's letter bored and irritated Hardy at first because it was untidy, written in halting English, and contained line after line of wild, fantastic-looking mathematical theorems without any proofs, which made it look like a curious kind of fraud.
(b) Hardy invited Littlewood for a discussion.
Hardy invited Littlewood for a discussion because the wild theorems from the manuscript kept nagging his mind all day, leading him to realize that the writer might actually be an unknown mathematical genius rather than a fraud.
(c) Mother agreed to send Ramanujan to England.
His mother agreed to send him because she had a dream in which she saw her son seated among a group of Europeans, and the goddess of Namakkal 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.
They could not talk freely outside of mathematics because Ramanujan had not been able to matriculate in English and found Hardy's conversations outside of mathematics more than a little baffling.
(e) Ramanujan had to be hospitalized.
Ramanujan had to be hospitalized because he soon became severely ill with tuberculosis in England.
(f) Ramanujan found the number 1729 very interesting.
Ramanujan found the number 1729 very interesting because it is the smallest number that can be expressed as the sum of two cubes in two different ways (13 + 123 and 93 + 103).
- Trinity College, Cambridge, gave him a place to live and work with Hardy.
- Within four years, the Royal Society elected him a Fellow at the very young age of thirty.
- Trinity College also elected him a Fellow in the same year.
- He achieved the unique distinction of being the very first Indian to be given either of these prestigious honours.
- (a) England gave Ramanujan great honours. — Active Voice
- (b) A large untidy envelope was decorated with Indian stamps. — Passive Voice
- (c) The timetable was not altered. — Passive Voice
- (d) She saw her son in a big hall. — Active Voice
- (e) Hardy corrected his statement. — Active Voice
- (f) Ramanujan was brought to England. — Passive Voice
- (a) Hardy taught Ramanujan.
Answer: Ramanujan was taught by Hardy. - (b) He knew nothing of the modern rigour.
Answer: Nothing of the modern rigour was known to him. - (c) Sheets of paper were found in it, by Hardy.
Answer: Hardy found sheets of paper in it. - (d) Hardy was bored by that manuscript.
Answer: That manuscript bored Hardy. - (e) Trinity supported unorthodox talent.
Answer: Unorthodox talent was supported by Trinity. - (f) He could not break the ban.
Answer: The ban could not be broken by him.
- (a) When he opened it, he found sheets of paper. — Complex Sentence
- (b) He glanced at a letter. — Simple Sentence
- (c) Hardy was not only bored but he was also irritated. — Compound Sentence
- (d) Ramanujan turned out to be a poor clerk. — Simple Sentence
- (e) If Ramanujan had been better educated, he would have been even more wonderful than he was. — Complex Sentence
- (f) Ramanujan was self-taught - he knew nothing of the modern rigour. — Compound Sentence
(1) Greeting:
Good morning! Heartiest congratulations to you on your remarkable victory at the National Level Mathematics Quiz.
(2) Introduction:
Today, we have with us our very own math prodigy, Amit Sharma, who has made the entire school proud by securing the first position nationally.
(3) Growing years:
• When did you first realize your deep love and passion for mathematics?
• Who encouraged you the most to participate in competitive quizzes during your early school days?
(4) Achievements:
• How did you prepare yourself for such a high-level national competition?
• Did you face any specific challenges while balancing your regular studies and the quiz preparation?
• Which round of the quiz did you find the most difficult, and how did you tackle it?
• How did you feel the exact moment they announced your name as the national champion?
(5) Future plans and prospects:
• Do you plan to pursue advanced mathematics or engineering for your higher studies?
• What is your ultimate career goal?
(6) Expression of thanks and good wishes:
Thank you so much, Amit, for sharing your inspiring journey with us. We wish you all the very best in your future endeavours!
In early 1913, G.H. Hardy received an untidy envelope from an unknown Indian named Ramanujan. The letter contained sheets filled with wild, unproven mathematical theorems in non-English script. Initially bored and irritated, Hardy suspected it to be a fraud and set the manuscript aside to continue his routine. However, the strange theorems kept nagging his mind all day, preventing him from enjoying his afternoon tennis game. Eventually realizing that the writer was more likely an unknown genius rather than a fraud, Hardy went back to his room and urgently invited his colleague Littlewood to discuss the extraordinary manuscript that evening.