4.2 The Indian Root of Mathematics
Complete textbook exercise solutions — Maharashtra State Board (Balbharati), Grade Six English.
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About the chapter
This lesson is about the book ‘Leelavati’, written by the great Indian mathematician Bhaskaracharya. The book teaches arithmetic through interesting sums written as verses. The sums use lotuses, peacocks, swans and monkeys from nature. The lesson also tells us that many mathematical ideas began in India.
Key points
- Bhaskaracharya lived in the 12th century and wrote ‘Leelavati’.
- The sums in ‘Leelavati’ are written in the form of verses.
- Nature was used to make mathematics interesting.
- The concept of zero and the decimal system came from India.
- ‘Leelavati’ was used as a mathematics textbook for centuries.
Words to remember
- verse – lines of a poem
- arithmetic – the study of numbers and calculations
- graceful – moving in a smooth and beautiful way
- serpent – a snake
- originate – to begin or start from
- (i) Mathematics can be taught through stories. — True
- (ii) India has a long history of mathematics. — True
- (iii) Nature doesn’t help to learn. — False
- (iv) Mathematics is easy if you practise exercises every day. — True
- (v) Mathematics sharpens your mind. — True
- (vi) All triangles have 4 sides. — False
| Ancient Inventor | Answer | Invention / Specialization |
|---|---|---|
| (i) Aryabhatta | (e) | Concept of zero |
| (ii) Sushruta | (c) | Surgery |
| (iii) Patanjali | (d) | Yoga |
| (iv) Charaka | (a) | Inventor of Ayurvedic medicine |
| (v) Nagarjuna | (b) | Ancient Alchemist |
- (i) ‘Leelavati’ lived in modern times. — False (She lived hundreds of years ago.)
- (ii) The book ‘Leelavati’ teaches mathematics using stories and verses. — True
- (iii) Indians learned algebra from other countries. — False (Indians knew algebra long before others.)
- (iv) The peacock flew very high in the sky. — False (It flew only up to the branches of trees.)
- (v) ‘Leelavati’ was used as a textbook for many years. — True
- (i) The concept of zero
- (ii) The decimal system
In ‘Leelavati’, the sums were written as verses. They used things from nature that Leelavati loved. These were the lotus, the peacock, the serpent, the swan and the monkeys. For example, one sum is about a peacock on a coconut tree that catches a serpent near its hole. So every sum reminded her of nature, and mathematics became a pleasure.
- The concept of zero originated in India.
- The world learned the decimal system from India.
- Indians knew square roots and cube roots before others.
- They knew algebra, geometry and trigonometry for hundreds of years.
- India produced great mathematicians like Aryabhata and Bhaskaracharya.
Bhaskaracharya wrote the book for Leelavati. She loved flowers, birds, animals and mathematics. The sums in the book were about the things she loved. So he named the book after her.
- (i) to be fond of — Leelavati was very fond of lotus flowers.
- (ii) to be afraid of — The little monkey was afraid of the serpent near the tree.
- (iii) in search of — The peacock came down from the branch in search of food.
- (i) The hole is far away from the tree.
- (ii) It saw a serpent moving to its hole.
- (iii) The graceful swan glided upon the lake.
- (iv) She loved to watch the lovely lotus.
- (v) The lotus stood straight in the water.
- How can I get to Mumbai? — By bus, train or car.
- Which is the best way to get there? — By train.
- How much does it cost? — About 45 rupees.
- How long does it take? — About an hour.
- When does the train leave? — At 8.45 am.
- When does the train arrive? — At about 10 am.
- How can I get to your house from the station? — By taxi.
Aryabhata
- Aryabhata was a great Indian mathematician and astronomer.
- He was born in 476 CE.
- He wrote a famous book called the Aryabhatiya.
- He calculated the value of pi (π) very accurately.
- India’s first satellite was named ‘Aryabhata’ after him.
Bhaskaracharya
- Bhaskaracharya lived in the 12th century.
- He is also known as Bhaskara II.
- He wrote the book ‘Leelavati’.
- His sums used lotuses, peacocks, swans and monkeys.
- ‘Leelavati’ was used as a textbook in India for centuries.
- /eɪ/ as in day — gaze, sway, great, straight, rain
- /aɪ/ as in time — cry, eye, like
- /ɔɪ/ as in boy — boy, boil
- /aʊ/ as in now — brow, plough, house
- /əʊ/ as in go — flow, slow, road
- /ɪə/ as in ear — fear, hear
- /eə/ as in air — fair, care
- /eɪ/ — name, wait, play, cake
- /aɪ/ — my, night, kite, fly
- /ɔɪ/ — oil, coin, toy, voice
- /aʊ/ — cow, cloud, town, out
- /əʊ/ — no, boat, home, coat
- /ɪə/ — here, near, dear, year
- /eə/ — chair, hair, share, pear
- /ʊə/ — tour, poor, pure, cure
Students should read a book of their own choice and write their own review, using the five points of a book review learnt in Lesson 3.5.
Books by Dr. Jayant Narlikar students may look for: The Return of Vaman, Virus, and his collections of Marathi science-fiction stories such as Yakshanchi Denagi.