Google+

Monday, June 8, 2015

Math of India -- Global Learning for Kids


Disclosure: Tuttle Publishing gave me a copy of Indian Children's Favorite Stories free of charge. All opinions in my review are my own and I did not receive any other compensation. They also sent me a copy to giveaway! As in all my reviews I am providing links for your ease, but receive no compensation.

This month we are exploring India as part of the Global Learning for Kids series. Today I thought I would focus on some Indian mathematicians and an Indian mathematical folk tale. Last month I shared the history of zero and the role the Indians played in it. First we will explore a few of the same mathematicians, Aryabhata and Brahmagupta, and introduce another Indian mathematician, Srinivasa Ramanujan. The Indians had a huge influence on our current number system and mathematics. Although it was the Arabs who took their number system and made it famous.



Aryabhata

2064 aryabhata-crp
Statue of Aryabhata 
See page for author [Public domain], via Wikimedia Commons
 Aryabhata was born in 476. He is best remembered for writing the Aryabhatiya, a summary of everything that Indian Mathematicians had learned up to that time. He wrote this summary when he was 23-years old. He did not name his summary, but his assistant did after he died. It included the Indian counting system, basic arithmetic, fractions, calculating area of triangles and rectangles, calculating the volume of a sphere and calculating the circumference of a circle. Not much is known about how he looked although this statue was created much later than his death. It is believed that he studied in Kusumapura. It is stated that he was the head of an institute there. In his work he approximated pi accurately to five decimal places. He also provides the sum of squares and the sum of cubes. Like most mathematicians of the time, Aryabhata was also an astronomer. (Sources: Wikipedia, Science in Ancient India by Melissa Stewart)

Brahmagupta

Brahmagupta
Brahmagupta By anonymous 
[Public domain], via Wikimedia Commons
Brahmagupta was born in 598. Although this was after the Gupta Period, he is still considered part of India's golden age. He wrote about mathematics and astronomy. His texts expanded on Aryabhata's ideas and showed a better understanding of numbers and math at his time than anyone else. He was the director of the astronomical observatory at Ujjain, which was the center of mathematics and space science in ancient India. He was the first to give a way to compute zero. As was common at the time, he wrote in an elliptic verse so his writings are a bit poetic. The Brahmasphutasiddhanta is probably his most famous work. In his work he gives the general solution to a linear equation. He also gives two equivalent solutions to quadratic equations (think quadratic formula). His Brahmasphutasiddhanta is the first to mention zero as a number. He gave rules for the arithmetic operations with zero. Although he did not really figure out division with zero accurately (but then again it is undefined and that may be why he didn't). His most famous formula in geometry is for cyclic quadrilaterals. Heron's formula is a special case of Brahmagupta's formula. He put pi as the square root of ten, but suggested the practical value was using three. (Sources: Wikipedia and Science in Ancient India by Melissa Stewart)

Srinivasa Ramanujan

Srinivasa Ramanujan - OPC - 2
Srinivasa Ramanujan By Konrad Jacobs 
(Oberwolfach Photo Collection, original location) 
[CC BY-SA 2.0 de], via Wikimedia Commons
Srinivasa Ramanujan was born December 22, 1887. He was an Indian mathematician who received little formal training in mathematics. He made extraordinary contributions to number theory, mathematical analysis, infinite series and continued fractions. He did much of his work alone and then reached out to English mathematicians (after being turned down by the Indian ones). He moved to England  and worked closely with G.H. Hardy (a famous English mathematician). G.H. Hardy was one of the only ones who saw promise in Ramanujan's scribbles. Since he had no formal education, most mathematicians had trouble following Ramanujan's work. G.H. Hardy offered him a career in England, but Ramanujan refused since his mother would not allow it. However she had a vivid dream in which the family goddess told her to stop standing in the way of her son trying to do what he is meant to do. She allowed him to go. He left India without his wife or parents. Ramanujan compiled nearly 3900 results independently and most of them have been proven to be true. Only a few were already known or proven false. His work often opened the doors to further research and new discoveries for other mathematicians. He was plagued with health issues for much of his life and returned to India in 1919. He had tuberculosis and died in 1920. On the 125th anniversary of his birth, India declared December 22nd National Mathematics Day in his honor. (Sources: Wikipedia and Mathematicians Are People, Too by Luetta Reimer and Wilbert Reimer.)

The books we used to learn a bit about the Indian Mathematicians are pictured above. 
http://www.tuttlepublishing.com/books-by-country/indian-childrens-favorite-stories-hardcover-with-jacket

Now Hazel got a bit bored with learning about the mathematicians who were doing things she could not understand. However she did enjoy the mathematical folk tale. We have read a few versions of the story and one version can be found in the book, Indian Children's Favorite Stories retold by Rosemarie Somaiah and illustrated by Ranjan Somaiah. The first story in the book is "Munna and the Grain of Rice". 
Source

Munna is the daughter of the elephant keepers at the palace. She loves the elephants and loves to spend time with them. She likes to pretend she is a rani (queen) when she rides on their backs. The Raja (king) of her small kingdom thought he was a kind and fair king, but the farmers did not agree. He ordered the farmers to bring him all the rice to store. He allowed them only enough rice to stay alive. One year there was a drought and the farmers had no rice to give to the Raja or feed themselves. They waited for the Raja to give them the rice he stored for them, but the Raja did not want to give it to them since there would be none left for him. 

One day Munna noticed that while the bags of rice were being transported to the king on the elephants back that one of the bags had a hole in it and the rice was spilling out. She gathered the fallen rice in her skirt and took them to the Raja. He decided to reward Munna for her honesty. He offered her gold, silver and jewels, but Munna was so hungry  and smart that she came up with a plan. She asked the Raja for one grain of rice and he demanded she have more. She said if he insisted she would take one grain the first day and have in give her twice the amount of rice the next day and to keep doubling the number of grains of rice for a month. The Raja thought it was too little, but he decided to go with it. Needless to say by the end of the month, Munna was able to feed the kingdom. We will leave the exact number for you to figure out in this activity.
https://drive.google.com/file/d/0B8PVW7zBWFxsbXdzZ1o3QzVmOW8/view?usp=sharing


The first page is for kids who are just learning how to double or need to practice. The second page is for more advanced kids who can come up with formulas from the pattern. Other ideas would be to introduce finding the area of triangles and rectangles, volume of spheres, and circumference of circles, or working with our place value system. This came from India!

As you can see in the pictures of the book, the illustrations are fun and go with the stories. The book has eight stories in it. They range from this fun mathematical tale to ones about the gods and so much more. Many have lessons are are fun to read. A couple Hazel found a little confusing, but I think it might because they were about their gods and it is completely different from our own beliefs (and perhaps my mispronunciation of the names). We really enjoyed this book!! We will share more about it next week when we share some of the resources we have been using to explore India. 



This post is part of the Global Learning for Kids series. Each month we explore a country and share our explorations in a link party. If you have any books, crafts, recipes, activities, lessons, etc. about India, please share them here. And if you are looking for ideas to explore India check them all out!