LILAVATI

Lilavati

Mathematics is generally considered a boring subject. But to show how mathematics can be taught in an interesting way, I want to tell a story... Through this we will also learn about a mathematician from our history.

Our country has had a very famous mathematician, astrologer and astronomer - Bhaskaracharya! He was born in 1114 in Bijapur, Karnataka. He was a disciple of 'Brahmagupta' and he took forward Brahmagupta's work in mathematics and astronomy. He is called Bhaskaracharya II. Before this, in the seventh century, there was another Acharya Bhaskar, he is known as Bhaskaracharya I. He took forward the work of Aryabhata.

Bhaskaracharya II had only one child, his daughter Lilavati. When Lilavati was 6 years old, Bhaskaracharya decided to get her married.  But after calculations, she found that her husband would die within a week of marriage. This death could be averted only if the marriage took place in a particular Lagna (ascendant).

Bhaskaracharya arranged for the marriage to take place at that particular time. He arranged for a water clock to tell the time. In this water clock, there was a hole in a vessel through which water drops would drip into the other vessel below and the vessel below would get filled in a specific time.

The story is that 6 year old Lilavati went to see the water clock kept in a special room out of curiosity. A pearl from her nose ring fell into the water pot and the hole got partially blocked. This led to a mistake in the calculation of time and the auspicious time was missed and Lilavati got married in a wrong time. Within a week of the marriage, Lilavati's husband died after falling from a cliff and the widow Lilavati came to live with her father. At that time, widow remarriage was also not allowed. Bhaskaracharya thought that perhaps there was some mistake in his astrological calculations. He became very sad.

I don't know how true this story is, it is also not certain that a person's future can be seen through astrology and doing something in a particular time or Muhurta can lead to different results, but further in this story it is told that the sad Bhaskaracharya decided to make his daughter study mathematics.  Lilavati also decided the same. For this, Bhaskaracharya used to teach his little daughter in a very interesting way. He wrote mathematical formulas in poetry and taught those formulas in a very loving and interesting way. He used to say, "My dear daughter Lilavati with eyes like deer! These are the formulas..."

An example of how Bhaskaracharya used to teach his daughter by combining entertainment, curiosity and joy is this question, "A third, a fifth and a sixth of a group of pure lotuses were used to worship Shiva, Vishnu and Surya respectively. A fourth was used to worship Parvati and the remaining 6 lotuses were used to worship the feet of the Guru. O girl Lilavati! Tell quickly how many flowers were there in that group of lotuses."

If we calculate this using algebra, considering the total number of flowers as 'X', then the answer will be 120 flowers.

Explaining the meaning of square and cube, Bhaskaracharya says, "O girl Lilavati! The square area and its area are called square. The product of two equal numbers is also a square. Similarly, the product of three equal numbers is called cube and a solid with twelve cells and equal sides is also a cube."

The word 'mool' is used as the root of a tree or plant, or in a broad sense, the origin of any object or cause. Therefore, in mathematics, the meaning of square root is the origin of the square, that is, one side of the square. Similarly, the meaning of cube root is one side of the cube. Bhaskaracharya has explained these things to his daughter in a very interesting and beautiful way.

Bhaskaracharya wrote a book 'Siddhanta Shiromani' at the age of 36 in 1150. It is in four parts. He named its first part or first chapter 'Lilavati'. This chapter mainly covers arithmetic. This chapter is also called Patiganitaadhyaya.  Other parts of this book include Algebra, Goladhyaya and Grahganitadhyaya.

In this book, and especially in the chapter 'Lilavati', the formulas of mathematics have been explained in a very beautiful and poetic form. Bhaskara II was also a good poet. He has composed many poems on mathematics in the form of Sanskrit verses. He has also written about himself in the form of poems in Sanskrit verses. Faizi, a scholar in Akbar's court, translated 'Lilavati' into Persian for the first time in 1587. The first translation of 'Lilavati' into English was done by J. Weller in 1716.

Similarly, nowadays some teachers teach mathematics in couplets. Like the multiplication table of fifteen... "Four sixty, six ninety, eight twenty two, nine thirty five..." The names of the months and the number of days in them are also memorized in poetic language... "Si up June thirty, the rest thirty one, twenty eight February, fourth year twenty nine."

With time Lilavati became a famous mathematician. Her father's love made her immortal. Today mathematics awards are given in her name.

The work of Brahmagupta, Mahavira and Shridhar has also been given a place in 'Siddhanta Shiromani'. Bhaskaracharya was the first to tell that dividing any number by zero gives infinity. Although now this division is considered undefined. In arithmetic, Bhaskaracharya gave the 'Chakrawal' formula. Six centuries later, European mathematicians Galois, Euler and Lagrange rediscovered it in the name of 'Inverse cyclic'.  Bhaskaracharya also discovered 'Differential Calculus' which is used in Trigonometry. He also gave the idea which is now called 'Differential coefficient' and 'Rolle's Theorem'. He created the 'Tatkalikagati' formula for calculating the speed of planets. At the age of 69, he wrote his second book 'Karan Kautool' which is dedicated to astronomical calculations. It is very useful in making calendars. He also wrote other books. He gave many principles, theorems and formulas in mathematics and discovered methods of calculation which were rediscovered hundreds of years later by many scientists of the West like Sir Isaac Newton and Gottfried Leibniz under different names. I am not mentioning all of them in this short article.

Bhaskaracharya II also talked about gravity. He told that the earth pulls things towards itself. Although he did not give the formulas like Newton did and from which we can find out the force of pulling any body by another body and the acceleration generated by it. He also calculated the value of solar year almost completely correctly. Bhaskaracharya was wrong in some places. According to the knowledge of that time, he considered the earth to be the center of the universe, whatever the concept of the universe was at that time. It is said that Bhaskar II was also the head of the observatory of Ujjain. India named its two satellites launched in 1979 and 1981 as Bhaskar 1 and Bhaskar 2. He died in 1185.

This story also shows the love between father and daughter, teaching mathematics in an interesting way and evils like child marriage and child widow not being allowed to remarry. It also shows the work of a great mathematician who did it a thousand years ago. This story also shows that knowledge belongs to the whole humanity, the whole world. There is no need to differentiate between East and West, new and old. Similarly, science is also a way of thinking logically. There is no need to divide it into science and science. Many scientists, wise men and thinkers of the whole world have given a lot to this world. It is because of them that we are where we are today. All those scientists, wise men and thinkers deserve respect. I saw a gentleman writing at a place on social media that Aryabhata had explained about relative motion just like Einstein. By saying this, that gentleman was calling the work of Aryabhata and Einstein in this field equivalent. But this is not true.  Einstein has done a lot of work in this field, has given many formulas, which Aryabhata did not do. But Aryabhata lived in the fifth and sixth century and Einstein in the twentieth century. This makes a difference. We should be unbiased in our analysis and should not be driven by any particular ideology.

This story also shows us that it is not necessary that all the ideas of a thinker are correct. He may make mistakes. There may be mistakes in any text. We should keep our minds open to understand them and take the essence and truth from the new and the old and leave the falsehood. Bhaskar Acharya's idea of ​​a geocentric universe was not true. Similarly, some Indian mathematicians of that time opposed the theory of the earth rotating, they called it Achala. They said that if the earth rotated and went from west to east, then the birds flying towards the east would automatically reach their nests. Since this does not happen, it means that the earth does not rotate on its axis. Now we know that this idea is false and the logic and ideology of those astrologers and mathematicians was wrong. The ideas of the great philosopher Aristotle were accepted as true for 2000 years and many of those ideas were later proved wrong. We should be careful in deciding what is true and what is false. Our way of seeing what is true and what is false should be authentic.  We have to be careful about what should be our criteria for this recognition. Knowledge develops gradually, man attains it slowly through his efforts and reaches the milestones of physical and mental change and development over millions of years. This work will be done in a better way only when he keeps the criteria of his judgment of truth and falsehood correct. Man makes mistakes in this matter, his path goes up and down, but ultimately he takes the path of development. Let us hope that standing on the shoulders of our great thinkers, we will move further on the path of development and truth.