Topics of Interest Greatest Indian Mathematicians

Raj Kumar Parashari 12 Nov, 2019 Views: 352

**Brahmagupt and his Introduction to ZERO**

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Who was Brahmagupt? According to Bhaskaracharya, an eminent mathematician and astronomer from Karnataka, he was ganaka-thakra-chudamani, i.e. the gem of the circle of mathematicians. George Alfred Leon Sarton, a Belgian-American chemist and historian from the 20th century, called Brahmagupt as 'one of the greatest scientists of his race and the greatest of his times'.

His works were translated in different languages across the world. His decimal number system and algorithms have spread throughout the world. Unlike the Greeks and Romans who considered zero as a symbol for a lack of quantity or the Babylonians as a placeholder digit, he deemed it as a number in its own right.

Brahmagupt introduced rules for dealing with the zero. So, 1× 0=0, 1+ 0=1, 1– 0=1 that we learn today were actually his calculations! According to him, positive numbers symbolize fortune and negative debt. This Indian mathematician and astronomer introduced the zero and argued that the earth is round.

A Shaivite, Brahmagupt considered numbers as abstract entities, rather than being used for just counting and measuring. This led him to introduce the concept of positive and negative numbers. Most of his works are on geometry and trigonometry. He was an astronomer of the Brahmapaksha school, one of the four major schools of Indian astronomy during his times.

**Early Life and Work**

The remarkable life of Brahmagupta began in 598 AD in northwestern India. He spent most of his life living near the modern Indian city of Bhinmal, which was then known as Bhillamala. It is sometimes referred to as Bhillamalacharya, which means the teacher from Bhillamala.

He began to study astronomy when he was a young man. At this time, Indian astronomy was quite advanced compared to the work being done in the rest of the world. When he was only 30 years old, he published his most famous book, the Brahmasphutasiddhanta. In this book, he mainly focused on issues related to astronomy. He asserted that the Earth was round and not flat, as many people still believed, and even calculated that the circumference of the Earth was approximately 36,000 km. Today, we know that the Earth's circumference is actually about 40,000 km, so Brahmagupta's calculations were pretty accurate!

He was also able to predict the motion of the planets and the timing of solar and lunar eclipses. He calculated the solar year very accurately, writing that one solar year was 365 days, 5 minutes, and 19 seconds. Down to the minute, this is what scientists have now measured the solar year to actually be!

His book also contained chapters on mathematics, and it was in these chapters that he explained the rules for using zero in mathematical calculations. He also explained how to work with negative numbers, which he referred to as debts. In his writing, positive numbers were called fortunes, and among other things, he was the first person to explain why the product of a positive and a negative number (fortune and debt) would also be negative. No one had ever done this before either!

He also made contributions to geometry, including accurately calculating the constant pi, and developing a way to calculate the area of a cyclic quadrilateral that is still known as Brahmagupta's Formula.

**About Brahmagupt at Glance**

- " According to the book Chronology of Ancient India by Vedveer Arya, he was born in Saka 520 elapsed (63-62 BCE). His birthplace was Bhillamala, now Bhinmal, of Jalore, Rajasthan.
- He was the son of an astrologer named Jisnugupta.
- King Vyaghramulcha was the ruler of Bhillamala during his time.
- He was the head of the astronomical observatory at Ujjain.
- He composed his works in elliptic verse with a poetic touch.
- He breathed his last in Ujjain.

During the time of Brahmagupt, astronomers and scientists across the world argued that the earth and the universe were flat. Though the concept about the earth & universe being round finds mention in ancient Indian scriptures dating back to thousands of years, debates and discussions that it is flat continued generation after generation, era after era across the world. Brahmagupt counter-argued that they were round.

Do you know Brahmagupt was the first astronomer in the world to use Mathematics to predict the positions of the planets? He neither used a telescope nor any scientific equipment to calculate thus! Using Mathematics, he also practically calculated the timing of the solar and lunar eclipses! He calculated length of solar year to be 365 days, 5 minutes and 19 seconds which is quite precise compared to present day calculations.

**Works of Brahmagupt on Mathematics, Science, and Astronomy **

- Cadamakela.
- Brahmasphutasiddhanta; this book contains 24 chapters in the form of verses numbering to 1008 with key focus on Mathematics, including Algebra, Geometry, Trigonometry, Algorithmics and Astronomy.
- Khandakhadyaka; the book is a practical manual of Indian Astronomy.
- Durkeamynarda.

Everyone is familiar with Isaac Newton's law of universal gravitation, giving him the credit for discovering the theory of gravity. But do you know, hundreds of years even before Isaac Newton was born, Brahmagupt talked about 'gravity'?

According to Brahmagupt's scientific calculations, the earth attracts bodies as inherent in its nature. He drew a comparison of the earth's nature to water that flows. Hence, according to him, bodies or objects fall towards the earth.

**Contribution of Brahmagupt to Mathematics **

- Introduced 'zero' to the number system
- Explained how to find the cube and cube-root of an integer
- Introduced rules for computation of squares and square roots
- Introduced rules for five types of combinations of fractions
- Introduced the theory of negative numbers
- Positive number × positive number = Positive
- Positive number ×negative number = Negative
- Negative number × positive number = Negative
- Negative number × negative number = Positive
- Introduced formula for cyclic quadrilaterals
- Introduced √10 (3.162277) as an approximation for π(3.141593).

The above is only a partial list of what Brahmagupt has introduced. His contributions in the field of Mathematics, Science, and Astronomy are phenomenal. This knowledge heritage is what we, Indians, proudly boast of!

Indian mathematicians and astronomers before Brahmagupt did have knowledge about the zero, but they did not use it as a number. Aryabhatt used letters of the alphabet to denote numbers and the zero. It was Brahmagupt who first used zero as a number besides introducing rules dealing with it.

--- Adopted from iapt magazine ( would like to mention contributor name which right now I do not know right now)

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