How Indian Mathematicians Contributed To The Evolution Of Pi & The Number Zero

L: A photo of Aryabhatta R: A photo of Brahmgupta
L: A photo of Aryabhatta R: A photo of BrahmguptaL: The wonder that was India R: Cuemath

Zero (0)

Have you ever wondered how chaotic the world would be without this tiny digit? It is a well-known fact that the great Indian mathematician, Aryabhatta was responsible for its development in the sixth century. Thanks to its invention of zero, negative integers and the concept of infinity were developed. The rise of calculus was also seen which is most prevalently used in predicting things ranging from Covid case curves to stock market prediction. But the number has its own unique and rich history. Let us delve a little deeper into that.

In the west, the use of zero(0) started in the 12th century. Before that, the concept of zero was non-existent. So in their numerical system, the number started with ‘1’. With the inclusion of zero, the one we use today, we have the advantage of allowing us to write any number with only ten different digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), which makes it easier to operate with very large quantities, in contrast to, for example, the Roman numerical system (based on the letters I, V, X, L, C, D, and M, which represent the numbers 1, 5, 10, 50, 100, 500 and 1,000).

The Mayan civilization used the zero between numbers to express durations and to mark the dates of the calendar. The philosophy behind zero is that it doesn't have any starting and end just like Nirvana( a philosophical concept stemming from Buddhism referring to the state achieved after the end of desire). Although developed by Aryabhatta, the first notable use of zero(0) was by the Indian mathematician Brahmgupta in 628 AD where he defined zero as a number when substracted by itself giving a number known as shunya (0). Eg: 2–2 = 0

Around the 7th century AD, with the rise of science and technology, astronomy, mathematics, and astrology flourished in the Middle East. The Arabs started to translate books on the subjects and started to use them. Here, they developed a number system where they adopted shunya (0) as the beginning of the number system and named it sifr (0). The development of Algebra (Al-Gebar) is also credited to this period by the Arabs. The Arabian number system was banned in churches in Europe during this period, so shunya(0) wasn’t introduced in Europe.

History changed its course in the the 12th century when Leonardo Fibonacci adopted sifr (0) and coined its name in Latin as Zephrium. This word was later changed to ‘zero’ in English. Zero (0) has been the only number that has never changed from the time it began to be used in a number system.

L: A photo of Aryabhatta R: A photo of Brahmgupta
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While the whole world is well-aware of the great Aryabhatta's contribution to the concept of zero, his work on the discovery of the important mathematical constant pi (π) is a relatively lesser-known fact. Pi is the ratio of the circumference of any circle to the diameter of that circle and has many practical applications in modern-day mathematics and engineering.

There are references to pi in Aryabhatta's seminal text, Aryabhatiya written more than 4700 years ago. In the second chapter of the book, titled Ganitapada (Ganita = Mathematics, pada = chapter) lies the reference to the concept and the approximate value of pi, which had previously not be calculated.

Aryabhata stated that the circumference of a circle with a diameter of 20000 is (4+100) x 8 + 62000, which equals 62832. It is known that the value of pi is the ratio of the circumference to the diameter, so in this case, it would be 62832/20000, which is approximately 3.1416. This approximation is accurate up to five decimal places. Aryabhata used the term āsanna to indicate that the value is not exact but rather an approximation. This is possibly the earliest reference to the irrationality of pi. It was only much later, in 1761, that Johann Heinrich Lambert in Europe proved that pi is irrational, long after Aryabhata's discovery.

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