Aryabhatta – Indian Mathematician Who Discovered Pi (π) | Achievements & Contributions
India has given the world many legendary scholars, but Aryabhatta (476 CE) stands as one of the best mathematicians and astronomers in ancient times. Known for introducing the decimal system, the concept of zero, algebra, and trigonometry, Aryabhatta also gave the world the value of Pi (π), which remains a cornerstone of mathematics and science.His famous work Aryabhatiya, written in Sanskrit poetic verses, contains 33 rules of arithmetic, algebra, and trigonometry along with detailed astronomical explanations. This remarkable text made Aryabhatta a pioneer in both mathematics and astronomy.
Aryabhatta: The Great Indian Mathematician & The Value of Pi (π)
Aryabhata was one of the best astronomers and mathematicians of ancient times.
Aryabhata, the great mathematician who invented the decimal system in mathematics and made the world aware of zero, had also propounded the principle of pi (π).
He was among the first to use algebra. He has written his famous work 'Aryabhatiya', which is a mathematics book, in poetic verses. Most of the information given in this book is related to astronomy and spherical trigonometry. 33 rules of arithmetic, algebra, and trigonometry are also given in 'Aryabhatiya'. Not only this, he invented equations to solve complex mathematical problems easily, which are still used by people all over the world today.
Aryabhatta’s Contribution to Mathematics -
Introduced the decimal place-value system.
Made the world aware of the concept of zero.
Solved complex algebraic problems with innovative equations.
Worked on spherical trigonometry and astronomy.
Calculated the Earth’s circumference and explained solar & lunar eclipses scientifically.
Most famously, he discovered the value of Pi (π).
Some Interesting Facts about Pi:
It is an indisputable truth that the exponent of the theory of Pi was also Aryabhatta, in other terms, Aryabhatta discovered pi.
Despite this, from Archimedes to Newton, everyone discovered about pi and put their values in front of the world.
Archimedes said that pi lies between 223/71 and 22/7. Archimedes is often called the designer of mechanical devices, but his contribution to mathematics is also incomparable. Archimedes could have used infinite series in the same manner as is used in modern divisible calculations. He used his 'method of technique completion' to find the approximate value of pi.
Brahmagupta, another Indian mathematician, advanced the discovery of pi to new heights.
It is believed that the pyramid builders of Egypt had knowledge of pi. However, no written proof of this is available.
Although the need for this ratio and related research has been going on for a long time, the sign of pi (π) was first used by William Jones in 1706, but in 1737 by the Swiss mathematician Leonard Euler. Since then it has gained fame.
What is Pi (π)? & Aryabhatta's contribution to Pi
Pi (π) is the 16th letter of the Greek alphabet.
In geometry, it represents the ratio of a circle’s circumference to its diameter. In each circle, this ratio's approximate value is 3.14159… (infinite and non-repeating), but the whole number after the decimal has not yet been calculated, so it is considered infinite.
Pi is an irrational number, meaning it cannot be expressed exactly as a fraction. But Commonly used fraction: 22/7.
Value of Pi by Indian Mathematician Aryabhatta -
It is historically accepted that Aryabhatta discovered Pi (π). In his book Aryabhatiya, he expressed Pi through the following Sanskrit shlok:"Chaturadhikam Shatmashtgunam Dwashashtistatha Sahastranam।
(चतुराधिकं शतमष्टगुणं द्वाषष्टिस्तथा सहस्त्राणाम्।)
Ayutadvaysya Vishkambhasya Aasannau Vritparinah ॥
(अयुतद्वयस्य विष्कम्भस्य आसन्नौ वृत्तपरिणाहः॥)"
Meaning: Add four to 100, multiply by 8, and then add 62,000. By this rule, the circumference of a circle with a diameter of 20,000 can be found. That is, if the diameter of a circle is 20,000, then its circumference will be 62,832.This formula gives Pi (π) ≈ 3.1416, which is accurate to four decimal places.
Aryabhatta himself mentioned it as an approximate value (āsanna), showing his commitment to truth and accuracy.
It is noteworthy that in spite of accurate and correct calculation to four decimal places, Aryabhata, who insists on truth, does not consider this value to be pure. Rather they were considered adjacent (near).
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Uses of Pi (π):
Pi is mostly used in geometry. The number Pi is used to calculate the area and circumference of a circle. Pi used in almost every branch of mathematics. It is one of the most important in mathematics, widely used in:
Geometry: Calculating the area and circumference of circles.
Trigonometry: Radians and angular measurements.
The tradition of writing numbers in radians made it an integral part of trigonometry.
Science, Engineering & Architecture: Designing structures, bridges, and buildings.
Physics & Quantum Mechanics: Wave functions, oscillations, relativity.
Space Science: NASA regularly uses Pi to calculate spacecraft trajectories.
Medical Science: Used in MRI scans, signal processing, and probability theory.
Everyday Technology: GPS, communications, and music theory.
Conjecture or Probability: It is also used extensively in conjecture or probability. Buffon's Needle problem is the biggest example of this.
You might not use it yourself every day, but Pi is used in most calculations for building and construction, quantum physics, communications, music theory, medical procedures, air travel and space flight.
The History of Pi (π) Across Civilizations
Archimedes (287–212 BCE): Calculated Pi between 223/71 and 22/7 using polygons.
Brahmagupta (598 CE): Advanced Aryabhatta’s Pi work further.
William Jones (1706): First used the symbol π for Pi.
Leonhard Euler (1737): Popularized π globally.
Egyptians & Babylonians: Early estimates of Pi used in pyramid construction.
Pi (π) Day – 14th March
The following pi-related questions are frequently asked: "Why do we celebrate Pi Day? What is the official Pi Day? Is March 14th National Pi Day? Why is 3.14 called Pi Day?"
The quick answers to these questions are provided below.
Pi has been assigned a value of around 3.14, so Pi Day is celebrated every year on March 14. In other words, Pi Day is celebrated every year on March 14 (3/14) as the digits match Pi’s value (3.14).
March 14 is also the birthday of the great scientist Einstein. Therefore, the importance of this day also increases.
Larry, a scientist working in San Francisco, first organized Pi Day in 1988, in which all employees ate fruit pies in a circle.
In 2009, the US House of Representatives also approved the celebration of Pi Day, after which this informal event was promoted not only throughout America, but all over the world, and now it is being celebrated in many countries.
The New Jersey city of Princeton has its unique way of celebrating Pi Day. Einstein had spent 20 years of his life here, so apart from eating pie, reading poetry, and discussing the importance of pie, there is also a competition for Einstein's lookalike.
What is Pi minute
'Pi minute' is also included in the series of interesting elements of mathematics, when seven decimal values of pi are obtained at exactly 1:59:26 on March 14, i.e. 3.1415926, then discussions and debates are started all over the world on the use, importance, etc. of Pi.
So, Pi is not just about math classrooms.
Calculation of Pi (How to calculate the value of Pi):
We have known about Pi for 4000 years, but even today, even with the world's fastest supercomputer, humans have not been able to calculate it correctly.
There are many examples of the calculation of Pi in the history of ancient India.
On the basis of the calculation, different sizes and types of Yagya-Altars (यज्ञ-वेदियां) were made.
Aryabhatta had solved some difficult questions. For example, the number that will come by adding the areas of two right equilateral squares, making a 'right' equilateral square of that area, and converting that shape into a circle equal to its area, etc.
Pi (π) is an irrational number. An irrational number means that it is a fractional number whose absolute value can never be worked out. If you write in a normal fraction, it is written as 22/7, but when you convert it to a decimal, no matter how many digits are removed after the decimal, the whole is not divided.
Value of Pi (π) after the decimal to trillions of digits (Modern Pi Calculations):
This time on Pi Day, we have rounded up the value of Pi after the decimal to 100 trillion digits.
In November 2016, Peter Trueb, a Swiss scientist, calculated Pi up to 22 trillion digits. This amazing Pi-enthusiast Peter Taub has done this after counting round the clock for 105 days.
He designed a computer with 24 hard disks (6 terabytes each) so that the information after each step could be saved. A special computer program was also used for this.
This value of pi, which is 220 trillion digits, the size of the computer file in which it is recorded is 9 terabytes. If this value is printed in book form, then a million books of 1-1 thousand pages will be less.
So after doing all this, the value of Pi that came out from the hard work of three and a half months is very accurate.
But the question arises, what is the need for such a precise value, why are we lying behind the Pi?
If seen, the value of Pi that the American space agency NASA uses only 15 digits after the decimal for accurate space calculations for rocket launches in space.
And it is said that to solve the complex and subtle mysteries of the universe, a maximum of 40 marks will be required.
So many believe that behind the craze to calculate the value of Pi to as many digits as possible is the urge to demonstrate the computer's ability.
Some believe that the motivation for finding the value of Pi more accurately is something else.
Pi is an irrational number. That is, we can go on calculating its marks. After counting the number of digits, it may be found that none of these numbers is repeated more often than any other. If no digit in an irrational number is repeated more often than other digits, then that irrational number is called 'normal'. There seems to be an attempt at increasing the value of Pi further to prove its 'normality', although in the real world this would not matter.
There is one more thing - proving Pi normal cannot be based on calculations alone. This would require mathematical proof.
Mathematicians keep pushing Pi’s digits further, not for practical use, but to test the limits of computing power and explore mathematical normality.
Conclusion
Aryabhatta’s genius reshaped mathematics and astronomy forever. His discovery of Pi (π), along with his works on algebra, trigonometry, and astronomy, made India a global center of knowledge in the ancient world.
Even today, Pi remains an eternal mystery—infinite, irrational, and fascinating—reminding us of the timeless contributions of Aryabhatta, the great Indian mathematician.
Important FAQs on Pi
Q1. Who discovered Pi (π)?
Aryabhatta, the great Indian mathematician, first calculated Pi’s value accurately to four decimal places.
Q2. What was Aryabhatta’s value of Pi?
Aryabhatta calculated Pi ≈ 3.1416, which is still accurate.
Q3. Why is Pi Day celebrated?
Pi Day is celebrated on March 14 (3/14) because the date matches Pi’s value (3.14).
Q4. Who gave the symbol π for Pi?
The symbol π was first used by William Jones in 1706 and later popularized by Leonhard Euler.
Q5. What are Aryabhatta’s main contributions?
Discovery of Pi (π)
Decimal system and zero
Aryabhatiya (a book of mathematics & astronomy)
Trigonometry and algebraic equations
Scientific explanation of eclipses
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