Aryabhata was one of the major Mathematician-Astronomers belonging to the classical age of Indian Astronomy and Mathematics. Born in Pataliputra,Magadha, he is regarded as one of the greatest Mathematician of all time. His famous works include the ‘Aryabhatiya’ whose Mathematical parts consists of topics on algebra, trigonometry and arithmetic, continued fractions, sum of power series, quadratic equations and sine tables.
One of his discoveries is the approximation of pi which is given by him in Aryabhatia,
“Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached.”
The calculation is obtained as 3.1416 which is close to the actual value of \(\pi\)(3.14159).
Before going to Aryabhata’s invention of zero lets know a little bit about the Indian History of number zero.
Acharya Pingala, a Sanskrit scholar and an Indian Mathematician first used the Sanskrit word ‘Sunya’, referred to as Zero.The word ‘Sunya’ means void or empty. It is believed that the first text to use the decimal place value system(includes zero) was first used in Jain text or Cosmology named ‘Lokavibhaga’ . This is where the term ‘Sunya’ was used.
‘Bakshali Manuscript’, an Arithmetic manual on merchants records the symbol of zero which is a dot like structure having a hollow structure signifying void or nothing..These manuscripts were brought up by Radiocarbon dating ( which is a method of determining the age of an object using radiocarbon) in 2017. The ages were recorded to come from 224-383 AD, 680-779 AD, and 885-993 AD. This marks the world’s oldest record of the application of the symbol of Zero.
In Mathematics there is a term called the Decimal place Value System also called Positional Notation. This means that the value of a number is determined by the position of the digit that is the value of a number is actually the product of the digit by a factor which is determined by the position of the digit.
For example lets take three identical digits 999. Here the interesting part is in words the number is written as nine hundred and ninety nine . The hundreds tens and the units here are being determined by the position of the digits that is digit at the first place represents the units, second place represents the tens and the third place represents hundreds. Similarly any digit at the fourth place shall reprimand thousands.
This concept of the place value system, although was first used in ‘Bakshali Manuscript’ held a very important place in Aryabhata’s work. But the symbol for Zero was not used by Aryabhata. The use of Zero as a ‘digit’ was first used in India during the Gupta Period.
George Ifrah, a French Mathematician stated that the concept and understanding of zero as a ‘digit’ was first given by Aryabhata in his place value system because the counting system of digits is not possible without the place value system or zero. Also calculation performed by Aryabhata on square and cubic roots cannot be done if the numbers are not arranged in accordance with the place value system or zero. This concept of Zero is considered to be one of the best and greatest achievements of Indian Mathematics.
Now the rules for using Zero as a digit was first introduced in Brahmasputha Siddhanta, by Bramhagupta whereas in some stances his rules differ from the modern rules, one being on dividing zero by zero the result yields zero.