Aryabhata’s magnum opus, the *Aryabhatiya* was translated into Latin in the 13th century. Through this translation, European mathematicians got to know methods for calculating the areas of triangles, volumes of sphere as well as square and cube root.

Aryabhata’s ideas about eclipses and the sun being the source of moonlight may not have caused much of an impression on European astronomers as by then they had come to know of these facts through the observations of Copernicus and Galileo. But considering that Aryabhata discovered these facts 1500 years ago, and 1000 years before Copernicus and Galileo makes him a pioneer in this area too. Aryabhata’s methods of astronomical calculations expounded in his Aryabhata siddhanta were reliable for practical purposes of fixing the Panchanga (Hindu calendar).Thus in ancient India, eclipses were also forecast and their true nature was perceived at least by the astronomers.

The lack of a telescope hindered further advancement of ancient Indian astronomy, though it should be admitted that with their unaided observations with crude instruments, the astronomers in ancient India were able to arrive at near perfect measurement of astronomical movements and predict eclipses.

Indian astronomers also propounded the theory that the earth was a sphere. Aryabhata was the first one to have propounded this theory in the 5th century. Another Indian astronomer, Brahmagupta estimated in the 7th century that the circumference of the earth was 5000 *yojanas*. A yojana is around 7.2 kms. Calculating on this basis we see that the estimate of 36,000 kms as the earths circumference comes quite close to the actual Circumference known today.

Aryabhata was the first scientist to provide an approximate value for the mathematical constant π(pi). Generally, we say π = 22/7, but actually Aryabhata had more to say! He gives the value correct to five decimal places. **A circle of diameter 20,000 units has a circumference approximately equal to (100 + 4) x 8 + 62,000 = 62,832**. This can be represented in the form of an equation:

π (circumference / diameter) = (62,832/20,000) = 3.1416.

What is really remarkable in the work of Aryabhata is the use of the word *aasanna*, which means approximately. This contribution of Aryabhata was proved only about 8 centuries later.

**Question for kutties**

*What is the circumference of the earth as per modern calculations?*

**Source**

*Sri Nrisimha Priya*

ಭುಮಿಯ ಮೇಲಿನ ಲೊಕದಲ್ಲಿ// .ವಾಸಿಸುವ ದೇವತೆಗಳೂ ಏಕಾದಶಿ ಆಚರಣೇ ಎದೇಯೆ// . ಈದ್ದರೆ ಯಾವ ಗಣೀತ ಪದ್ದತಿ// ಮೂಲ ಸ್ವರೂಪದ ಏಕಾದಶಿ ಗಣೀತಕ್ಕು// ಭುಮಿಯಲ್ಲಿ ಅವತಾರ ಮಾಡೀದಾಗ //ಆಚರಿಸುವ ಏಕಾದಶಿ ಗಣೀತಕ್ಕು ವ್ಯತ್ಯಾಸಗಳಿವೆಯೆ