### Remembering the two great mathematicians named Bhaskaracharyas and the two Indian Satellites named Bhaskara !!

Today is 7th June 2020 and would like to humbly write few words about the two Satellites launched by India named after two Great Mathematicians Bhaskaracharya-I and Bhaskaracharya-II

Bhaskara-I was the second Indian satellite launched on 7th June 1979. The first was Aryabhata with 3 nonmeteorological experiments. Bhaskara-I was launched as part of the satellite-for-earth-observations (SEO) program, and was placed in orbit by a Soviet vehicle launched from a Cosmodrome in the USSR. The main objectives were to conduct earth observation experiments for applications related to hydrology, telemetry, oceanography forestry and geology using a two-band TV camera system and a a two-frequency satellite microwave radiometer (SAMIR) system.

Secondary objectives were to test engineering and data processing systems, to collect limited meteorological data from remote platforms, and to conduct scientific investigations in X-ray astronomy. Thereafter Bhaskar-II was launched on November 20, 1981.

Bhaskara was a 26-faced quasi-s3pherical polyhedron. It had a height of 1.66 m, and a diameter of 1.55 m. Named after the two “Bhaskaracharyas,” astronomer-mathematicians of ancient India. Information and data are available from the Space Application Centre, Ahmedabad, India.

The first amongst the two Mathematicians, Bhaskaracharya – I

Bhaskaracharya-I was a seventh-century Indian mathematician. In mathematics, Bhaskara-I’s sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines ( Circa 600 – 680). This formula is given in his treatise titled Mahabhaskariya. It is not known how Bhaskara I arrived at his approximation formula. However, several historians of mathematics were surprised with its near accuracy and have put forward different hypotheses as to the method Bhaskara might have used to arrive at his formula. The formula is elegant, simple and enables one to compute reasonably accurate values of trigonometric sines. The formula is given in verses 17 – 19, Chapter VII, Mahabhaskariya of Bhaskara I.

The second amongst the two Mathematicians, Bhaskaracharya – II

Bhaskaracharya-II ( Circa 1114 – 1185 ) was an Indian mathematician who extended the work of Brahmagupta ( another Indian Mathematician ) work on number systems. He was born near Bijjada Bida (in present day Bijapur district, Karnataka state in India). Bhaskara was head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India. Other Indian mathematicians Brahmagupta (598–c. 665) and Varahamihira were also in the same observatory. His father Mahesvara was as an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. Loksamudra’s son helped to set up a school in 1207 for the study of Bhāskara’s writings.

He wrote a treatise named Siddhant Shiromani. One of the most important characteristic of Siddhant Shiromani is, it consists of simple methods of calculations from Arithmetic to Astronomy. Essential knowledge of ancient Indian Astronomy can be acquired by reading this book which had surpassed all the ancient books on astronomy in India.

Siddhant Shiromani is divided into four parts, Lilawati, Beejaganit, Ganitadhyaya and Goladhyaya. In fact each part can be considered as separate book. The numbers of verses in each part are as follows, Lilawati on Arithmatic has 278, Beejaganit on Algebra has 213, Ganitadhyaya on Mathematical Learnings has 451 and Goladhyaya on Astronomy has 501 verses.

Siddhant Shiromani is unparalleled and a memorial to his profound intelligence. After Bhaskaracharya nobody could write excellent books on mathematics and astronomy in lucid language in India. In India, Siddhant ( theory ) works used to give no proofs of any theorem. Bhaskaracharya has also followed the same tradition. Its translation in several languages of the world bear a testimony to its eminence.

Bhaskaracharya was the first to make a note on gravity, much before Sir Isaac Newton.

At the age of 36, in his treatise Siddhant Shiromani he wrote on planetary positions, eclipses, cosmography, mathematical techniques and astronomical equipment. In the Surya ( Sun ) Siddhanta he made a note on the force of gravity

“Objects fall on earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to this attraction.”

Bhaskaracharya was given an apt title ‘Ganakchakrachudamani’, which means, ‘a gem among all the calculators of astronomical phenomena’.

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