The period between 500 and 1200 AD was the golden age of Indian Astronomy. During this golden period an Indian wizard was born who contributed greatly to the conception of Astronomy and Mathematics. He was none other than Bhaskaracharya.

Bhaskaracharya was the leading mathematician and Astronomer of the 12th century, who wrote the first work with full and systematic use of the decimal number system. He was born near Vijjadavida (Bijapur in modern Karnataka). Bhaskaracharya’s name was actually ‘Bhaskara’ only but the title ‘Acharya’ was added and conferred to mean “Bhaskara the Teacher”. He is also known as Bhaskaracharya II.

Bhāskara and his works represent a significant contribution to mathematical and astronomical knowledge in the 12th century. He became head of the astronomical observatory at Ujjain, the leading mathematical centre in India at that time. Outstanding mathematicians such as Varahamihira and Brahmagupta had worked there and built up a strong school of mathematical astronomy.

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His observations are mainly included in his most celebrated work known as Siddhanta Shiromani which is further divided into four parts known as Lilavati, Bijaganita, Grahaganita and Goladhyaya. Each part of the book consists of huge number of verses and can be considered as a separate book: Lilawati has 278, Beejaganit has 213, Ganitadhyaya has 451 and Goladhyaya has 501 verses.
Bhaskara wrote Siddhanta Shiromani at the age of 36 in 1150 AD. In his book he wrote on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, geography, the mathematical techniques and given the references of many of the instruments used by the astronomers before him. Similarly he has documented the various methods for the use of these instruments.

There are six well known works of Bhaskaracharya. They are :- Lilavathi – Mathematics, Bijaganita – Algebra, Ganitadhyaya – mathematical astronomy, Goladhyaya – sphere, Karanakutuhala – Calculation of Astronomical Wonders, Vasanabhasya – Bhaskara’s own commentary on the Siddhanta Shiromani, and Vivarana which is a commentary on the Shishyadhividdhidatantra of Mathematician and Astronomer Lalla.

Bhaskara was known not only for his mathematical scholarship, but also for his poetic inclinations. He wrote Lilawati in an excellent lucid and poetic language. It has been translated in various languages throughout the world. It was written for his daughter, Lilavati. The Lilavati deals with arithmetic and geometry; it is said that the name is after his daughter Lilavati, who was according to her horoscope to remain unmarried.

 Lilavati of Bhaskracarya
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There is a story which says that Bhaskara put to use all his astrological knowledge to find out an auspicious moment for her marriage, and on the marriage day had a water-clock fixed up as to hit the exact time favourable for her happy marriage, but his efforts were foiled by the child-bride herself. Impelled by girlish curiosity she kept on running to the water clock and bending to peer at it. In one of these visits to the water clock, a pearl loosened from her neck and got stuck to the hole of the water-clock. The auspicious moment passed unnoticed and the girl had to remain unmarried. To console her and perpetuate her name Bhaskara called his treatise on arithmetic and geometry by her name. According to others sources, Lilavati was the name of Bhaskara’s wife.

In his mathematical works, particularly Lilavati and Bijaganita, he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation (x2 = 1 + py2) and in giving many particular solutions.

Bhaskara anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero. Bhaskara used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees.

Brahmagupta was Bhaskara’s role model. To Brahmagupta he pays homage at the beginning of his Siddhanta Siromani. Using an astronomical model developed by Brahmagupta in the 7th century, Bhaskara accurately calculated the time that earth took to revolve around the Sun as 365.2588 days that is a difference of 3 minutes of modern acceptance of 365.2563 days.

Bhaskaracharya was the first to discover gravity, 500 years before Sir Isaac Newton. He is also known in the discovery of the principles of differential calculus and its application to astronomical problems and computations. Bhaskara’s work on calculus predates Newton and Leibniz by over half a millennium.

Bhaskara has given a very simple method to determine the circumference of the Earth. According to this method, first find out the distance between two places, which are on the same longitude. Then find the correct latitudes of those two places and difference between the latitudes. Knowing the distance between two latitudes, the distance that corresponds to 360 degrees can be easily found, which the circumference of the Earth.

He also showed that when a planet is farthest from, or closest to, the Sun, the difference between a planet’s actual position and its position according to the equation of the centre(which predicts planets’ positions on the assumption that planets move uniformly around the Sun) vanishes. He therefore concluded that for some intermediate position the differential of the equation of the centre is equal to zero.

Some other achievements of Bhaskaracharya were:

  • The Earth is not flat, has no support and has a power of attraction.
  • The north and south poles of the Earth experience six months of day and six months of night.
  • One day of Moon is equivalent to 15 earth-days and one night is also equivalent to 15 earth-days.
  • Bhaskaracharya had accurately calculated apparent orbital periods of the Sun and orbital periods of Mercury, Venus, and Mars. There is slight difference between the orbital periods he calculated for Jupiter and Saturn and the corresponding modern values.
  • Earth’s atmosphere extends to 96 kilometers and has seven parts.
  • There is a vacuum beyond the Earth’s atmosphere.

Bhaskaracharya, or Bhaskara II (1114 – 1185) is regarded almost without question as the greatest mathematician of all time and his contribution to not just Indian, but world mathematics is undeniable. He was perhaps the last and the greatest astronomer that India ever produced.

 Source: Free Press Journal & Veda Wikidot

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