Varahamihira: History Disputed Mythology of Bihar(Magadha)

What we know about varahamihira is very limited,IT is said Aryabhatta had many students and his next successor Lalla was one of his pupils and some say Varahamihira, too, was his pupil.

According to one of his works, he was educated in Kapitthaka.it is not clear weather he was born in Kapitthaka,but We do know, however, that he worked at Ujjain which had been an important centre for mathematics since around 400 AD. The school of mathematics at Ujjain was increased in importance due to Varahamihira working there and it continued for a long period to be one of the two leading mathematical centres in India, in particular having Brahmagupta as its next major figure.
Astrologer, astronomer and mathematician, Mihira or Daivajna Mihira, became famous as Varaha Mihira (499-587 CE).

Some scholars suggest him to be One  amongst the Navarathnas(nine jewels) in the court of King Vikramaditya (Chandragupta II - Gupta dynasty)of Ujjain.
As already mentioned Aryabhatta had another celebrated astronomer as his contemporary. who was Varahamihira. In his Vrhajja- taka in the 26th chapter, he says that he was son of Adityadasa, that he was an Avantaka, that he   received his knowledge from his father and that he obtained a book from the Sun-God at Kampillaka or Kapitthaka. Bhattotpala tells us that he was a Migadha dvija. Some say that he was a Magadvija, i.e., one of the Magii long settled in India. From all this the late Pandit Sudhakara Dvivedi in his Ganakatarangiui infers that it is not impossible that Varaha was a Magadha Brahmin. He might have gone to Ujjain for livelihood He studied with his father at his own house in Magadha and also studied the works of Aryabhatta there, he travelled to make himself known, he worshipped Sun-God at Kampillaka (Kalpi) and obtained a book from him. I acquired a manuscript of his son's work Prthuyasah-Sastra at Samkhu the northernmost part of the Nepal valley, the opening verse of which says that the son Varahamihira asked his father some questions while he was residing at the beautiful city of Kanyakubja on the Ganges.
Varaha might have retired to Kanyakubja in his old age to be on the Ganges and there imparted his knowledge to his son Prthuyasah. Amaraja, the commentator of Khandanakhandakhadya says that Varahamihira died in the Saka year 509 that is 587 A.D. Some people think that Varaha wrote his Panca-Siddhantika in 505 A.D. that is Saka 4:27. But this is impossible if we are to believe Amaraja. Varaha would then be only 18. Therefore Dr Thibaut after carefully considering all the facts of the case thinks that 427 Saka was the date when Lalla revised the Romaka-Siddhanta and that the Panca-SiddhSnta was composed about 550 A.D. So Varahamihira was a later contemporary and perhaps a student of Aryabhata.
The Ganakatarangiui has given a list of Varaha’s works and thinks that the Vrhat-Saipbita is his last work. It is an Eucyclopoedic work. It treats not only of Astronomy and Astrology but of such subjects as gardening, agriculture, sculpture, strilak^ana, purusalakgana and so on. This great work is the Pafica-Sidhantta in which he gives a summary of all the Sidhantas current in his time. They are five in number Paulisa, Romaka. VaSi^tha, Paitamaha and Sur.yyasiddhaata. Varaha says that of these five PmiliSa and Roraaka have been explained by Latadeva.
The Siddhanta made by PauliSa is accurate. Near to it stands the Siddhanta proclaimed by Romaka, more accurate is the Savitra (Saura) and the two remaining are far from the truth.
Kern says that the third Skandha of Jyotisa "'namely, its Jataka section has been borrowed from the Yavanas or Greeks. This is a fact. The Yavana-Jataka of Yavan&caryya is still regarded as an authoritative work on the subject and there are other works like Miuaraja Jataka also taken from the Yavanas. some scholars  found in Nepal a manuscript of a Yavana-Jataka written in the character of the tenth century oa palm-leaf which contains the following statement at the end.
Varahamihira’s knowledge of Western astronomy
was thorough. In five sections, his monumental work progresses through native Indian astronomy and culminates in two treatises on Western astronomy, showing calculations based on Greek and Alexandrian reckoning and even giving complete Ptolemaic mathematical charts and tables.
Although Varahamihira’s writings give a comprehensive picture of 6th-century India, his real interest lay in astronomy and astrology. He repeatedly emphasized the importance of astrology and wrote many treatises on shakuna (augury) as well as the Brihaj-Jataka (“Great Birth”) and  in the Laghu-Jataka (“Short Birth”), two well-known works on the casting of horoscopes.
The most famous work by Varahamihira is the Pancasiddhantika (The Five Astronomical Canons) dated 575 AD. This work is important in itself and also in giving us information about older Indian texts which are now lost. The work is a treatise on mathematical astronomy and it summarises five earlier astronomical treatises, namely the Surya, Romaka, Paulisa, Vasistha and Paitamaha siddhantas. Shukla states in:-
The Pancasiddhantika of Varahamihira:
is one of the most important sources for the history of Hindu astronomy before the time of Aryabhata I .
One treatise which Varahamihira summarises was the Romaka-Siddhanta which itself was based on the epicycle theory of the motions of the Sun and the Moon given by the Greeks in the 1^st century AD. The Romaka-Siddhanta was based on the tropical year of Hipparchus and on the Metonic cycle of 19 years. Other works which Varahamihira summarises are also based on the Greek epicycle theory of the motions of the heavenly bodies. He revised the calendar by updating these earlier works to take into account precession since they were written. The Pancasiddhantika also contains many examples of the use of a place-value number system.
There is, however, quite a debate about interpreting data from Varahamihira's astronomical texts and from other similar works. Some believe that the astronomical theories are Babylonian in origin, while others argue that the Indians refined the Babylonian models by making observations of their own. Much needs to be done in this area to clarify some of these interesting theories.

n Ifrah notes that Varahamihira was one of the most famous astrologers in Indian history. His work Brihatsamhita (The Great Compilation) discusses topics such as :-

... descriptions of heavenly bodies, their movements and conjunctions, meteorological phenomena, indications of the omens these movements, conjunctions and phenomena represent, what action to take and operations to accomplish, sign to look for in humans, animals, precious stones, etc.

Varahamihira made some important mathematical discoveries. Among these are certain trigonometric formulae which translated into our present day notation correspond to

sin x = cos(π/2 - x),
sin²x + cos²x = 1, and
(1 - cos 2x)/2 = sin²x.

Another important contribution to trigonometry was his sine tables where he improved those of Aryabhata I giving more accurate values. It should be emphasised that accuracy was very important for these Indian mathematicians since they were computing sine tables for applications to astronomy and astrology. This motivated much of the improved accuracy they achieved by developing new interpolation methods.
The Jaina school of mathematics investigated rules for computing the number of ways in which r objects can be selected from n objects over the course of many hundreds of years. They gave rules to compute the binomial coefficients _nC_r which amount to

_nC_r = n(n-1)(n-2)...(n-r+1)/r!

However, Varahamihira attacked the problem of computing _nC_r in a rather different way. He wrote the numbers n in a column with n = 1 at the bottom. He then put the numbers r in rows with r = 1 at the left-hand side. Starting at the bottom left side of the array which corresponds to the values n = 1, r = 1, the values of _nC_r are found by summing two entries, namely the one directly below the (n, r) position and the one immediately to the left of it. Of course this table is none other than Pascal's triangle for finding the binomial coefficients despite being viewed from a different angle from the way we build it up today. Full details of this work by Varahamihira is given in .
Hayashi, in , examines Varahamihira's work on magic squares. In particular he examines a pandiagonal magic square of order four which occurs in Varahamihira's work.