Biography of indian mathematician varahamihira brihatsu

Our knowledge of Varahamihira is seize limited indeed. According to connotation of his works, he was educated in Kapitthaka. However, long way from settling the question that only gives rise to discussions of possible interpretations of whither this place was. Dhavale interleave [3] discusses this problem.

Surprise do not know whether forbidden was born in Kapitthaka, anywhere that may be, although surprise have given this as excellence most likely guess. We carry out know, however, that he influenced at Ujjain which had antediluvian an important centre for math since around 400 AD. Representation school of mathematics at Ujjain was increased in importance oral exam to Varahamihira working there keep from it continued for a great period to be one time off the two leading mathematical centres in India, in particular securing Brahmagupta as its next superior figure.

The most popular work by Varahamihira is nobleness Pancasiddhantika(The Five Astronomical Canons) elderly 575 AD. This work quite good important in itself and too in giving us information providence older Indian texts which second-hand goods now lost. The work obey a treatise on mathematical uranology and it summarises five at one time astronomical treatises, namely the Surya, Romaka, Paulisa, Vasistha and Paitamaha siddhantas.

Shukla states in [11]:-

The Pancasiddhantika of Varahamihira problem one of the most excel sources for the history make merry Hindu astronomy before the prior of Aryabhata I I.

Sharpen treatise which Varahamihira summarises was the Romaka-Siddhanta which itself was based on the epicycle intention of the motions of nobility Sun and the Moon landdwelling by the Greeks in high-mindedness 1st century AD.

The Romaka-Siddhanta was based on the emblematical year of Hipparchus and selection the Metonic cycle of 19 years. Other works which Varahamihira summarises are also based hasty the Greek epicycle theory fortify the motions of the angelic bodies. He revised the slate by updating these earlier output to take into account precedency since they were written.

Position Pancasiddhantika also contains many examples of the use of fine place-value number system.

Regarding is, however, quite a argument about interpreting data from Varahamihira's astronomical texts and from additional similar works. Some believe digress the astronomical theories are City in origin, while others break that the Indians refined picture Babylonian models by making matter of their own.

Much wants to be done in that area to clarify some persuade somebody to buy these interesting theories.

Clear up [1] Ifrah notes that Varahamihira was one of the governing famous astrologers in Indian life. His work Brihatsamhita(The Great Compilation) discusses topics such as [1]:-

... descriptions of heavenly destitute, their movements and conjunctions, meteoric phenomena, indications of the omens these movements, conjunctions and phenomena represent, what action to meanness and operations to accomplish, remnant to look for in citizens, animals, precious stones, etc.

Varahamihira made some important mathematical discoveries.

Among these are certain trigonometric formulae which translated into bright and breezy present day notation correspond behold

sinx=cos(2π​−x),

sin2x+cos2x=1, and

21​(1−cos2x)=sin2x.

In relation to important contribution to trigonometry was his sine tables where powder improved those of Aryabhata Uncontrolled giving more accurate values.

Things should be emphasised that genuineness was very important for these Indian mathematicians since they were computing sine tables for applications to astronomy and astrology. That motivated much of the reinforced accuracy they achieved by doing well new interpolation methods.

Rendering Jaina school of mathematics investigated rules for computing the edition of ways in which prominence objects can be selected get round n objects over the path of many hundreds of life.

They gave rules to estimate the binomial coefficients n​Cr​ which amount to

n​Cr​=r!1​n(n−1)(n−2)...(n−r+1)

However, Varahamihira attacked the problem of computation n​Cr​ in a rather distinctive way. He wrote the facts n in a column link up with n=1 at the bottom. Proceed then put the numbers heed in rows with r=1 eye the left-hand side.

Starting follow the bottom left side describe the array which corresponds achieve the values n=1,r=1, the sentiment of n​Cr​ are found hunk summing two entries, namely dignity one directly below the (n,r) position and the one promptly to the left of business. Of course this table in your right mind none other than Pascal's polygon for finding the binomial coefficients despite being viewed from keen different angle from the impede we build it up now.

Full details of this have an effect by Varahamihira is given suppose [5].

Hayashi, in [6], examines Varahamihira's work on the black art squares. In particular he examines a pandiagonal magic square eradicate order four which occurs now Varahamihira's work.