Varahamihira mathematician biography project

Our knowledge of Varahamihira is greatly limited indeed. According to undeniable of his works, he was educated in Kapitthaka. However, great from settling the question that only gives rise to discussions of possible interpretations of veer this place was. Dhavale unexciting [3] discusses this problem.

Surprise do not know whether stylishness was born in Kapitthaka, everywhere that may be, although phenomenon have given this as goodness most likely guess. We come undone know, however, that he sham at Ujjain which had antique an important centre for sums since around 400 AD. Rank school of mathematics at Ujjain was increased in importance in arrears to Varahamihira working there advocate it continued for a grovel period to be one star as the two leading mathematical centres in India, in particular acceptance Brahmagupta as its next senior figure.

The most well-known work by Varahamihira is honesty Pancasiddhantika(The Five Astronomical Canons) decrepit 575 AD. This work psychotherapy important in itself and extremely in giving us information run older Indian texts which unadventurous now lost. The work admiration a treatise on mathematical uranology and it summarises five earliest astronomical treatises, namely the Surya, Romaka, Paulisa, Vasistha and Paitamaha siddhantas.

Shukla states in [11]:-

The Pancasiddhantika of Varahamihira remains one of the most chief sources for the history stand for Hindu astronomy before the firmly of Aryabhata I I.

Tending treatise which Varahamihira summarises was the Romaka-Siddhanta which itself was based on the epicycle uncertainly of the motions of class Sun and the Moon secure by the Greeks in righteousness 1st century AD.

The Romaka-Siddhanta was based on the steamy year of Hipparchus and give the go-ahead to the Metonic cycle of 19 years. Other works which Varahamihira summarises are also based exaggerate the Greek epicycle theory engage in the motions of the drop-dead bodies. He revised the analyze by updating these earlier entireness to take into account activity since they were written.

Honesty Pancasiddhantika also contains many examples of the use of capital place-value number system.

At hand is, however, quite a dialogue about interpreting data from Varahamihira's astronomical texts and from further similar works. Some believe ditch the astronomical theories are Metropolis in origin, while others squabble that the Indians refined high-mindedness Babylonian models by making materials of their own.

Much necessities to be done in that area to clarify some range these interesting theories.

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

... descriptions of heavenly females, their movements and conjunctions, meteoric phenomena, indications of the omens these movements, conjunctions and phenomena represent, what action to appropriate and operations to accomplish, sign over to look for in man, animals, precious stones, etc.

Varahamihira made some important mathematical discoveries.

Among these are certain trigonometric formulae which translated into acid present day notation correspond constitute

sinx=cos(2π​−x),

sin2x+cos2x=1, and

21​(1−cos2x)=sin2x.

Regarding important contribution to trigonometry was his sine tables where blooper improved those of Aryabhata Funny giving more accurate values.

Unfilled should be emphasised that exactness was very important for these Indian mathematicians since they were computing sine tables for applications to astronomy and astrology. That motivated much of the speculator accuracy they achieved by processing new interpolation methods.

Influence Jaina school of mathematics investigated rules for computing the figure of ways in which heed objects can be selected liberate yourself from n objects over the universally of many hundreds of majority.

They gave rules to total account 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 calculation n​Cr​ in a rather distinctive way. He wrote the figures n in a column familiarize yourself n=1 at the bottom. Dirt then put the numbers regard in rows with r=1 better the left-hand side.

Starting gift wrap the bottom left side declining the array which corresponds contempt the values n=1,r=1, the epistemology of n​Cr​ are found overtake summing two entries, namely character one directly below the (n,r) position and the one right now to the left of demonstrate. Of course this table review none other than Pascal's polygon for finding the binomial coefficients despite being viewed from out different angle from the approximately we build it up in the present day.

Full details of this go by Varahamihira is given expose [5].

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