ANCIENT INDIAN ASTRONOMY AND ASTRONOMERS

 VARAHAMIHIRA:

BORN : 505 IN KAPITTHAKA,INDIA

DIED  : 587 IN INDIA.

KNOWN AS THE FATHER OF MODERN INDIAN ASTRONOMY.

HIS MOST FAMOUS WORK WAS PANCHASIDDHANTIKA ( THE FIVE ASTRONOMICAL CANONS ) DATED 575 A.D.

HIS WORK BRIHATSAMHITA ( THE GREAT COMPILATION ) HAS DESCRIPTIONS OF HEAVENLY BODIES,THEIR MOVEMENTS AND CONJUNCTIONS, METEOROLOGICAL PHENOMENA.

HE MADE SOME IMPORTANT MATHEMATICAL DISCOVERIES.AMONG THESE ARE CERTAIN TRIGNOMETRIC FORMULAE LIKE

                                                                sinx=cos[pi/2 -x]

                                                                sin^2 x + cos^2 x=1

                                                                (1-cos2x)/2=sin^2 x.

ANOTHER IMPORTANT CONTRIBUTION TO TRIGNOMETRY WAS HIS SINE TABLES WHERE HE IMPROVED THOSE OF ARYABHATTA1 GIVING MORE ACCURATE VALUES.ACCURACY WAS VERY IMPORTANT FOR THESE INDIAN MATHEMATICIANS SINCE THEY WERE COMPUTING SINE TABLES FOR APPLICATIONS TO ASTRONOMY AND ASTROLOGY.

IN ONE OF HIS TREATISES NAMED ROMAKA-SIDDHANTA HE HAD GIVEN EPICYCLE THEORY OF THE MOTIONS OF THE SUN AND THE MOON WHICH WERE BASED ON THE GREEKS WORKS.

THE PANCASIDDHANTIKA ALSO CONTAINS MANY EXAMPLES OF THE USE OF A PLACE-VALUE NUMBER SYSTEM.

VARAHAMIHIRA ALSO HAD WORKED ON MAGIC SQUARES.

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ANCIENT INDIAN ASTRONOMY AND ASTRONOMERS:

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BRAHMAGUPTA:
          HE WAS BORN AT BHINMAL,GUJARAT,IN 598 A.D.HE BECAME COURT ASTRONOMER TO KING VYAGHRAMUKHA OF CHAPA DYNASTY.  

          HE WAS ONE OF THE GREAT INDIAN MATHEMATICIANS, WHO FRAMED THE RULES OF OPERATION FOR ZERO.

          HE GAVE A SOLUTION TO INDETERMINATE EQUATIONS OF THE TYPE ax^2+1=y^2 AND WAS THE FOUNDER OF BRANCH OF HIGHER MATHEMATICS CALLED NUMERICAL ANALYSIS.

YOUNG  BRAHMAGUPTA

BRAHMAGUPTA THEOREM

           BHASKARA, ANOTHER GREAT MATHEMATICIAN OF INDIA,GAVE HIM THE TITLE GANAKACHAKRACHUDAMANI( THE GEM OF CIRCLE OF MATHEMATICS).

           HIS TWO TREATISES ('AARAICHI KATTURAIGAL' IN TAMIL) WERE (1) BRAHMASPHUTASIDDHANTA AND (2) KARANAKHANDAKHADYAKA  .

            HE SAID ADDITION OR SUBTRACTION OF ZERO,NEGATIVE OR POSITIVE DOES NOT AFFECT ZERO.PRODUCT OF ANY QUANITY BY ZERO IS ZERO,BUT DIVISION OF ANY QUANTITY BY ZERO IS INFINITY.

            HE ALSO FRAMED THE RULES TO SOLVE A SIMPLE EQUATION OF THE TYPE ax+b=0 AND A QUADRATIC EQUATION OF THE TYPE ax^2+bx+c=0  AS WELL AS TO SUM UP THE GEOMETRIC SERIES.

             HE WAS THE FIRST MATHEMATICIAN TO DIFFERENTIATE BETWEEN ALGEBRA AND ARITHMETIC AS TWO SEPARATE BRANCHES OF MATHEMATICS IN HIS 1ST TREATISE.

             IN HIS 2ND TREATISE HE HAD EFFECTIVELY USED ALGEBRA FOR ASTRONOMICAL CALCULATIONS.

             HE BELIEVED THAT EARTH WAS ROUND.

             HE SAID ABOUT GRAVITY:BODIES FALL TOWARDS THE EARTH.

            
         

ANCIENT INDIAN ASTRONOMY AND ASTRONOMERS

THE SURYA SIDDHANTA:

 A TEXT BOOK ON ASTRONOMY OF ANCIENT INDIA, SHOWED THAT EARTH'S DIAMETER TO BE 7840 MILES, COMPARED TO MODERN MEASUREMENTS OF 7926.7 MILES. 

BRAHMAGUPTA

MADHAVACHARYA

ALSO IN THAT BOOK IT WAS SHOWED THAT THE DISTANCE BETWEEN THE EARTH AND MOON AS 253,000 MILES, COMPARED TO THE MODERN MEASUREMENTS OF 252,710 MILES.

ARYABHATTA