Science for a gracious woman

«A particle of tuition conveys a science to a comprehensive mind: and having reached it, expands of its own impulse. As oil poured on water, as a secret entrusted to the vile, as alms bestowed upon the worthy, however little, so does science infused into a wise mind spread by intrinsic force

– Bhaskara

 

Bhaskaracharya (1114-1185), also known as Bhaskara II, son of a famous astrologer, Mahesvara, was born in Akaria (Vijayapura, India).

Bhaskaracharya contributed for a greater understanding of number systems and advanced methods of equation solving, particularly, the formula of quadratic equation.

His concept of differential calculus predates Newton and Leibniz by half a millennium.

He was able to accurately calculate the sidereal year, the time it takes for the earth to orbit the sun: there is but a scant difference in his figure of 365.2588 days and the modern figure of 365.2596 days.

His main work, “Siddhanta Siromani” (Sanskrit for “Crown Jewel of Accuracy”), written in the year of 1150 A.D., was divided into four sections:
– Lilavati (“Gracious”) – on arithmetics;
– Bijaganita (“Seed counting”) – on algebra;
– Goladhyaya (“Celestial globe”);
– Grahaganita (“Mathematics of the planets”).

Līlāvatī means “gracious woman” (from Sanskrit लीलावती, Līlā = gracious, -vatī = female possessing the quality). 

Many of the arithmetical problems are addressed to Līlāvatī. For example:

«Oh Līlāvatī, intelligent girl, if you understand addition and subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10, and 100, as well as [the remainder of] those when subtracted from 10000.» 

«Fawn-eyed child Līlāvatī, tell me, how much is the number [resulting from] 135 multiplied by 12, if you understand multiplication by separate parts and by separate digits. And tell [me], beautiful one, how much is that product divided by the same multiplier?»

«Whilst making love a necklace broke.
A row of pearls mislaid.
One sixth fell to the floor.
One fifth upon the bed.
The young woman saved one third of them.
One tenth were caught by her lover.
If six pearls remained upon the string
How many pearls were there altogether?» (*)

Bhaskaracharya’s conclusion to “Lilavati” states:

«Joy and happiness is indeed ever increasing in this world for those who have Lilavati clasped to their throats, decorated as the members are with neat reduction of fractions, multiplication and involution, pure and perfect as are the solutions, and tasteful as is the speech which is exemplified.»

 

(*) Resolution:

1/6 x + 1/5 x + 1/3 x + 1/10 x + 6 = x

5/30 x + 6/30 x + 10/30 x + 3/30 x – 30/30 x + 6 = 0

– 6/30 x + 6 = 0

x = 30

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