Knowledge is ever expanding and never stagnant like the pond water, it is all pervading like a meandering river. Knowledge is supreme energy. Such an energy is ever lasting. Today we look around us the marvels of science and the achievements of great scientists. All these scientists-converted-philosophers have felt that this energy has to be used to establish peace in the world. The lives of Indian scientists have established this fact and as much as they contributed for science experiments, they have also contributed to the discrimination of knowledge of non-violence, religion, God etc., among the common folk.
Scientific temperament originated nearly 5000 years ago. Ramayana and Mahabharata have established, beyond doubts, among their readers as to how far India has achieved scientific marvels very much earlier to the birth of real scientific temperament. These scientists never cease to work till they reach their goal or procure the scientific truth. Scientists and their inventions cannot be numbered. Our scientists have contributed their mite not only in the field of Physics, Chemistry, Biology and Mathematics they have made marvelous contributions in applied sciences as well. One such scientist is Bhaskaracharya popularly known as Bhaskara-II. Apart from being a scientist he was also a renowned poet of high caliber. His father was a great learned mathematician known by the name Maheshwaropadhyaya. At the age of 36, Bhaskara wrote a mammoth work entitled "Siddhantha Shiromani". This work is of four volumes. They are as listed below:
- "Lilavati" or "Mathematics of Lilavati"
- Algebra
- Planetary motions
- Astronomy
HISTORY BEHIND LILAVATI
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LILAVATI |
Though not much is about
Bhaskaracharya's personal life, it is said that he had a son by name Lakshmidhara who was an
intelligent mathematician. It is also believed that Bhaskara had a daughter by name
Lilavati from the mention made by this name in his famous work "Anka Ganitha".
Bhaskara learns from the horoscope of his daughter that she might become a
widow after her marriage. With the parental compassion and responsibilities,
Bhaskara thought of certain ways and means by which the state of widow-hood
maybe warded off; he proceeded to select a proper MUHURTHA (fixed time) for the
marriage. But, lo! Where from could he get a watch to know the time to set the
Muhurtha? Bhaskara invented his own KALACHAKRA (time-clock). This clock was a
hydro-wheeled vessel into which a funnel was inserted and the container had to
be filled with a certain amount of sand grains. The mechanism was set into
operation at the time of sunrise and Bhaskara thought when the whole sand of
grains got into the vessel and drain out from the funnel, the time for the
marriage had to be fixed. But, as destiny had it, Lilavati, who was also gazing
the machine, moved a bit away by which her nose-stud slipped into the funnel
and blocked the path for the sand grains to move down into the vessel below. By
this, the time that was awaited for the marriage was an entirely a different
one and Lilavati's widowhood could not be warded off! Lilavati's face had lost its initial charm. She seemed disinterested in the normal day to day activities. She sat by the pond looking into nothingness and wept. She remained silent most of the time. Bhaskara found it very difficult to see these changes in his beautiful daughter. He thought of a way to get her out of her depressed state. He posed arithmetic problems at Lilavati about the things around her and asked her to find solutions to the problems. Lilavati, the brilliant girl that she was, solved all the problems posed to her. Lilavati's mind which was busy in solving the mathematical problems posed by her father, never again got depressed. It is believed that the problems posed to Lilavati form the major portion of Bhaskara's treatise which is named after Lilavati.Though this appears to be a myth but the work of this great scientist leaves us all spellbound.
CONTENTS OF LILAVATI
Lilavati was a collection of what we call as 'Arithmetic' in today's mathematical parlance. It consists of 279 verses in Sanskrit in poetic form. There are certain verses which deal with Mensuration (measurement of various geometrical objects), Volume of pyramid, cylinders, heaps of grains etc., wood cutting, shadows, trigonometric relations and also on certain elements of Algebra such as finding an unknown quantity subject to certain constraints.
MANUSCRIPTS OF LILAVATI
Those interested can actually solve them too :-)
1. Of a of elephants, half and one third of the half went into a cave, one sixth and one seventh of one sixth was drinking water from a river. One eight and one ninth of one eighth were sporting in a pond full of lotuses. The lover king of the elephants was leading three female elephants; how many elephants were there in the flock?
2. Oh! You auspicious girl with enchanting eyes of a fawn, Lilavati. If you have well understood the above methods of multiplication, what is the product of 135 and 12?
Also, tell me what number will you obtain when the product is divided by 12?
Bhaskara concludes Lilavati by saying-
"Joy and happiness in this world shall continually increase for those who hold her kanthasakta, close in their arms or clasped to their bosoms"
courtesy: http://archive.indianexpress.com/news/pearls-of-wisdom/995252/0
Lilavati was a collection of what we call as 'Arithmetic' in today's mathematical parlance. It consists of 279 verses in Sanskrit in poetic form. There are certain verses which deal with Mensuration (measurement of various geometrical objects), Volume of pyramid, cylinders, heaps of grains etc., wood cutting, shadows, trigonometric relations and also on certain elements of Algebra such as finding an unknown quantity subject to certain constraints.
MANUSCRIPTS OF LILAVATI
Those interested can actually solve them too :-)
1. Of a of elephants, half and one third of the half went into a cave, one sixth and one seventh of one sixth was drinking water from a river. One eight and one ninth of one eighth were sporting in a pond full of lotuses. The lover king of the elephants was leading three female elephants; how many elephants were there in the flock?
2. Oh! You auspicious girl with enchanting eyes of a fawn, Lilavati. If you have well understood the above methods of multiplication, what is the product of 135 and 12?
Also, tell me what number will you obtain when the product is divided by 12?
Bhaskara concludes Lilavati by saying-
"Joy and happiness in this world shall continually increase for those who hold her kanthasakta, close in their arms or clasped to their bosoms"
courtesy: http://archive.indianexpress.com/news/pearls-of-wisdom/995252/0
http://www.mlbd.com/BookDecription.aspx?id=1589
image courtsey:http://www.maa.org/publications/periodicals/
convergence/mathematical-treasures-lilavati-of-bhaskara
