Friday, December 13, 2013

Great Indian Scientists

Indian scientists have played a stellar role in the development of India. In the short span of its post-independence history India has achieved several great scientific achievements. Indian scientists have proved their mettle in the face of international sanctions and have made India one of the scientific powerhouses of the world. Here is a brief profile of famous Indian scientists.

Bhaskara II (Born 1114 A.D.in Biddur, Died c.1185, probably Ujjain India)
Bhaskara(Bhaskaracharya) is the most celebrated mathematician of ancient India.
Born in 1114 A.D. at Vijjadavida (Bijapur, Karnataka), Baskara was the first to say that any number divided by zero is infinity, and the sum of infinity and any number is also infinity. His most famous work is Siddhanta Siromani,  which is divided into four sections, namely, Leelavati (a book on arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere -celestial globe), and Grahaganita (mathematics of the planets).
Bhaskara, also known as the father of differential calculus, formulated chakrawal, or the cyclic method, to resolve algebraic equations. 600 years later, European mathematicians such as Lagrange, Galois and Euler revived this method and called it ‘inverse cyclic’.
In the field of astronomy, Bhaskara is well known for his concept of instantaneous motion (Tatkalikagati).

Bhāskara II, also called Bhāskarācārya, or Bhaskara The Learned    (born 1114, Biddur, India—died c.1185, probably Ujjain), the leading mathematician of the 12th century, who wrote the first work with full and systematic use of the decimal number system.
Bhāskara II was the lineal successor of the noted Indian mathematician Brahmagupta (598–c. 665) as head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India.
In his mathematical works, particularly Līlāvatī (“The Beautiful”) and Bījagaita (“Seed Counting”), he not only used the decimal system but also compiled problems from Brahmagupta and others. He filled many of the gaps in Brahmagupta’s work, especially in obtaining a general solution to the Pell equation(x2 = 1 + py2) and in giving many particular solutions. Bhāskara II anticipated the modern convention of signs (minus by minus makes plus, minus by plus makes minus) and evidently was the first to gain some understanding of the meaning of division by zero, for he specifically stated that the value of 3/0 is an infinite quantity, though his understanding seems to have been limited, for he also stated wrongly that a0 × 0 = a. Bhāskara II used letters to represent unknown quantities, much as in modern algebra, and solved indeterminate equations of 1st and 2nd degrees. He reduced quadratic equations to a single type and solved them and investigated regular polygons up to those having 384 sides, thus obtaining a good approximate value of π = 3.141666.
In other of his works, notably Siddhāntaśiromai (“Head Jewel of Accuracy”) and Karaakutūhala(“Calculation of Astronomical Wonders”), he wrote on his astronomical observations of planetary positions, conjunctions, eclipses, cosmography, geography, and the mathematical techniques and astronomical equipment used in these studies. Bhāskara II was also a noted astrologer, and tradition has it that he named his first work, Līlāvatī, after his daughter in order to console her. His astrological meddling coupled with an unfortunate twist of fate is said to have deprived her of her only chance for marriage and happiness.

was an Indian mathematician who wrote the Aryabhatiya which summarises Hindu mathematics up to that 6th Century.

Aryabhatta   (Born  476 A.D, Died 550 A.D)
Influence of Aryabhatta on science and mathematics
Aryabhatta is considered to be one of the mathematicians who changed the course of mathematics and astronomy to a great extent. He is known to have considerable influence on Arabic science world too, where he is referred to as Arjehir. His notable contributions to the world of science and mathematics includes the theory that the earth rotates on its axis, explanations of the solar and lunar eclipses, solving of quadratic equations, place value system with zero, and approximation of pie (π).
Aryabhatta worked out the value of pi.
He worked out the area of a triangle. His exact words were, “ribhujasya phalashariram samadalakoti bhujardhasamvargah” which translates “for a triangle, the result of a perpendicular with the half side is the area”.
He worked on the summation of series of squares and cubes (square-root and cube-root).
He talks about the “rule of three” which is to find the value of x when three numbers a, b and c is given.
Aryabhatta calculates the volume of a sphere.
Aryabhatta described the model of the solar system, where the sun and moon are each carried by epicycles that in turn revolve around the Earth. He also talks about the number of rotations of the earth, describes that the earth rotating on its axis, the order of the planets in terms of distance from earth.
Aryabhatta describes the solar and lunar eclipses scientifically.
Aryabhatta describes that the moon and planets shine by light reflected from the sun.
Aryabhatta calculated the sidereal rotation which is the rotation of the earth with respect to the stars as 23 hours, 56 minutes and 4.1 seconds.
He calculated the length of the sidereal year as 365 days, 6 hours, 12 minutes and 30 seconds. The actual value shows that his calculations was an error of 3 minutes and 20 seconds over a year.
Indian scientists have played a stellar role in the development of India. In the short span of its post-independence history India has achieved several great scientific achievements. Indian scientists have proved their mettle in the face of international sanctions and have made India one of the scientific powerhouses of the world. Here is a brief profile of famous Indian scientists.

Aryabhata II. (950 and 1100.)
Essentially nothing is known of the life of Aryabhata II. Historians have argued about his date and have come up with many different theories. In [1] Pingree gives the date for his main publications as being between 950 and 1100. This is deduced from the usual arguments such as which authors Aryabhata II refers to and which refer to him. G R Kaye argued in 1910 that Aryabhata II lived before al-Biruni but Datta [2] in 1926 showed that these dates were too early.

The article argues for a date of about 950 for Aryabhata II's main work, the Mahasiddhanta, but R Billiard has proposed a date for Aryabhata II in the sixteenth century. Most modern historians, however, consider the most likely dates for his main work as around 950 and we have given very approximate dates for his birth and death based on this hypothesis. See [7] for a fairly recent discussion of this topic.

The most famous work by Aryabhata II is the Mahasiddhanta which consists of eighteen chapters. The treatise is written in Sanskrit verse and the first twelve chapters form a treatise on mathematical astronomy covering the usual topics that Indian mathematicians worked on during this period. The topics included in these twelve chapters are: the longitudes of the planets, eclipses of the sun and moon, the projection of eclipses, the lunar crescent, the rising and setting of the planets, conjunctions of the planets with each other and with the stars.

The remaining six chapters of the Mahasiddhanta form a separate part entitled On the sphere. It discusses topics such as geometry, geography and algebra with applications to the longitudes of the planets.

In Mahasiddhanta Aryabhata II gives in about twenty verses detailed rules to solve the indeterminate equation: by = ax + c. The rules apply in a number of different cases such as when c is positive, when c is negative, when the number of the quotients of the mutual divisions is even, when this number of quotients is odd, etc. Details of Aryabhata II's method are given in [6].

Aryabhata II also gave a method to calculate the cube root of a number, but his method was not new, being based on that given many years earlier by Aryabhata I, see for example [5].

Aryabhata II constructed a sine table correct up to five decimal places when measured in decimal parts of the radius, see [4]. Indian mathematicians were very interested in giving accurate sine tables since they were used to calculate the planetary positions as accurately as possible.

Article by: J J O'Connor and E F Robertson

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Subrahmanyan Chandrasekhar
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Anil Kakodkar
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Birbal Sahni
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