ARYABHATA - I
Aryabhatta was born in 476A.D in Kusumpur, India. He was the first person to say that Earth is spherical and it revolves around the sun.
He gave the formula (a + b)2 = a2 + b2 + 2ab
He taught the method of solving the following problems:
Brahma Gupta was born in 598A.D in Pakistan.
He gave four methods of multiplication and also he gave the following formula, used in G.P series
a + ar + ar2 + ar3 +……….. + arn-1 = (arn-1) ÷ (r – 1)
He gave the following formulae :
Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s -c)(s- d) where 2s = a + b + c + d Length of its diagonals =
ARYABHATA – II
Essentially nothing is known of the life of Aryabhata II. Historians have argued about his date and have come up with many different theories.
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.
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. .
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.
Aryabhata II constructed a sine table correct up to five decimal places when measured in decimal parts of the radius. Indian mathematicians were very interested in giving accurate sine tables since they were used to calculate the planetary positions as accurately as possible.
He was born in a village of Mysore district. He was the first to give that any number divided by 0 gives infinity (00). He has written a lot about zero, surds, permutation and combination. He wrote, “The hundredth part of the circumference of a circle seems to be straight. Our earth is a big sphere and that’s why it appears to be flat.”
He gave the formulae like sin(A ± B) = sinA.cosB ± cosA.sinB
He was born on 22nd of December 1887 in a small village of Tanjore district. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England.
Ramanujan showed that any big number can be written as sum of not more than four prime numbers. He showed that how to divide the number into two or more squares or cubes.
When Mr Litlewood came to see Ramanujan in taxi number 1729, Ramanujan said that 1729 is the smallest number which can be written in the form of sum of cubes of two numbers in two ways, i.e. 1729 = 93 + 103 = 13 + 123 since then the number 1729 is called Ramanujan’s number.
She was born in 1939. In 1980, she gave the product of two, thirteen digit numbers within 28 seconds, many countries have invited her to demonstrate her extraordinary talent.
In Dallas she competed with a computer to see who give the cube root of 188138517 faster, she won.
At university of USA she was asked to give the 23rd root of 9167486769200391580986609275853801624831066801443086224071265164279346570408670965932792057674808067900227830163549248523803357453169351119035965775473400756818688305 620821016129132845564895780158806771.
She answered in 50seconds. The answer is 546372891. It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions. Now she is known to be Human Computer.