2. Also Listed In : Mathematicians ,Astronomers
Nationality : Indian , Famous Indian Men
Born : 476 AD
Born In : Assaka, Patna, Bihar
Religion : Hinduism
Died At Age : 74
Died On : 550 AD
3. Aryabhata was an acclaimed mathematician astronomer. He was born in
Kusumapura [present day in Patna] in Bihar, India. His contribution to
mathematics, science and astronomy is immense, and yet he has not been
accorded the recognition in the world history of science. At the age of 24, he
wrote his famed “Aryabhatiya”. He was aware of the concept of zero, as well as
the use of large numbers up to 1018.
He was the first known astronomer to devise a continuous counting of solar
days, designating each day with a number. He asserted that the planets shine
due to the reflection of sunlight, and that the eclipses occur due to the shadows
of moon and earth. His observations discount the “flat earth” concept, and lay
the foundation for the belief that earth and other planets orbit the sun.
4. Major Works
Aryabhata’s major work is Aryabhatiya, a compendium of
mathematics and astronomy, was extensively referred to in
the Indian mathematical literature, and has survived to
modern times. The Aryabhatiya covers arithmetic, algebra,
and trigonometry.
5. Contribution to mathematics
Place value system and zero:
The place-value system, first seen in the 3rd-
century Bakhshali Manuscript, was clearly in place in his work.
While he did not use a symbol for zero, the French mathematician
Georges Ifrah argues that knowledge of zero was implicit in
Aryabhata's place-value system as a place holder for the powers
of ten with null coefficients.
6. Value of pi
He also worked on the approximation for pi , and may have come
to the conclusion that pi is irrational. In the second part of the
Aryabhatiyam (gaṇitapāda 10), he writes:
caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām
ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ.
"Add four to 100, multiply by eight, and then add 62,000. By this
rule the circumference of a circle with a diameter of 20,000 can be
approached."
This implies that the ratio of the circumference to the diameter is
((4 + 100) × 8 + 62000)/20000 = 62832/20000 = 3.1416, which is
accurate to five significant figures.
7. Trigonometry
He gave the area of a triangle as:
tribhujasya phalashariram samadalakoti bhujardhasamvargah
that translates to: "for a triangle, the result of a perpendicular with
the half-side is the area.“
He also discussed the concept of sine in his work by the name
of ardha-jya, which literally means "half-chord".
Sine Table: Aryabhatta gave a table of sines for calculating the
approximate values at intervals of 90/24 = 3 45’. This was done
using the formula for
sin (n+1)x - sin nx in terms of sin nx and sin (n-1) x.
Versine: He introduced the versine (versin = 1-cosine) into
trigonometry.
8. Algebra
In Aryabhatiya, he provided elegant results for the summation of
series of squares and cubes
Integer solutions: Aryabhatta was the first one to explore integer
solutions to the equations of the form by =ax+c and by =ax-c,
where a,b,c are integers. He used kuttuka method to solve
problems.
Indeterminate equations: He gave general solutions to linear
indeterminate equations ax+by+c= 0 by the method of continued
fraction.
Identities: He had dealt with identities like (a+b)2=a2+2ab+b2and
ab={(a+b)2-(a2-b2)}/2
9. He has given the following formula in Aryabhatiya
12+22+32+---------+n2=n(n+1)(2n+1)/6
13+23+33+---------+n3 = (1+2+3+------------+)2= {n2(n+1)2}/4
Algebraic quantities: He has given the method of addition,
subtraction, multiplication of simple and compound algebraic
quantities
Arithmetic series: He was given a formula for summing up of
the arithmetic series after the Pth term The rule is S= n[a+{(n-
1)/2+p} d]
S=(a+1) n/2
