ARYABHATTA:
Aryabhatta contibution in the field of mathematics was not limited to any single field ,but provided a best base for the modern maths to take platform
He gave out studies on trigonometry,algebra,geometry,discovered zero and lot of stuff , can be listed as under..
Aryabhata also wrote the Arya Siddhanta, which is now lost. Aryabhata's contributions include:
1।Trigonometry:
a.Introduced the trigonometric functions
b.Defined the sine (jya) as the modern relationship between half an angle and half a chord
c.Defined the cosine (kojya)
d.Defined the versine (utkrama-jya)
e.Defined the inverse sine (otkram jya)
f.Gave methods of calculating their approximate numerical values
g.Contains the earliest tables of sine, cosine and versine values, in 3।75° intervals from 0° to 90°, to 4 decimal places
h.Contains the trigonometric formula
sin (n + 1) x - sin nx = sin nx - sin (n - 1) x - (1/225)sin nx
i.Spherical trigonometry
b.Defined the sine (jya) as the modern relationship between half an angle and half a chord
c.Defined the cosine (kojya)
d.Defined the versine (utkrama-jya)
e.Defined the inverse sine (otkram jya)
f.Gave methods of calculating their approximate numerical values
g.Contains the earliest tables of sine, cosine and versine values, in 3।75° intervals from 0° to 90°, to 4 decimal places
h.Contains the trigonometric formula
sin (n + 1) x - sin nx = sin nx - sin (n - 1) x - (1/225)sin nx
i.Spherical trigonometry
2.Arithmetic:
a.Continued fractions।
a.Continued fractions।
3.Algebra:
a.Solutions of simultaneous quadratic equations
b.Whole number solutions of linear equations by a method equivalent to modern method
a.Solutions of simultaneous quadratic equations
b.Whole number solutions of linear equations by a method equivalent to modern method
c.General solution of the indeterminate linear equation
4।Mathematical astronomy:
a.Proposed for the first time, a heliocentric solar system with the planets spinning on their axes and following an elliptical orbit around the Sun
a.Proposed for the first time, a heliocentric solar system with the planets spinning on their axes and following an elliptical orbit around the Sun
5. Accurate calculations for astronomical constants, such as the:
a.solar eclipse.
b.Lunar eclipse.
a.solar eclipse.
b.Lunar eclipse.
6.The formula for the sum of the cubes, which was an important step in the development of
7.integral calculus
8.Calculus:
9.Infinitesimals:
a.In the course of developing a precise mapping of the lunar eclipse, Aryabhatta was obliged to introduce the concept of infinitesimals (tatkalika gati) to designate the near instantaneous motion of the moon.
a.In the course of developing a precise mapping of the lunar eclipse, Aryabhatta was obliged to introduce the concept of infinitesimals (tatkalika gati) to designate the near instantaneous motion of the moon.
10.Differential equations:
a. He expressed the near instantaneous motion of the moon in the form of a basic differential equation.
11. Exponential function:
He used the exponential function e in his differential equation of the near instantaneous motion of the moon
Thus he not only worked for the global mathematics but also for the universal mathematics
He used the exponential function e in his differential equation of the near instantaneous motion of the moon
Thus he not only worked for the global mathematics but also for the universal mathematics
THIS IS JUST A SMALL INSTANCE OF THE THE DISCOVERY AND INVENTIONS DONE BY THE INDIAN MATHEMATICIAN WHICH HAS BEEN FORGOTTEN BY THE WORLD !!!!!
