VEDIC MATHS ---THE FORGOTTEN PAST - 3

  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

2.Arithmetic:
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

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

5. Accurate calculations for astronomical constants, such as the:
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.

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

THIS IS JUST A SMALL INSTANCE OF THE THE DISCOVERY AND INVENTIONS DONE BY THE INDIAN MATHEMATICIAN WHICH HAS BEEN FORGOTTEN BY THE WORLD !!!!!

VEDIC MATHS --- THE FORGOTTEN PAST -2

There were several theories which were discussed by the indian astronomers beforehand and were used as the base for the Modern Maths which includes the "pythagorans theorem"
BAUDHAYANA:

Baudhayana (c. 8th century BCE) composed the Baudhayana Sulba Sutra, the best-known Sulba Sutra, which contains examples of simple Pythagorean triples, such as: (3,4,5), (5,12,13), (8,15,17), (7,24,25), and (12,35,37)[28] as well as a statement of the Pythagorean theorem for the sides of a square: "The rope which is stretched across the diagonal of a square produces an area double the size of the original square." It also contains the general statement of the Pythagorean theorem (for the sides of a rectangle): "The rope stretched along the length of the diagonal of a rectangle makes an area which the vertical and horizontal sides make together." Baudhayana gives a formula for the square root of two,

The formula is accurate up to five decimal places
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BRAHMAGUPTA :




THEORY:


Brahmagupta's theorem states that AF = FD.

In the seventh century, two separate fields, arithmetic (which included mensuration) and algebra, began to emerge in Indian mathematics. The two fields would later be called pāṭī-gaṇita (literally "mathematics of algorithms") and bīja-gaṇita (lit. "mathematics of seeds," with "seeds"—like the seeds of plants—representing unknowns with the potential to generate, in this case, the solutions of equations). Brahmagupta, in his astronomical work Brāhma Sphuṭa Siddhānta (628 CE), devoted to these fields. Chapters, containing 66 Sanskrit verses, was divided into two sections: "basic operations" (including cube roots, fractions, ratio and proportion, and barter) and "practical mathematics" (including mixture, mathematical series, plane figures, stacking bricks, sawing of timber, and piling of grain). In the latter section, he stated his famous theorem on the diagonals of a cyclic quadrilateral:

Brahmagupta's theorem: If a cyclic quadrilateral has diagonals that are perpendicular to each other, then the perpendicular line drawn from the point of intersection of the diagonals to any side of the quadrilateral always bisects the opposite side.

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VEDIC MATHS --- THE FORGOTTEN PAST-1

वेदिक गणीत

Everyone must be thinking tat wat the heck this "VEDIC MATHEMATICS" is!!!!, most of you dont even know abt the research work done by the Saints and philosophers of the Ancient India.
You must all be knowing abt the "Aristotle" works and "Phytagorain's theorems" or research paper provided by the great "Eienstien","Galileo galilie","Sir Iscass Newton" but how many of you know abt the "RAMANUJAN","BHRAMAGUPTA","BHASKARA-I","BHASKARA-II","Varahamihira","Surya Siddhanta ","Shripati Mishra" and the most important research work done in field of matheatics by "AARYABHATTA". I am sure very few of you know abt the research work done by them.

Prehistory:
Excavations at Harappa, Mohenjo-daro and other sites of the Indus Valley Civilization have uncovered evidence of the use of "practical mathematics". The people of the IVC manufactured bricks whose dimensions were in the proportion 4:2:1, considered favorable for the stability of a brick structure. They used a standardized system of weights based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, with the unit weight equaling approximately 28 grams (and approximately equal to the English ounce or Greek uncia). They mass produced weights in regular geometrical shapes, which included hexahedra, barrels, cones, and cylinders, thereby demonstrating knowledge of basic geometry.
The inhabitants of Indus civilization also tried to standardize measurement of length to a high degree of accuracy. They designed a ruler—the Mohenjo-daro ruler—whose unit of length (approximately 1.32 inches or 3.4 centimetres) was divided into ten equal parts. Bricks manufactured in ancient Mohenjo-daro often had dimensions that were integral multiples of this unit of length.

THE VEDIC PERIOD........

VEDIC MATHEMATICS ,one of the most oldest work in the history of maths started in India before the 400 BCE( the dramatic digit) ,its not only this but before that the whole mathematics was done verbally after the 400BCE the whole vedic mathematics came into existence .Whole of the mathematics was describe verbally before 400 BCE ,so many of the important research were not conserved...........

Describing abt the vedic maths it includes many works like pythagorian theorem, decimal invention, zero.... the biggest invention of all.Many of the geometric theorem came into existence from the analysis of the ancient work provided the base to the modern athematics..

The vedic mathematics was subdivided as per the era's of the time , it divided into two parts
1.Samhitas and Brahmanas
and
2.Śulba Sūtras

by the way not etting too details of the timeline let me introduce you to the extra-ordinary part of the vedic works

The classical mathematics of indian orgin ,important concepts of the decimal numbers were invented in India
The concept of zero came into being withe help of the Sir ARYABHATTA
The ideas of the negative number was originated from the vedic mathematics
Several definition of the cosine and sine were introduced to the modern era using indian classical mathematics......