He wrote the Katyayana Sulba Sutra, which presented much geometryincluding the general Pythagorean theorem and a computation of the square root of 2 correct to five decimal places. Jain mathematicians are important historically as crucial links between the mathematics of the Vedic period and that of the "classical period. In particular, their fascination with the enumeration of very large numbers and infinities led them to classify numbers into three classes: Not content with a simple notion of infinity, they went on to define five different types of infinity:
Miscellaneous Articles History of Mathematics in India In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems.
Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols as in India or were designated by alphabetic letters such as in Rome.
Although today, we take our decimal system for granted, not all ancient civilizations based their numbers on a ten-base system. In ancient Babylon, a sexagesimal base 60 system was in use.
The Decimal System in Harappa In India a decimal system was already in place during the Harappan period, as indicated by an analysis of Harappan weights and measures.
Weights corresponding to ratios of 0. A particularly notable characteristic of Harappan weights and measures is their remarkable accuracy. A bronze rod marked in units of 0. Such scales were particularly important in ensuring proper implementation of town planning rules that required roads of fixed widths to run at right angles to each other, for drains to be constructed of precise measurements, and for homes to be constructed according to specified guidelines.
The existence of a gradated system of accurately marked weights points to the development of trade and commerce in Harappan society. Mathematical Activity in the Vedic Period In the Vedic period, records of mathematical activity are mostly to be found in Vedic texts associated with ritual activities.
However, as in many other early agricultural civilizations, the study of arithmetic and geometry was also impelled by secular considerations. Thus, to some extent early mathematical developments in India mirrored the developments in Egypt, Babylon and China. The system of land grants and agricultural tax assessments required accurate measurement of cultivated areas.
As land was redistributed or consolidated, problems of mensuration came up that required solutions. In order to ensure that all cultivators had equivalent amounts of irrigated and non-irrigated lands and tracts of equivalent fertility - individual farmers in a village often had their holdings broken up in several parcels to ensure fairness.
Since plots could not all be of the same shape - local administrators were required to convert rectangular plots or triangular plots to squares of equivalent sizes and so on.
Tax assessments were based on fixed proportions of annual or seasonal crop incomes, but could be adjusted upwards or downwards based on a variety of factors.
This meant that an understanding of geometry and arithmetic was virtually essential for revenue administrators. Mathematics was thus brought into the service of both the secular and the ritual domains.
Arithmetic operations Ganit such as addition, subtraction, multiplication, fractions, squares, cubes and roots are enumerated in the Narad Vishnu Purana attributed to Ved Vyas pre BC. Examples of geometric knowledge rekha-ganit are to be found in the Sulva-Sutras of Baudhayana BC and Apasthmaba BC which describe techniques for the construction of ritual altars in use during the Vedic era.
It is likely that these texts tapped geometric knowledge that may have been acquired much earlier, possibly in the Harappan period.
Baudhayana's Sutra displays an understanding of basic geometric shapes and techniques of converting one geometric shape such as a rectangle to another of equivalent or multiple, or fractional area such as a square.
While some of the formulations are approximations, others are accurate and reveal a certain degree of practical ingenuity as well as some theoretical understanding of basic geometric principles. Modern methods of multiplication and addition probably emerged from the techniques described in the Sulva-Sutras.
Pythagoras - the Greek mathematician and philosopher who lived in the 6th C B. C was familiar with the Upanishads and learnt his basic geometry from the Sulva Sutras.
An early statement of what is commonly known as the Pythagoras theorem is to be found in Baudhayana's Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size.
A similar observation pertaining to oblongs is also noted. His Sutra also contains geometric solutions of a linear equation in a single unknown. Examples of quadratic equations also appear. Apasthamba's sutra an expansion of Baudhayana's with several original contributions provides a value for the square root of 2 that is accurate to the fifth decimal place.
Apasthamba also looked at the problems of squaring a circle, dividing a segment into seven equal parts, and a solution to the general linear equation.
Modern-day commentators are divided on how some of the results were generated. Some believe that these results came about through hit and trial - as rules of thumb, or as generalizations of observed examples.
Others believe that once the scientific method came to be formalized in the Nyaya-Sutras - proofs for such results must have been provided, but these have either been lost or destroyed, or else were transmitted orally through the Gurukul system, and only the final results were tabulated in the texts.
In any case, the study of Ganit i. The Vedang Jyotish BC includes the statement: Panini and Formal Scientific Notation A particularly important development in the history of Indian science that was to have a profound impact on all mathematical treatises that followed was the pioneering work by Panini 6th C BC in the field of Sanskrit grammar and linguistics.
Besides expounding a comprehensive and scientific theory of phonetics, phonology and morphology, Panini provided formal production rules and definitions describing Sanskrit grammar in his treatise called Asthadhyayi.Introduction: Mathematics is an indispensable subject of yunusemremert.com plays an important role in forming the basis of all other sciences which deal with the material substance of space and time.
What is the meaning of Mathematics? Srinivasa Ramanujan, (born December 22, , Erode, India—died April 26, , Kumbakonam), Indian mathematician whose contributions to the theory of numbers include pioneering discoveries of the properties of the partition function.
History of Mathematics in India In all early civilizations, the first expression of mathematical understanding appears in the form of counting systems. Numbers in very early societies were typically represented by groups of lines, though later different numbers came to be assigned specific numeral names and symbols (as in India) or were.
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MATHEMATICS IN INDIA The history of maths in india is very great & yunusemremert.coms gave the system of numerals, zero, geometry & equations to the world. India was the mother of our philosophy, of much of our mathematics, of the ideals embodied in Christianity of self-government and democracy.
In many ways, Mother India is the mother of us all.” – Will Durant, American Historian The picture is not yet complete, and it seems that there is much work to do in the field of the history of Indian mathematics.
The challenges are two-fold. First, there is the task of locating and identifying manuscripts and of translating them into a language that is more familiar to modern scholars.