# Archive for April 7th, 2008

## India n its contribution towards Mathematics!

The concept of zero also originated in ancient India. It is derived from the concept of a void. The concept of void existed in Hindu Philosophy – hence the derivation of a symbol for it.

In India, mathematics has its roots in Vedic literature which is nearly 4000 years old. Between 1000 B.C. and 1000 A.D. various treatises on mathematics were authored by Indian mathematicians in which were set forth for the first time, the concept of zero, the techniques of algebra and algorithm, square root and cube root.

A method of graduated calculation was documented in the Pancha-Siddhantika (Five Principles) in the 5th Century. But the technique is said to be dating from Vedic times circa 2000 B.C.

The rudiments of Geometry called Rekha-Ganita in ancient India – were formulated and applied in the drafting of Mandalas for architectural purposes.

They were also displayed in the geometric patterns used in many temple motifs.(adj fig)

The technique of calculation, called algorithm, which is today widely used in designing soft ware programs (instructions) for computers was also derived from Indian mathematics. In this chapter we shall examine the advances made by Indian mathematicians in ancient times.

In India around the 5th century A.D. a sys tem of mathematics that made astronomical calculations easy was developed. In those times its application was limited to astronomy as its pioneers were Astronomers. As tronomical calculations are complex and involve many variables that go into the derivation of unknown quantities. Algebra is a short-hand method of calculation and by this feature it scores over conventional arithmetic.

In ancient India conventional mathematics termed Ganitam was known before the development of algebra. This is borne out by the name – Bijaganitam, which was given to the algebraic form of computation.

Bijaganitam means *the other mathematics* (Bija means ‘another’ or ‘second’ and Ganitam means mathematics).

The fact that this name was chosen for this system of computation implies that it was recognized as a parallel system of computation, different from the conventional one which was used since the past and was till then the only one.

Some have interpreted the term Bija to mean seed, symbolizing origin or beginning. And the inference that Bijaganitam was the original form of computation is derived.

Credence is lent to this view by the existence of mathematics in the Vedic literature which was also shorthand method of computation.

But whatever the origin of algebra, it is certain that this technique of computation originated in India and was current around 1500 years back.

Aryabhatta an Indian mathematician who lived in the 5th century A.D. has referred to Bijaganitam in his treatise on Mathematics, Aryabhattiya.

An Indian mathematician – astronomer, Bhaskaracharya has also authored a treatise on this subject. [more…]

The Concept of Zero or Shunya

The concept of zero also originated in ancient India. It is derived from the concept of a void. The concept of void existed in Hindu Philosophy – hence the derivation of a symbol for it.

The concept of Shunyata, influenced South-east asian culture through the Buddhist concept of Nirvana ‘attaining salvation by merging into the void of eternity’

A concept and symbol that connotes nullity represents a qualitative advancement of the human capacity of abstraction. In absence of a concept of zero there could have been only positive numerals in computation, the inclusion of zero in mathematics opened up a new dimension of negative numerals and gave a cut off point and a standard in the measurability of qualities whose extremes are as yet unknown to human beings, such as temperature.

In ancient India this numeral was used in computation, it was indicated by a dot and was termed Pujyam. Even today we use this term for zero along with the more current term Shunyam meaning a blank. But queerly the term Pujyam also means holy. Param-Pujya is a prefix used in written communication with elders. In this case it means respected or esteemed. The reason why the term Pujya – meaning blank – came to be sanctified can only be guessed.

Indian philosophy has glorified concepts like the material world being an illusion Maya), the act of renouncing the material world (Tyaga) and the goal of merging into the void of eternity (Nirvana). Herein could lie the reason how the mathematical concept of zero got a philosophical connotation of reverence.

It is possible that like the technique of algebra; the concept of zero also reached the west through the Arabs. In ancient India the terms used to describe zero included Pujyam, Shunyam, Bindu the concept of a void or blank was termed as Shukla and Shubra. The Arabs refer to the zero as Siphra or Sifr from which we have the English terms Cipher or Cypher. In English the term Cipher connotes zero or any Arabic numeral. Thus it is evident that the term Cipher is derived from the Arabic Sifr which in turn is quite close to the Sanskrit term Shubra.[more…]

Extracted from :Crystalinks

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