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History and Implications including Functionality - Essay Example

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History and Implications including Functionality

Pascal, whose name was subsequently bequeathed to it though Chinese mathematician Yangsui generated it almost 500 years earlier than that. In China it became known as Yangsui's triangle while Persian astronomer-poet Omar Khayyam also studied it in some details.(Mathworld, Pascal's Triangle, 2006) Indian mathematicians like Pingalacharya also knew of it even earlier than the Chinese and all these shall be discussed subsequently together with some of this number triangle's unique properties.
Though not much is known about how Pascal exactly came upon this number triangle it is obvious that since he was well-known as a mathematician, philosopher and religious figure in the France of that time he made it famous. This is one of his lesser-known achievements. He is much better known for his discovery of the constant pressure within a static fluid (Pascal's Principle). (Scienceworld, 2006)
The first known description of a binary numeral system, that ultimately generates the triangle, is to be found in the works of Pingalacharya, the famous circa 5th century B.C. Indian scholar on prosody. He is supposed to be the younger brother of the more famous Sanskrit Grammarian Panini, whose grammar is still considered to provide the basic guidelines for that language. Actually, Pingala was exploring the listing of Vedic meters in short and long syllables when he came upon the system of binary numerals. His discussions of the combinations possible for the meters describes the binomial theorem. His works were later taken up by the 10th century Indian mathematician Halayudha whose commentary presents a form of the Pascal's triangle. It is described as the 'Meru-prastaara', as the rudimentary form of the Pascal's triangle was known then in Sanskrit. Pingala was also the first person to make mention of the Fibonacci Numbers, as they are known now. The paper shall touch upon the Fibonacci numbers later on. In Sanskrit, as Pingala would have it, these numbers were known as 'maatraameru'. (Wikipedia, Pingala, 2006) It is noted here that Indian astronomers and mathematicians were quite advanced in those days and quite a few important concepts such as that of zero, attributed to ...Show more

Summary

where (n, r) is a binomial coefficient which signifies coefficient of the number in the row of the triangle. The number rows can be staggered such that they conform to the shape of a triangle in which each subsequent row is obtained by adding the two numbers diagonally above…
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