*chhanda*. For example, readers familiar with the

*Bhagavad Gita*will recall that in the 10

^{th}chapter, the chapter on

*Vibhuti Yoga*, Lord Sri Krishna calls the

*Gayatri chhanda*as His

*vibhuti*among the

*chhandas*. A commonly found

*chhanda*in Sanskrit is the

*Anushtup chhanda*. For example, the following verse from the

*Bhagavad Gita*is in the

*Anushtup chhanda*:

*upajati chhanda*. Another example, again from the

*Bhagavad Gita*, is

*chhandas*and rhythms are possible. The study of these meters is called prosody. Creating algorithms to classify and arrange these meters, as well as to generate new meters, forms a major part of the work of the Sanskrit prosodists. As a consequence, there are hundreds of Sanskrit

*chhanda*s categorized and classified, while only a dozen or so meters are identified in English poetry. The meters used in Sanskrit poetry often form the base for the corresponding rhythms, and as a result the art of rhythm is developed to such a high degree of sophistication in Indian classical music.

*chhanda sutra*(

*sutra*s on the

*chhanda*). In this treatise, he obtained the result which is today known as the binomial theorem for integral index, which in modern notation is expressed as

Where

*is :*^{n}C_{r}^{n }without calculating

*in Eqn. (1). For example, if we want (*

^{n}C_{r}*x*+

*y*)

^{5}, then we just look at the 5

^{th}row of the

*Meru Prastara*, and the numbers in this row, 1, 5, 10, 10, 5, 1, immediately give us the answer:

*Meru Prastara*.

*Meru*is a mountain which appears frequently in Sanskrit literature.

*Meru Prastara*is called Pascal’s triangle even though it was discovered several centuries earlier.

*Meru Prastara*. If we add these numbers as shown in the figure above, we get the sequence of numbers

*(mentioned in Prakrta Paingala – early 14*:

^{th}century, as mentioned in R. W. Hall’s Math for poets and drummers)
1,1,2,3,5,8,13,...

^{th}century), Gopala (1135), and Hemachandra (1089-1172). In particular, Hemachandra posed the question: “If a long syllable is twice as long as a short syllable, in how many ways can a line of n time units be created?”, and showed that the answer is the n+1th term in the sequence. Thus, due to their precedence in discovery, a more proper name would be the Hemachandra numbers, at least in India.

^{th}century BC. The beauty of Panini’s work, the most famous of which is the

*Ashtadhyayi*, is that its study of grammar is independent of language, and hence several modern day linguists and computer scientists have been deeply influenced by his work. There are deep similarities between Panini’s work and the works of modern day linguists and computer scientists such as Leonard Bloomfield, Zellig Harris, Axel Thue, Emil Post, AlanTuring, Noam Chomsky, and John Backus. In computer science, the notation technique known as the Backus Naur form, which is used by most computer programming languages, was described by Panini around 2,500 years earlier ago. It actually ought to be called the Panini-backus form, as suggested by Peter Zilahy Ingerman [6]. The figure below shows the short article in the communications of the ACM (Association for Computing Machinery):

*(quoted directly from R.W.Hall’s math for pets and drummers).*In many ways Panini was the first computer scientist with the software but without the hardware. The Indian government issued a postal stamp in honor of Panini.

References:

[3]
Rachel W. Hall, Math for poets and drummers

[4]
Being different, Rajiv Malhotra

[5] A. K. Bag, "Binomial theorem in ancient India", Indian Journal of History of Science, 1966. (click here for online access.)

[6] Peter Zilahy Ingerman, "Panini Backus form suggested", Communications of the ACM, 1967. (click here for online access; a subscription will be required for the pdf file.)

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