Sarngadeva was amongst the earliest to develop sophisticated algorithms for combinatorial sequence generation.
In this article we are discussing on Sarngadeva had given the Uddishta pratyayas.
Systematic study of combinatorics in music was done Sarngadeva – hence the seven svaras can be arranged in 7! (factorial)= 5040 ways.
In general in a n matra vrutta prastaar, if n is even the metrical forms will have only even number of Laghus. And if n is odd the metrical forms will have only odd number of Laghus
An amazing property of Virahanka’s numbers: Any positive integer can be represented either as a Virahanka number or as a sum of non-consecutive Virahanka numbers (Sankhyaank), without repetition.
For the tree graphs used to generate the matra prastaar for quarter having ‘n’ matras, every node will have two branches – first one for G and second one for L, & the branches end when their total matra values become equal to ‘n’
Virahanka gave a comprehensive explanation of the Prastaar and Sankhya pratyays for matra vrutta in his Prakrit work Vrattajati samuccaya – Fibonacci sequence is actually the sequence of Virahanka’s Sankhyankas
In previous articles, we have dealt with poetic meters where all the four quarters of a verse had the same pattern of Laghus and Gurus. Such meters are called Samavrutta.
This is one amongst many inventions that we think are modern but which have their roots in ancient India.
Pingala’s Meru Prastaar which is popularly known as Pascal’s Triangle. It predates the Pascal triangle by at least 1800 years
Pingala’s Algorithm was the earliest and quickest methods to calculate exponential of any number
Pingala’s Algorithm for Binary sequence is used to represent instructions to the computer and various types of data depending on the context
This is in continuation of my two previous articles – How Pingala created the Binary Number System and Pingala’s Algorithm for Binary Conversion. In the 11th century CE, Kedar Bhatt…
Binary numbers are the basic language in which computer programs are written which was first developed in India by Acharya Pingala
Ancient Indian prosodist and mathematician Pingala was the first to develop and use the binary number system