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Ācārya Hemacandra and the So-called Fibonacci Numbers 109 We have also seen that metres in Sanskrit poetry mainly fall under the following three categories viz., (i) varna vrttas i. e., metres where the number of letters remains con
stant and the number of syllables is arbitrary, matrā vrttas i. e., metres where the number of syllables remains
constant and the number of letters is arbitrary, and (iii) metres consisting of groups of syllables such as the āryā and the
vaitāliya etc. Expansion of Varna Vrttas.
It has also been observed that a metre of this kind and having one ietter has two variations, S and I and the latter is written below the tormer :S. Variations of such a metre having two letters are obtained
trom those of the former by repetition with S and I, in order : SS
IS
ST
II. Same process of repetition of variations is followed in the case of metres having more than 2 letters.
SI
Fxpansion of Matrā Vritas.
The above process of expansion is also applicable to matrā vsttas. The number of variations of a metre having one syllable is I and that of a metre baving two syllables is two viz., S
II. For a metre having three syllables, these are repeated with S and I, in order, thus : IS
III. The same process of repetition of variations is followed in the case of metres having more than 3 syllables. Partitions
The above process of expansion of mātrā vrttas is a kind of partitioning of a number (the number being the number of syllables in the metre) where the digits take the values 2 and 1, only and the order is relevant, the number of digits in a particular partition being arbitrary, Throughout the paper, partition stands for partition of this kind. The (So-called) Fibonacci Numbers.
It will be observed that the variations of mātrā vrttas form the sequence of numbers which are now called Fibonacci Numbers. For, the numbers of variations of matra metres having 1, 2, 3, 4, 5, 6,... syllables
enci, Numbers. For the
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