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Vaishali Institute Research Bulletin No. 4
are 1, 2, 3, 5, 8, 13,...respectively and these are the (so-called) Fibonacci Numbers.
108
Rule for finding the numbers of variations of mätra vṛttas, the (so-called) Fibonacci Numbers
The above method for finding the numbers of variations of mātrā vrttas, leads us to the following general rule (n) (n-1)+ (n-2), (n) being the number of variations of the metre having n syllables.
Acarya Hemacandra and the (so-called) Fibonacci Numbers.
Acarya Hemacandra says, "Sum of the last and the last but one numbers (of variations) is (the number of variations) of the mātrā vṛttas coming afterwards.' 8
He explains his rule as follows.
"From amongst the numbers 1, 2, etc. those which are the last and the last but one, are added (and) the sum, kept thereafter, gives the number of variations of the mäträ vṛttas.
For example the sum of 2 and 1, the last and the last but one, is 3 (which) is kept afterwards and is the number of variations (of the metre) having 3 syllables.
The sum of 3 and 2 is 5 (which) is kept afterwards and is the number of variations (of the metre) having 4 syllables.
The sum of 5 and 3 is 8 (which) is kept afterwards and is the number of variations (of the metre) having 5 syllables.
The sum of 8 and 5 is 13 (which) is kept afterwards and is the number of variations (of the metre) having 6 syllables.
The sum of 13 and 8 is 21 (which) is kept afterwards and is the number of variations (of the metre) having 7 syllables.
The sum of 21 and 13 is 34 (which) is kept afterwards and is the number of variations (of the metre) having 8 syllables. Thus 1,2,3,5,8,13,21,34 and so on, also."4
L. Fibonacci and the (So-called) Fibonacci Numbers.
L. Fibonacci, born in the commercial centre of Pisa and brought up in Bongai in the north coast of Africa, travelled5 far and wide and came in Velankar, H. D. (Ed.): Chandonusāsana of Hemacandra, Bhartiya Vidya Bhavan, Bombay, 1961, viii, 16 (p. 239)
3.
Ref. 3, viii, 16 ff.
4.
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