Sanskrit Poetry Math

By Manjul Bhargava
Professor of Mathematics
Princeton University

In the rhythms of Sanskrit poetry, there are 2 kinds of syllables – long with 2 beats (^^) and short with 1 beat (*)

Question: how many rhythms can we construct having n beats, using long and short syllables ?
(Example n=8: ***^^*^^)

Solution:

Case: n=1 beat
*
=> 1 rhythm

Case: n= 2 beats
**
^^
=> 2 rhythms

Case: n=3 beats
***
*^^
^^*
=> 3 rhythms

Case: n= 4 beats
****
^^^^
*^^*
**^^
^^**
=> 5 rhythms


This is the Fibonacci sequence;
1 2 3 5 8 13 21 34 …

For n = 5 beats, 8 rhythms
For n = 6 beats, 13rhythms
For n = 7 beats, 21 rhythms
For n = 8 beats, 34 rhythms