The Hemchandra Sequence

Mathematics in early days was seen as some kind of tool to make particular art forms perfect and in sync with nature. Now here comes the story of perfecting the art of poetry from 11th century India. Acharya Hemchandra Suri born in 1088 AD was a prodigy in himself to have expanded in vast fields like Grammar, Poetry, Lexicography, and most famously Mathematics. As we are particularly interested in mathematics I must acknowledge his enormous achievement in this area. Hemchandra described the Fibonacci sequence in 1150 AD fifty years before Fibonacci himself. He was considering a sequence of notes of length n, and he showed that these could be formed  by adding a short syllable to a note of length n − 1, or a long syllable to one of n − 2. The recursion relation F(n)= F(n-1) +F(n-1) represents the Fibonacci sequence. Hemchandra studied the rhythms of Sanskrit poetry. Syllables in Sanskrit are either long or short. Long syllables have twice the length of short syllables. The question he asked is ‘How many rhythm patterns with a given total length can be formed from short and long syllables?’ And this led to a revolution of beats and rhythms and even mathematics.

In the sunflower, individual

flowers are arranged along

curved lines which rotate

clockwise and counterclockwise.

Credits: The Fibonacci sequence in phyllotaxis.

– Laura Resta (Degree Thesis in Bio-mathematics)