**Who is Hemachandra?**

Born to Pahini and Chachadev in 1088, Acharya Hemachandra was named Chandradeva at birth. He was born in Dhanduka, a village in Gujarat. Several works on science, languages and philosophy are accredited to him. . As a young child, he was taken to a Jain temple where he was initiated as a monk, and his name was changed to Somachandra.

In 1110, he was ordained into Shvetambhara, the White robed sect of Jainism. He was given the name Acharya Hemchandra. He was instructed in religion, philosophy, the sacred scriptures, logic and grammar.

Gujarat, at that time, was ruled by King Siddharaja of the Chalukya dynasty. Gujarat is said to have flourished in the fields of economy and culture under the monarchy of King Siddharaja. Later, Hemachandra became an adviser to King Kumarapala who succeeded King Siddharaja Hemchandra is said to have had a broad-minded attitude and a firm believer in non-violence which pleased King Kumarapala.

It is said that he convinced King Kumarapala to adopt the rule of compassion for all living creatures, thereby enacting laws prohibiting the slaughter of animals. Kumarapala eventually came to accept the Jaina faith.

**Works of Hemachandra**

Hemachandra was an Indian Jain scholar, and Poet. He wrote extensively on grammar, philosophy, prosody, and contemporary history. Recognised for his diverse knowledge in various fields, he gained the title Kalikāl Sarvagya, (all-knowing of the Kali age)

**Mathematics:**

Hemachandra presented an earlier version of the Fibonacci^{[} sequence. It was presented around 1150, about fifty years before Fibonacci.

Sanskrit poetry has two kinds of syllables, a long syllable and a short one. The long syllable lasts two beats, and the short syllable lasts one beat.

Hemchnadra found out the number of different ways to construct an eight beat taal.

The relation between Maths and music shows certain ideas and principles, which were fundamental to ancient music and particularly Sanskrit poetry, could be well understood only on the basis of mathematics. Indian poets would explore rhythms in Sanskrit poetry.

Before Fibonacci wrote his work, the sequence Fn had already been discussed by Indian scholars, who had long been interested in rhythmic patterns that are formed from one-beat and two-beat notes. The number of such rhythms having n beats altogether is Fn+1; therefore and Hemachandra) mentioned the numbers \(1, 2, 3, 5, 8, 13, 21, …\) explicitly.

Today they are referred to as Hemchandra Fibonacci numbers duly giving recognition to Hemchandra.

The Fibonacci series is the set of numbers beginning with \(1, 1\) where every number is the sum of the previous two numbers. The series begins with \(1, 1, 2, 3, 5, 8, 13,\) and so on.

The Fibonacci Sequence is the series of numbers:

\(0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...\)

The next number is found by adding up the two numbers before it:

- the 2 is found by adding the two numbers before it \((1+1),\)
- the 3 is found by adding the two numbers before it \((1+2),\)
- the 5 is \((2+3),\) etc.

Therefore for 8 beats, the answer is 34 which is the 8^{th} number in that series.

Similarly, answers can be found for any number of beats.

Consider all the possible combinations of 8 beats. Let us separate all these combinations into two different blocks If the different combinations are separated into two different blocks where the last syllable either the long one is one block, and the last syllable which is short is another block.

Now remove the last syllable from all the combinations in both the blocks.

All the eight beat rhythms have been divided into two blocks. These blocks contain all possible seven beat rhythms or six-beat rhythms because we have removed the last syllable, which is either a short or a long syllable.

All possible 8 beat rhythms is basically the sum of all possible sum of 7 beat rhythms and 6 beats rhythm

8 beat couplets \((f8)=6\) beat couplets \(( f8-2)+ 6\) beat couplets \(f(8-2)\)

\(Fn=( fn-1)+ ( fn-2)\)