|Born: 1089 in Dhandhuka, Gujarat, India
Died: 1173 in Gujarat, India
was named Pahini and his father Chachadev. The name Hemchandra was
one he took later in life and he was named Candradeva after he was
born. The city of Dhandhuka where he was born is about 50 km south
west of Ahmadabad the capital of Gujarat. Candradeva, when still
young, was taken to a Jain temple where he became a monk and changed
his name to Somacandra. He was instructed in religion, Indian
philosophy, the sacred scriptures, logic and grammar. When Candradeva
was ordained in 1110 into the Shvetambara (White-robed) sect of
Jainism and he was given the name Acharya Hemchandra.
Gujarat at this time was ruled by the Solanki dynasty.
Gujarat expanded to its largest extent under this dynasty and
learning flourished, particularly in the economic and cultural
fields. King Siddharaja made excellent use of Hemchandra's great
skills, knowledge and learning in ruling Gujarat. King Kumarapala
succeeded King Siddharaja and from 1125 he was advised by Hemchandra.
Of course as a spiritual leader, Hemchandra was in a strong position
to see that his ideas were put into practice and indeed this led to
Gujarat becoming considerable more advanced in culture and learning.
Hemchandra was a strong believer in non-violence and Gujarat
flourished in peace for many years. He convinced King Kumarapala to
bring in laws which not only prohibited violence between people, but
also made it illegal to kill animals. Hemchandra convinced the King
to make the Jain religion the official religion of Gujarat.
Hemchandra was an eloquent religious teacher, skilful
political advisor, and a scholar of the highest standing :-
A prodigious writer, [Hemchandra] produced Sanskrit and
Prakrit grammars, textbooks on science and practically every branch
of Indian philosophy, and several poems, including the
Trishashtishalakapurusha-carita (Deeds of the 63 Illustrious Men), a
Sanskrit epic of the history of the world as understood by Jain
teachers. He was also a logician. Although derivative in many ways,
his works have become classics, setting high standards for Sanskrit
The book Deeds of the 63
Illustrious Men mentioned in the above quote has now been translated
into English by Fynes and published by Oxford University Press. The
book recounts in a collection of fascinating stories historical myths
of the Jain religion.
One might reasonably
ask at this point why we have included Hemchandra in an archive of
mathematicians. The answer lies in his contribution to the Fibonacci
numbers which was made fifty years before Fibonacci wrote Liber Abaci
with its famous rabbit problem. Kak, in , explains how these
entered Hemchandra's writings. In a text written about 1150 he looked
at the following problem. Suppose we assume that lines are composed
of syllables which are either short or long. Suppose also that each
long syllable takes twice as long to articulate as a short syllable.
A line of length n contains n units where each short syllable is one
unit and each long syllable is two units. Clearly a line of length n
units takes the same time to articulate regardless of how it is
composed. Hemchandra asks: How many different combinations of short
and long syllables are possible in a line of length n?
Hemchandra then finds the answer explicitly. Suppose that
there are f(n) possibilities for a line of length n. The line of
length n either ends in a short syllable or in a long syllable. If it
is the former than there remains a line of length n-1 which can be
composed in f(n-1) ways and if the line of length n ends in a long
syllable then there is a line of length n-2 remaining which can be
composed in f(n-2) ways. Hence, argues Hemchandra,
f(n) = f(n-1) + f(n-2).
Before we rush to
try to change the name of the Fibonacci numbers into Hemchandra
number it is worth noting that Gopala had studied these numbers in
about 1135 and Indian mathematicians as early as the 7th century had
looked at sequences which are produced by the familiar Fibonacci
Article by: J J O'Connor and E F