BHASKARA
I – REPRESENTATION OF
NUMBERS
Bhaskara's probably most important
mathematical contribution concerns the representation of numbers in a positional
system. The first positional representations had been known to
Indian astronomers approximately 500 years prior to this work. However, these
numbers, prior to Bhaskara, were written not in figures but in words or allegories,
and were organized in verses. For instance, the number 1 was given as moon,
since it exists only once; the number 2 was represented by wings, twins,
or eyes, since they always occur in pairs; the number 5 was given
by the (5) senses. Similar to our current decimal system,
these words were aligned such that each number assigns the factor of the power
of ten corresponding to its position, only in reverse order: the higher powers
were right from the lower ones.
His
system is truly positional, since the same words representing, can also be used
to represent the values 40 or 400.[5] Quite
remarkably, he often explains a number given in this system, using the
formula ankair api ("in figures this reads"), by
repeating it written with the first nine Brahmi numerals,
using a small circle for the zero .
Contrary to his word system, however, the figures are written in descending
valuedness from left to right, exactly as we do it today. Therefore, at least
since 629 the decimal system is definitely known to the Indian
scientists. Presumably, Bhaskara did not invent it, but he was the first having
no compunctions to use the Brahmi numerals in
a scientific contribution in Sanskrit.
