|Born: about 920 in India
1000 in India
Essentially nothing is known of the
life of Aryabhata II. Historians have argued about his date and have
come up with many different theories. In  Pingree gives the date
for his main publications as being between 950 and 1100. This is
deduced from the usual arguments such as which authors Aryabhata II
refers to and which refer to him. G R Kaye argued in 1910 that
Aryabhata II lived before al-Biruni but Datta  in 1926 showed that
these dates were too early.
The article  argues
for a date of about 950 for Aryabhata II's main work, the
Mahasiddhanta, but R Billiard has proposed a date for Aryabhata II in
the sixteenth century. Most modern historians, however, consider the
most likely dates for his main work as around 950 and we have given
very approximate dates for his birth and death based on this
hypothesis. See  for a fairly recent discussion of this topic.
The most famous work by Aryabhata II is the Mahasiddhanta
which consists of eighteen chapters. The treatise is written in
Sanskrit verse and the first twelve chapters form a treatise on
mathematical astronomy covering the usual topics that Indian
mathematicians worked on during this period. The topics included in
these twelve chapters are: the longitudes of the planets, eclipses of
the sun and moon, the projection of eclipses, the lunar crescent, the
rising and setting of the planets, conjunctions of the planets with
each other and with the stars.
The remaining six
chapters of the Mahasiddhanta form a separate part entitled On the
sphere. It discusses topics such as geometry, geography and algebra
with applications to the longitudes of the planets.
In Mahasiddhanta Aryabhata II gives in about twenty verses detailed
rules to solve the indeterminate equation: by = ax + c. The rules
apply in a number of different cases such as when c is positive, when
c is negative, when the number of the quotients of the mutual
divisions is even, when this number of quotients is odd, etc. Details
of Aryabhata II's method are given in .
Aryabhata II also gave a method to calculate the cube root of a
number, but his method was not new, being based on that given many
years earlier by Aryabhata I, see for example .
Aryabhata II constructed a sine table correct up to five decimal
places when measured in decimal parts of the radius, see . Indian
mathematicians were very interested in giving accurate sine tables
since they were used to calculate the planetary positions as
accurately as possible.
Article by: J J
O'Connor and E F Robertson