Biography
Born: about 920 in India
Died: about 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 [1] 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 [2] in 1926 showed that these dates were too early.
The article [3] 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 [7] 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 [6].
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 [5].
Aryabhata II constructed a sine table correct up to five decimal places when measured in decimal parts of the radius, see [4]. Indian mathematicians were very interested in giving accurate sine tables since they were used to calculate the planetary positions as accurately as possible.
- Yavanesvara
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- Claudius Ptolemy
Born: About AD 85 in Egypt Died: About AD 165 in Alexandria, Egypt One of the most influential Greek astronomers and geographers of his time, Ptolemy propounded the geocentric theory in a form that prevailed for 1400 years. However, of all the ancient...
- Panini
Born: about 520 BC in Shalatula (near Attock), now Pakistan Died: about 460 BC in India Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in...
- Apastamba
To write a biography of Apastamba is essentially impossible since nothing is known of him except that he was the author of a Sulbasutra which is certainly later than the Sulbasutra of Baudhayana. It would also be fair to say that Apastamba's Sulbasutra...
- Baudhayana
To write a biography of Baudhayana is essentially impossible since nothing is known of him except that he was the author of one of the earliest Sulbasutras. We do not know his dates accurately enough to even guess at a life span for him, which is why...
Biography
Aryabhata II
Born: about 920 in India
Died: about 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 [1] 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 [2] in 1926 showed that these dates were too early.
The article [3] 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 [7] 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 [6].
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 [5].
Aryabhata II constructed a sine table correct up to five decimal places when measured in decimal parts of the radius, see [4]. Indian mathematicians were very interested in giving accurate sine tables since they were used to calculate the planetary positions as accurately as possible.
- Yavanesvara
Born: about 120 in Western India Died: about 180 in India Indian astrology was originally known as Jyotisha, which means "science of the stars". Until around the first century AD no real distinction was made between astrology and astronomy and in fact...
- Claudius Ptolemy
Born: About AD 85 in Egypt Died: About AD 165 in Alexandria, Egypt One of the most influential Greek astronomers and geographers of his time, Ptolemy propounded the geocentric theory in a form that prevailed for 1400 years. However, of all the ancient...
- Panini
Born: about 520 BC in Shalatula (near Attock), now Pakistan Died: about 460 BC in India Panini was born in Shalatula, a town near to Attock on the Indus river in present day Pakistan. The dates given for Panini are pure guesses. Experts give dates in...
- Apastamba
To write a biography of Apastamba is essentially impossible since nothing is known of him except that he was the author of a Sulbasutra which is certainly later than the Sulbasutra of Baudhayana. It would also be fair to say that Apastamba's Sulbasutra...
- Baudhayana
To write a biography of Baudhayana is essentially impossible since nothing is known of him except that he was the author of one of the earliest Sulbasutras. We do not know his dates accurately enough to even guess at a life span for him, which is why...