Parameshvara
Encyclopedia
Vatasseri Parameshvara Nambudiri (Malayalam: വടശ്ശേരി പരമേശ്വരന്) (ca.1380–1460) was a major India
n mathematician
and astronomer
of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama
. He was also an astrologer
. Parameshvara was a proponent of observational astronomy
in medieval India
and he himself had made a series of eclipse
observations to verify the accuracy of the computational methods then in use. Based on his eclipse observations, Parameshvara proposed several corrections to the astronomical parameters which had been in use since the times of Aryabhata
. The computational scheme based on the revised set of parameters has come to be known as the Drgganita system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.
of Bhrgugotra
following the Ashvalayanasutra of the Rgveda. Parameshvara's family name (Illam) was Vatasseri (also called Vatasreni) and his family resided in the village of Alattur (Sanskritised as Asvatthagrama) in Kerala
. Alattur is situated on the northern bank of the river Nila (river Bharathappuzha
) at its mouth in Kerala. He was a grandson of a disciple of Govinda Bhattathiri
(1237–1295 CE), a legendary figure in the astrological traditions of Kerala
.
Parameshvara studied under teachers Rudra and Narayana, and also under Sangamagrama Madhava (c. 1350 – c. 1425) the founder of the Kerala school of astronomy and mathematics. Damodara
, another prominent member of the Kerala school
, was his son and also his pupil. Parameshvara was also a teacher of Nilakantha Somayaji
(1444–1544) the author of the celebrated Tantrasamgraha
.
and Aryabhata
. He made a series of eclipse observations over a 55 year period, and constantly attempted to compare these with the theoretically computed positions of the planets. He revised planetary parameters based on his observations.
Parameshvara's most significant contribution is his mean value type formula
for the inverse interpolation of the sine. He was the first mathematician to give the radius
of circle
with an inscribed quadrilateral, an expression that is normally attributed to Lhuilier (1782), 350 years later. With the sides of the cyclic quadrilateral
being a, b, c, and d, the radius R of the circumscribed circle is:
India
India , officially the Republic of India , is a country in South Asia. It is the seventh-largest country by geographical area, the second-most populous country with over 1.2 billion people, and the most populous democracy in the world...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and astronomer
Astronomer
An astronomer is a scientist who studies celestial bodies such as planets, stars and galaxies.Historically, astronomy was more concerned with the classification and description of phenomena in the sky, while astrophysics attempted to explain these phenomena and the differences between them using...
of the Kerala school of astronomy and mathematics founded by Madhava of Sangamagrama
Madhava of Sangamagrama
Mādhava of Sañgamāgrama was a prominent Kerala mathematician-astronomer from the town of Irińńālakkuţa near Cochin, Kerala, India. He is considered the founder of the Kerala School of Astronomy and Mathematics...
. He was also an astrologer
Astrologer
An astrologer practices one or more forms of astrology. Typically an astrologer draws a horoscope for the time of an event, such as a person's birth, and interprets celestial points and their placements at the time of the event to better understand someone, determine the auspiciousness of an...
. Parameshvara was a proponent of observational astronomy
Observational astronomy
Observational astronomy is a division of the astronomical science that is concerned with getting data, in contrast with theoretical astrophysics which is mainly concerned with finding out the measurable implications of physical models...
in medieval India
Medieval India
Medieval India refers to the Middle Ages i.e. 5th to 15th century AD in the Indian subcontinent, it includes:*Early Middle Ages: Middle kingdoms of India*Hoysala Empire*Kakatiya Kingdom*Delhi Sultanate*Ahom Kingdom*Reddy Kingdom...
and he himself had made a series of eclipse
Eclipse
An eclipse is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer...
observations to verify the accuracy of the computational methods then in use. Based on his eclipse observations, Parameshvara proposed several corrections to the astronomical parameters which had been in use since the times of Aryabhata
Aryabhata
Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
. The computational scheme based on the revised set of parameters has come to be known as the Drgganita system. Parameshvara was also a prolific writer on matters relating to astronomy. At least 25 manuscripts have been identified as being authored by Parameshvara.
Biographical details
Parameshvara was a HinduHindu
Hindu refers to an identity associated with the philosophical, religious and cultural systems that are indigenous to the Indian subcontinent. As used in the Constitution of India, the word "Hindu" is also attributed to all persons professing any Indian religion...
of Bhrgugotra
Gotra
In the Hindu society, the term Gotra broadly refers to people who are descendants in an unbroken male line from a common male ancestor. Panini defines gotra for grammatical purposes as apatyam pautraprabhrti gotram , which means "the word gotra denotes the progeny beginning with the son's son"...
following the Ashvalayanasutra of the Rgveda. Parameshvara's family name (Illam) was Vatasseri (also called Vatasreni) and his family resided in the village of Alattur (Sanskritised as Asvatthagrama) in Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
. Alattur is situated on the northern bank of the river Nila (river Bharathappuzha
Bharathappuzha
Bharathappuzha , also known as River Nila, is a river in India in the state of Kerala. With a length of 209 km, it is the second-longest river in Kerala, after the Periyar River. The word "Nila" indicates the culture more than just a river. Nila has groomed the culture and life of south...
) at its mouth in Kerala. He was a grandson of a disciple of Govinda Bhattathiri
Govinda Bhattathiri
Govinda Bhaṭṭatiri was an Indian astrologer and astronomer who flourished in Kerala during the thirteenth century CE. His major work was Daśādhyāya a commentary on the first ten chapters of the astrological text Bṛhajjātaka composed by Varāhamihira...
(1237–1295 CE), a legendary figure in the astrological traditions of Kerala
Kerala
or Keralam is an Indian state located on the Malabar coast of south-west India. It was created on 1 November 1956 by the States Reorganisation Act by combining various Malayalam speaking regions....
.
Parameshvara studied under teachers Rudra and Narayana, and also under Sangamagrama Madhava (c. 1350 – c. 1425) the founder of the Kerala school of astronomy and mathematics. Damodara
Damodara
Vatasseri Damodara Nambudiri was an astronomer-mathematician of the Kerala school of astronomy and mathematics who flourished during the fifteenth century CE. He was a son of Vatasseri Paramesvara who developed the drigganita system of astronomical computations...
, another prominent member of the Kerala school
Kerala school
Kerala school may refer to*Kerala school of astronomy and mathematics, a school of mathematics and astronomy founded by Madhava of Sangamagrama in Kerala, South India which flourished between the 14th and 16th centuries CE....
, was his son and also his pupil. Parameshvara was also a teacher of Nilakantha Somayaji
Nilakantha Somayaji
Kelallur Nilakantha Somayaji was a major mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehensive astronomical treatise Tantrasamgraha completed in 1501...
(1444–1544) the author of the celebrated Tantrasamgraha
Tantrasamgraha
Tantrasamgraha is an important astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathematics....
.
Work
Parameshvara wrote commentaries on many mathematical and astronomical works such as those by Bhaskara IBhaskara I
Bhāskara was a 7th century Indian mathematician, who was apparently the first to write numbers in the Hindu-Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work...
and Aryabhata
Aryabhata
Aryabhata was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy...
. He made a series of eclipse observations over a 55 year period, and constantly attempted to compare these with the theoretically computed positions of the planets. He revised planetary parameters based on his observations.
Parameshvara's most significant contribution is his mean value type formula
Mean value theorem
In calculus, the mean value theorem states, roughly, that given an arc of a differentiable curve, there is at least one point on that arc at which the derivative of the curve is equal to the "average" derivative of the arc. Briefly, a suitable infinitesimal element of the arc is parallel to the...
for the inverse interpolation of the sine. He was the first mathematician to give the radius
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...
of circle
Circle
A circle is a simple shape of Euclidean geometry consisting of those points in a plane that are a given distance from a given point, the centre. The distance between any of the points and the centre is called the radius....
with an inscribed quadrilateral, an expression that is normally attributed to Lhuilier (1782), 350 years later. With the sides of the cyclic quadrilateral
Cyclic quadrilateral
In Euclidean geometry, a cyclic quadrilateral is a quadrilateral whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. Other names for these quadrilaterals are chordal quadrilateral and inscribed...
being a, b, c, and d, the radius R of the circumscribed circle is:
Works by Parameshvara
The following works of Parameshvara are well-known. A complete list of all manuscripts attributed to Parameshvara is available in Pingree.- Bhatadipika - Commentary on Aryabhatiya of Aryabhata I
- Karmadipika - Commentary on Mahabhaskariya of Bhaskara I
- Paramesvari - Commentary on Laghubhaskariya of Bhaskara I
- Sidhantadipika - Commentary on Mahabhaskariyabhashya of Govindasvami
- Vivarana - Commentary on Suryasidhanta and Lilavati
- Drgganita - Description of the Drk system (composed in 1431 CE)
- Goladipika - Spherical geometry and astronomy (composed in 1443 CE)
- Grahanamandana - Computation of eclipses (Its epoch is 15 July 1411 CE.)
- Grahanavyakhyadipika - On the rationale of the theory of eclipses
- Vakyakarana - Methods for the derivation of several astronomical tables
Further reading
- D Pingree, Biography in Dictionary of Scientific Biography (New York 1970-1990).
- Bhaskara, Laghubhaskariyam : With Parameshvara's commentary (Poona, 1946).
- Bhaskara, Mahabhaskariyam: With Parameshvara's commentary called Karmadipika (Poona, 1945).
- Munjala, Laghumanasam : with commentary by Parameshvara (Poona, 1944).
- T.A. Sarasvati AmmaT.A. Sarasvati AmmaT.A. Sarasvati Amma was a scholar born in Kerala, India who specialized in the geometry of ancient and medieval India....
, Geometry in ancient and medieval India (Delhi, 1979). - K Shankar Shukla, The Surya-siddhanta with the commentary of Parameshvara (Lucknow, 1957).
- R C Gupta, Parameshvara's rule for the circumradius of a cyclic quadrilateral, Historia Math. 4 (1977), 67-74.
- R C Gupta, A mean-value-type formula for inverse interpolation of the sine, Ganita 30 (1-2) (1979), 78—82.
- K Plofker, An example of the secant method of iterative approximation in a fifteenth-century Sanskrit text, Historia Math. 23 (3) (1996), 246-256.
- K K Raja, Astronomy and mathematics in Kerala, Brahmavidya 27 (1963), 136-143.
External links
(PDF version)- http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Parameshvara.html