Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major

India India, officially the Republic of India, is a country in South Asia. It is the List of countries and dependencies by area, seventh-largest country by area; the List of countries by population (United Nations), most populous country since ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

and

astronomer An astronomer is a scientist in the field of astronomy who focuses on a specific question or field outside the scope of Earth. Astronomers observe astronomical objects, such as stars, planets, natural satellite, moons, comets and galaxy, galax ...

of the

Kerala school of astronomy and mathematics The Kerala school of astronomy and mathematics or the Kerala school was a school of Indian mathematics, mathematics and Indian astronomy, astronomy founded by Madhava of Sangamagrama in Kingdom of Tanur, Tirur, Malappuram district, Malappuram, K ...

founded by

Madhava of Sangamagrama Mādhava of Sangamagrāma (Mādhavan) Availabl/ref> () was an Indian mathematician and astronomer who is considered to be the founder of the Kerala school of astronomy and mathematics in the Late Middle Ages. Madhava made pioneering contributio ...

. He was also an

astrologer Astrology is a range of Divination, divinatory practices, recognized as pseudoscientific since the 18th century, that propose that information about human affairs and terrestrial events may be discerned by studying the apparent positions ...

. Parameshvara was a proponent of

observational astronomy Observational astronomy is a division of astronomy that is concerned with recording data about the observable universe, in contrast with theoretical astronomy, which is mainly concerned with calculating the measurable implications of physical ...

medieval India Medieval India was a long period of post-classical history in the Indian subcontinent between the ancient and modern periods. It is usually regarded as running approximately from the break-up of the Gupta Empire in the 6th century to the star ...

and he himself had made a series of

eclipse An eclipse is an astronomical event which occurs when an astronomical object or spacecraft is temporarily obscured, by passing into the shadow of another body or by having another body pass between it and the viewer. This alignment of three ...

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 ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the '' Āryabhaṭīya'' (which mentions that in 3600 ' ...

. The computational scheme based on the revised set of parameters has come to be known as the ''Drgganita'' or

Drig system Drigganita (दृग्गणित; IAST: dṛggaṇita, from dṛk-gaṇita, "sight-calculation"), also called the Drik system, is a system of astronomical computations followed by several traditional astronomers, astrologers and almanac maker ...

. 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

Hindu Hindus (; ; also known as Sanātanīs) are people who religiously adhere to Hinduism, also known by its endonym Sanātana Dharma. Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pp. 35–37 Historically, the term has also be ...

of Bhrgu

gotra In Hindu culture, the term gotra (Sanskrit: गोत्र) is considered to be equivalent to lineage. It broadly refers to people who are descendants in an unbroken male line from a common male ancestor or patriline. Generally, the gotr ...

following the

Ashvalayana A shakha () is a Hindu theological school that specializes in learning certain Vedic texts, or else the traditional texts followed by such a school.V. S. Apte. A Practical Sanskrit Dictionary, p. 913, left column.Monier-Williams, A Sanskrit-Engl ...

sutra of the

Rigveda The ''Rigveda'' or ''Rig Veda'' (, , from wikt:ऋच्, ऋच्, "praise" and wikt:वेद, वेद, "knowledge") is an ancient Indian Miscellany, collection of Vedic Sanskrit hymns (''sūktas''). It is one of the four sacred canoni ...

. Parameshvara's family name (''Illam'') was Vatasseri and his family resided in the village of Alathiyur (Sanskritised as ''Asvatthagrama'') in

Tirur Tirur is a major municipal town in Tirur Taluk, Malappuram district, in the Indian state of Kerala, spread over an area of . It is one of the major business centers in Malappuram district and is situated west of Malappuram and south of Kozh ...

Kerala Kerala ( , ) is a States and union territories of India, state on the Malabar Coast of India. It was formed on 1 November 1956, following the passage of the States Reorganisation Act, by combining Malayalam-speaking regions of the erstwhile ...

. Alathiyur is situated on the northern bank of the river Nila (river

Bharathappuzha The Bharathappuzha ("River of Bhārata"), also known as the Nila River, is a river in the Indian states of Tamil Nadu and Kerala. With a length of 209 km, it is the second longest river that flows through Kerala after the Periyar. It flo ...

) at its mouth in Kerala. He was a grandson of a disciple of

Govinda Bhattathiri Govinda Bhaṭṭathiri (also known as Govinda Bhattathiri of Thalakkulam or Thalkkulathur) ( 1237 – 1295) (p.15) was an Indian astrologer and astronomer who flourished in Kerala during the thirteenth century BCE, CE. Govinda Bhaṭṭatir ...

(1237–1295 CE), a legendary figure in the astrological traditions of

. Parameshvara studied under teachers Rudra and Narayana, and also under

(c. 1350 – c. 1425) the founder of the

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 Paramesvara (1360–1425) who developed the ''drigganita'' system of a ...

, another prominent member of the Kerala school, was his son and also his pupil. Parameshvara was also a teacher of

Nilakantha Somayaji Keļallur Nīlakaṇṭha Somayāji (14 June 1444 – 1544), also referred to as Keļallur Comatiri, was a mathematician and astronomer of the Kerala school of astronomy and mathematics. One of his most influential works was the comprehens ...

(1444–1544) the author of the celebrated

Tantrasamgraha Tantrasamgraha, or Tantrasangraha, (literally, ''A Compilation of the System'') is an important astronomy, astronomical treatise written by Nilakantha Somayaji, an astronomer/mathematician belonging to the Kerala school of astronomy and mathemat ...

Work

Parameshvara wrote commentaries on many mathematical and astronomical works such as those by

Bhāskara I Bhāskara (; commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a ...

and

. He made a series of eclipse observations over a 55-year period. Constantly attempted to compare these with the theoretically computed positions of the planets. He revised planetary parameters based on his observations. One of Parameshvara's more significant contributions was his mean value type formula for the inverse interpolation of the sine. He was the first mathematician to give a formula for the

radius In classical geometry, a radius (: radii or radiuses) of a circle or sphere is any of the line segments from its Centre (geometry), center to its perimeter, and in more modern usage, it is also their length. The radius of a regular polygon is th ...

of the

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

circumscribing a cyclic quadrilateral. The expression is sometimes attributed to Lhuilier

782 __NOTOC__ Year 782 ( DCCLXXXII) was a common year starting on Tuesday of the Julian calendar, the 782nd year of the Common Era (CE) and Anno Domini (AD) designations, the 782nd year of the 1st millennium, the 82nd year of the 8th century, and ...

350 years later. With the sides of the

cyclic quadrilateral In geometry, a cyclic quadrilateral or inscribed quadrilateral is a quadrilateral (four-sided polygon) whose vertex (geometry), vertices all lie on a single circle, making the sides Chord (geometry), chords of the circle. This circle is called ...

being ''a, b, c,'' and ''d'', the radius ''R'' of the circumscribed circle is: :

R = \sqrt .

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

Āryabhaṭīya ''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Indian astronomy, Sanskrit astronomical treatise, is the ''Masterpiece, magnum opus'' and only known surviving work of the 5th century Indian mathematics, Indian mathematician Aryabhata. Philos ...

Āryabhaṭa I Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the ''Āryabhaṭīya'' (which mentions that in 3600 '' ...

*''Karmadipika'' – Commentary on ''Mahabhaskariya'' of Bhaskara I *''Paramesvari'' – Commentary on ''Laghubhaskariya'' of Bhaskara I *''Sidhantadipika'' – Commentary on ''Mahabhaskariyabhashya'' of

Govindasvāmi Govindasvāmi (or Govindasvāmin, Govindaswami) (c. 800 – c. 860) was an Indian mathematical astronomer most famous for his ''Bhashya'', a commentary on the ''Mahābhāskarīya'' of Bhāskara I, written around 830. The commentary contains many ...

*''Vivarana'' – Commentary on

Surya Siddhanta The ''Surya Siddhanta'' (; ) is a Sanskrit treatise in Indian astronomy dated to 4th to 5th century,Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017)Mathematics Encyclopaedia Britannica, Quote: "(...) i ...

and Lilāvati *''Drgganita'' – Description of the

(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

References

External links

*
PDF version
* {{Authority control 1380s births 1425 deaths Indian Hindus 14th-century Indian mathematicians 15th-century Indian astronomers Medieval Indian astrologers Kerala school of astronomy and mathematics 15th-century Indian mathematicians 14th-century astrologers 15th-century astrologers Scientists from Kerala People from Malappuram district Scholars from Kerala

Biographical details

Work

Works by Parameshvara

See also

References

Further reading

External links