Vatasseri Parameshvara Nambudiri ( 1380–1460) was a major

India India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...

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, structure, space, models, and change. History On ...

and

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

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 Iriññāttappiḷḷi Mādhavan known as Mādhava of Sangamagrāma () was an Indian mathematician and astronomer from the town believed to be present-day Kallettumkara, Aloor Panchayath, Irinjalakuda in Thrissur District, Kerala, India. He is ...

. He was also an

astrologer Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Dif ...

. 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 m ...

medieval India Medieval India refers to a long period of Post-classical history of the Indian subcontinent between the "ancient period" and "modern period". It is usually regarded as running approximately from the breakup of the Gupta Empire in the 6th cent ...

and he himself had made a series of

eclipse An eclipse is an astronomical event that 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 ce ...

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 an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the ''Aryabhatiya'' (which ...

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

Drig system Drigganita (ದೃಗ್ಗಣಿತ; 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 makers ...

. 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 (; ) are people who religiously adhere to Hinduism.Jeffery D. Long (2007), A Vision for Hinduism, IB Tauris, , pages 35–37 Historically, the term has also been used as a geographical, cultural, and later religious identifier for ...

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 gotra fo ...

following the

Ashvalayana A shakha (Sanskrit ', "branch" or "limb") 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.Moni ...

sutra of the

Rigveda The ''Rigveda'' or ''Rig Veda'' ( ', from ' "praise" and ' "knowledge") is an ancient Indian collection of Vedic Sanskrit hymns (''sūktas''). It is one of the four sacred canonical Hindu texts (''śruti'') known as the Vedas. Only one Sh ...

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

Tirur Tirur is a Municipality in Malappuram district in the Indian state of Kerala spread over an area of . It is one of the business centers of Malappuram district and is situated west of Malappuram and south of Kozhikode, on the Shoranur–Mangalor ...

Kerala Kerala ( ; ) is a 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 regions of Cochin, Malabar, South ...

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

Bharathappuzha Bharathappuzha ("River of Bhārata"), also known as the Nila or Ponnani River, is a river in India in the state of Kerala. With a length of 209 km, it is the second longest river that flows through Kerala after the Periyar. It flows throu ...

) 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 CE. Govinda Bhaṭṭatiri w ...

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

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

Sangamagrama Madhava Iriññāttappiḷḷi Mādhavan known as Mādhava of Sangamagrāma () was an Indian mathematician and astronomer from the town believed to be present-day Kallettumkara, Aloor Panchayath, Irinjalakuda in Thrissur District, Kerala, India. He is ...

(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 as ...

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

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

(1444–1544) the author of the celebrated

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

Work

Parameshvara wrote commentaries on many mathematical and astronomical works such as those by Bhaskara I 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) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...

of the

circle A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

circumscribing a cyclic quadrilateral. The expression is sometimes attributed to

Lhuilier Simon Antoine Jean L'Huilier (or L'Huillier) (24 April 1750 in Geneva – 28 March 1840 in Geneva) was a Swiss mathematician of French Huguenot descent. He is known for his work in mathematical analysis and topology, and in particular the ge ...

782 __NOTOC__ Year 782 ( DCCLXXXII) was a common year starting on Tuesday of the Julian calendar. The denomination 782 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in ...

350 years later. With the sides of the

cyclic quadrilateral In Euclidean geometry, a cyclic quadrilateral or inscribed 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 ''c ...

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 Sanskrit astronomical treatise, is the ''magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that th ...

Āryabhaṭa I Aryabhata (ISO: ) or Aryabhata I (476–550 CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta Era and produced works such as the ''Aryabhatiya'' (which ...

*''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 e ...

*''Vivarana'' – Commentary on

Surya Siddhanta The ''Surya Siddhanta'' (; ) is a Sanskrit treatise in Indian astronomy dated to 505 CE,Menso Folkerts, Craig G. Fraser, Jeremy John Gray, John L. Berggren, Wilbur R. Knorr (2017)Mathematics Encyclopaedia Britannica, Quote: "(...) its Hindu inven ...

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 1380 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

References

Further reading

External links