Sankara Narayana (c. 840 – c. 900 AD) was an Indian astronomer-mathematician in the court of
Ravi Kulasekhara (c. 844 – c. 883 AD) of the
Chera Perumal kingdom of
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 ...
.
[Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79 and 390-91.] He is best known as the author of ''Laghu Bhaskariya Vivarana'' or ''Vyakha'' (869/870 AD), a detailed commentary on treatise ''Laghu Bhaskariya'' by 7th century mathematician
Bhaskara I (which in turn was based on the works of the 5th century polymath
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 ...
).
Sankara Narayana is known to have established an astronomical observatory at the port of
Kodungallur
Kodungallur (; also Cranganore, Portuguese: Cranganor; formerly known as Mahodayapuram, Shingly, Vanchi, Muchiri, Muyirikkode, and Muziris) is a historically significant town situated on the banks of river Periyar on the Malabar Coast in Thr ...
in central Kerala.
''Laghu Bhaskariya Vivarana'' (Chapter VII), produced in the court of king Ravi Kulasekhara at Kodungallur, explicitly states that it was composed in
Saka Year
The Shaka era (IAST: Śaka, Śāka) is a historical Hindu calendar era (year numbering), the epoch (its year zero) of which corresponds to Julian year 78.
The era has been widely used in different regions of India as well as in SE Asia.
Hist ...
791 (=869/70 AD).
It is also mentions that the year was the 25th regnal year of king Ravi Kulasekhara.
[Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.] In the second verse of the ''vivarana'' Narayana remembers five major precessors in the field of mathematics (Aryabhata, Varahamihira, Bhaskara I, Govinda and Haridatta), including his possible master
Govinda
Govinda (), also rendered Govind and Gobind, is an epithet of Vishnu which is also used for his avatars such as Krishna. The name appears as the 187th and the 539th name of Vishnu in '' Vishnu Sahasranama''. The name is also popularly addresse ...
(c. 800 – c. 860 AD).
Observatory
* The ''vivarana'' mentions a royal observatory (under the charge of Sankara Narayana) at Mahodayapura (Kodungallur).
* There are references to an instrument called "Rashi Chakra" marked by a "Yanthra Valaya" in the ''vivarana''. This instrument might be the same as the Gola Yanthra/Chakra Yanthra mentioned by famous polymath
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 Chakra Yanthra was developed further and called Phalaka Yanthra by Bhaskara I.
[Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 390-391 and 408-409.]
* At the directions of Sankara Narayana, in every 'katikai' (= 34 minutes), bells were sounded at different important centres of Mahodayapura to announce correct time.
Mathematical contributions
* ''Laghu Bhaskariya Vivarana'' covers the standard mathematical methods of
Aryabhata I
Aryabhata (ISO 15919, ISO: ) or Aryabhata I (476–550 Common Era, CE) was an Indian mathematician and astronomer of the classical age of Indian mathematics and Indian astronomy. He flourished in the Gupta era, Gupta Era and produced works su ...
such as the solution of the
indeterminate equation In mathematics, particularly in algebra, an indeterminate equation is an equation for which there is more than one solution. For example, the equation ax + by =c is a simple indeterminate equation, as is x^2=1. Indeterminate equations cannot be solv ...
by = ax ± c (a, b, c integers) in integers which is then applied to astronomical problems. The Indian method involves using the
Euclidean algorithm
In mathematics, the Euclidean algorithm,Some widely used textbooks, such as I. N. Herstein's ''Topics in Algebra'' and Serge Lang's ''Algebra'', use the term "Euclidean algorithm" to refer to Euclidean division or Euclid's algorithm, is an effi ...
. It is called
kuttakara ("pulveriser").
* The most unusual feature of the Laghubhāskarīyavivaraṇa is the use of
katapayadi system
''Kaṭapayādi'' system (Devanagari: कटपयादि, also known as ''Paralppēru'', Malayalam: :ml:പരല്പ്പേര്, പരല്പ്പേര്) of numerical notation is an ancient Indian alphasyllabic numeral s ...
of
numeration
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The same sequence of symbo ...
as well as the
place-value
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or decimal system). More generally, a positional system is a numeral system in which the ...
Sanskrit
Sanskrit (; attributively , ; nominally , , ) is a classical language belonging to the Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had diffused there from the northwest in the late ...
numerals which Laghubhāskarīyavivaraṇa frequently uses.
Identification of king Ravi Kulasekhara with Sthanu
* The opening verse of ''Laghu Bhaskariya Vyakha'' gives an indirect invocation to the lord called "Sthanu" (carefully composed to be applicable to god
Siva and the ruling king).
[Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.]
*Sankara Narayana also mentions that the full name of his king as "Ravi Varma Kulasekhara".
[Narayanan, M. G. S. ''Perumāḷs of Kerala.'' Thrissur (Kerala): CosmoBooks, 2013. 78-79.]
*''Laghu Bhaskariya Vivarana'' was composed in the 25th regnal year of king Kulasekhara.
Date of ''Laghu Bhaskariya Vivarana''
* "Angartvambara nanda devamanubhir yate dinanam gane"
** Anga = 6, Rtu = 6, Ambara = 0, Nanda = 9, Veda = 4, and Manu = 14
** Order - 6609414
** Reverse Order - 1449066
* Kali Date - 3967 years and 86 days = 25 Mithuna,
Kollam Era
The Malayalam Calendar is a sidereal solar calendar used in Kerala. The origin of the calendar has been dated to 825 CE, the beginning of the Kollam Era.
There are many theories regarding the origin of the era, but according to recent schola ...
41 = 870 AD
* "Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah"
** Candra = 1, Randhra = 9, and Muni = 7
** Order - 197
** Reverse Order - 791 (
Saka Year
The Shaka era (IAST: Śaka, Śāka) is a historical Hindu calendar era (year numbering), the epoch (its year zero) of which corresponds to Julian year 78.
The era has been widely used in different regions of India as well as in SE Asia.
Hist ...
) = 870 AD
* Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king = 870 AD
See also
*
Indian mathematics
Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta ...
*
History of mathematics
The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments ...
References
{{DEFAULTSORT:Sankaranarayana
Hindu astronomy
People from Thrissur district
Kerala school of astronomy and mathematics
Year of birth uncertain
9th-century Indian mathematicians
10th-century Indian mathematicians
Scientists from Kerala
9th-century Indian astronomers
10th-century Indian astronomers
Scholars from Kerala
Chera dynasty