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Śaṅkaranārāyaṇa

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This article is about an Indian astronomer. For the Diwan, see Sankaranarayana Iyen.

Sankara Narayana
Bornc. 840 CE
NationalityIndian
OccupationAstronomer-mathematician
Notable workLaghu Bhaskariya Vivarana

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.[1][2] 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).[3][4] Sankara Narayana is known to have established an astronomical observatory at the port of Kodungallur in central Kerala.[2][5]

Laghu Bhaskariya Vivarana (Chapter VII), produced in the court of king Ravi Kulasekhara at Kodungallur, explicitly states that it was composed in Saka Year 791 (=869/70 AD).[4][1] It is also mentions that the year was the 25th regnal year of king Ravi Kulasekhara.[6] 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 (c. 800 – c. 860 AD).[6]

Observatory

  • The vivarana mentions a royal observatory (under the charge of Sankara Narayana) at Mahodayapura (Kodungallur).[2]
  • 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. The Chakra Yanthra was developed further and called Phalaka Yanthra by Bhaskara I.[7]

"Oh [king] Ravi Varma Deva, now deign to tell us quickly, reading off from the armillary sphere installed [at the observatory] in Mahodayapura, duly fitted with all the relevant circles and with the sign (degree-minute) markings, the time of the rising point of the ecliptic (lagna) when the Sun is at 10° in the sign of Capricorn, and also when the Sun is at the end of the sign Libra, which I have noted."[8]

  • 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 such as the solution of the indeterminate equation by = ax ± c (a, b, c integers) in integers which is then applied to astronomical problems. The Indian method involves using the Euclidean algorithm. It is called kuttakara ("pulveriser").[4]

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).[9]


"Sa Sthanurjayati trirupasahito lingepi lokarcitah".

— Sankara Narayana, Laghu Bhaskariya Vyakha, Chapter I (c. 870 AD)
  • Sankara Narayana also mentions that the full name of his king as "Ravi Varma Kulasekhara".[10]
  • Laghu Bhaskariya Vivarana was composed in the 25th regnal year of king Kulasekhara.[10]

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 41 = 870 AD
  • "Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah"
    • Candra = 1, Randhra = 9, and Muni = 7
    • Order - 197
    • Reverse Order - 791 (Saka Year) = 870 AD

"Angartvambara nanda devamanubhir yate dinanam gane
Graste tigma mayukhamalinitamobhute parahne divi
Prsta praggrahanad dvitiyaghatika grasa pramanam raver
Bharta sri Kulasekharena vilasad velavrtaya bhuva".

— Sankara Narayana, Laghu Bhaskariya Vyakha, Chapter IV (c. 870 AD)

"Evam Sakabdah punariha candra randhramuni sankhyaya asambhiravagatah".

— Sankara Narayana, Laghu Bhaskariya Vyakha, Chapter 1 (c. 870 AD)

"Capapravista guru sauri samatva kalam
Yamyottaram gamanamantaratah pramanam
Acaksvya sarvamavagamya bhatoktamargad
Ityuktavan ravirasena nrpabhivandya".
"Tada pancavimsati Varsanyatitani devasya".

— Sankara Narayana, Laghu Bhaskariya Vyakha, Chapter VII (c. 870 AD)
  • Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king = 870 AD

See also

References

  1. ^ a b Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79 and 390-91.
  2. ^ a b c George Gheverghese Joseph (2009). A Passage to Infinity. New Delhi: SAGE Publications Pvt. Ltd. p. 13. ISBN 978-81-321-0168-0.
  3. ^ S. Venkitasubramonia Iyar; S.Kochukunju Asari, eds. (1949). Laghubhaskariyavivarana. Vol. 162. Trivandrun: TSS.
  4. ^ a b c d O'Connor, John J.; Robertson, Edmund F., "Sankara Narayana", MacTutor History of Mathematics Archive, University of St Andrews
  5. ^ Virendra Nath Sharma (1995). Sawai Jai Singh and His Astronomy. Delhi: Motilal Banarsidass Publishers. ISBN 81-208-1256-X.
  6. ^ a b Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79.
  7. ^ Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 390-391 and 408-409.
  8. ^ J.B. harley; David Woodward, eds. (1992). The history of cartography : Volume 2 Book 1 : Cartography in the traditional Islamic and South Asian societies. University of Chicago Press. p. 360. ISBN 0-226-31635-1.
  9. ^ Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79.
  10. ^ a b Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79.
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