Śaṅkaranārāyaṇa Explained

Sankara Narayana
Birth Date:	c. 840 CE
Nationality:	Indian
Notable Works:	Laghu Bhaskariya Vivarana
Occupation:	Astronomer-mathematician

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] Sankara Narayana is known to have established an astronomical observatory at the port of Kodungallur in central Kerala.^[4]

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). It is also mentions that the year was the 25th regnal year of king Ravi Kulasekhara.^[5] 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).^[5]

Observatory

• 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.^[6]

• 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").
• The most unusual feature of the Laghubhāskarīyavivaraṇa is the use of katapayadi system of numeration as well as the place-value Sanskrit 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).^[5]

• Sankara Narayana also mentions that the full name of his king as "Ravi Varma Kulasekhara".^[5]
• 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 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

• Meeting of Guru (=Jupiter) and Sauri (=Saturn) in Capa (Dhanu) = 25th regnal year of the king = 870 AD

See also

• Indian mathematics
• History of mathematics
• List of astronomers and mathematicians of the Kerala school

Notes and References

1. Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79 and 390-91.
2. Book: George Gheverghese Joseph. A Passage to Infinity. SAGE Publications Pvt. Ltd.. New Delhi. 2009. 13. 978-81-321-0168-0.
3. Book: Laghubhaskariyavivarana. 1949. TSS. S. Venkitasubramonia Iyar. 162. Trivandrun. S.Kochukunju Asari.
4. Book: Virendra Nath Sharma. Sawai Jai Singh and His Astronomy. 1995. Motilal Banarsidass Publishers. Delhi. .
5. Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 78-79.
6. Narayanan, M. G. S. Perumāḷs of Kerala. Thrissur (Kerala): CosmoBooks, 2013. 390-391 and 408-409.