Hemachandra

Hemachandra was a 12th century Śvetāmbara Jaina ācārya, scholar, poet, mathematician, philosopher, yogi, grammarian. Quotes The ‘Fibonacci sequence’ The sum of the last and the one before the last is the number ... of the next mātrā-vṛtta. Hemachandra (c. 1150), in Livio, Mario (2003) [2002], The Golden Ratio: The Story of Phi, the World's Most Astonishing Number [archive] (First trade paperback ed.), New York City: Broadway Books, ISBN 0-7679-0816-3, and in Shah, Jayant (1991), A History of Piṅgala's Combinatorics, Northeastern University The number of combinations for matra meters are stated [as follows]. The sum (योगः) of the last and last-but-one (अन््त्ययौपान््ततौ) terms is the number of meters possible for a given number of matras. अथ मात्राविकल््पपानां संख््ययामाह -अङ्कान््त्ययोपान््त््ययोगः परे परे मात्राणाम॥् १६॥अङ्कानामेकद््वव््ययादीनां यौ अन््त्ययौपान््त्ययौ तयोर्योगःपरस््परमीलनं परे परे स््थथाने न््यस््ततौ मात्राणां संख््यया भवति। Hence, the sum of 2 and 1 is three, which is the number of meters with 3 matras. यथा - द््व््ययेकयोरन््त्ययोपान््त््ययोर्योगे त्रयः परस््थथाने न््यस््ततास्त्रिमात्रस््य विकल््पसंख््यया। The sum of 3 and 2 is five, which is the number of meters with 4 matras. द्विकत्रिकयोर्योगे पञ््च परे स््थथाने न््यस््तताश्चतुर््ममात्रस््य विकल््पसंख््यया। The sum of 5 and 3 is eight, which is the number of meters with 5 matras. पञ््चकत्रिकयोर्योगेऽष्टौ परे स््थथाने न््यस््ततााः पञ््चमात्रस््य विकल््पसंख््यया। The sum of 8 and 5 is thirteen, which is the number of meters with 6 matras. टकपञ््चकयोर्योगे त्रयोदश परे स््थथाने न््यस््ततााः षण््ममात्रस््य विकल््पसंख््यया। The sum of 13 and 8 is twenty-one, which is the number of meters with 7 matras. त्रयोदशकाष्टकयोर्योगे एकविंशतिः परे स््थथाने न््यस््ततााः सप्तमात्रस््य विकल््पसंख््यया। Likewise, 34, which is the sum of 21 and 13, is the number of meters with 8 matras. [Hence you have the sequence] 1, 2, 3, 5, 8, 13, 21, 34, ... एकविंशतित्रयोदशयोर्योगे चतुस्तत्ररिंशत््परे स््थथाने न््यस््ततााः अष्टमात्रस््य विकल््पसंख््यया।स््थथापना - १।२।३।५।८।१३।२१।३४। एवमत्तु रत्रापि॥१६॥ The ‘Fibonacci sequence’, the recurrence relation Sn = Sn-1 + Sn-2 Chhandonushasana 8.16 Velankar, H. D. (ed.). Chando’nushasana of Hemachandrasuri. Bombay: Bharatiya Vidya Bhavan: 1961. quoted in : Bhaskar Kamble, The Imperishable Seed: How Hindu Mathematics Changed the World and why this History was Erased, Garuda Prakashan Private Limited, 2022 ISBN 9798885750189 External links Category:1080s births Category:1172 deaths Category:12th-century Indian mathematicians Category:12th-century Indian philosophers Category:Jain acharyas Category:History of Gujarat Category:Fibonacci numbers Category:Gujarati-language writers Category:Gujarati people Category:Cultural history of Gujarat Category:Indian Jain monks Category:12th-century Indian Jain writers Category:12th-century Indian poets Category:12th-century Jain poets Category:Medieval Indian Jain poets Category:12th-century Jain monks Category:12th-century Indian monks Category:Jain law Category:Indian male writers Category:12th-century Indian historians Category:Scholars from Gujarat Category:Śvetāmbara monks