Meta tags:

Headings (most frequently used words):

vyavahāra, contents, ganita, kaumudi, editions, references, external, links, prakīrṇaka, miśraka, śreḍhī, kṣetra, khāta, citi, rāśi, chāyā, kuṭṭaka, 10, vargaprakṛti, 11, bhāgādāna, 12, rūpādyaṃśāvatāra, 13, aṅka, pāśa, 14, bhadragaṇita,

Text of the page (most frequently used words):
the (44), and (33), edit (22), frac (22), rules (20), vyavahāra (18), displaystyle (16), cdot (16), examples (15), mathematics (13), for (13), #kaumudi (12), ganita (11), fractions (10), with (8), contents (7), wikipedia (7), links (7), indian (7), narayana (7), rule (7), dots (7), institute (6), fraction (6), contains (6), sum (6), unit (6), page (5), articles (5), external (5), from (5), science (5), history (5), mathematical (5), siddhanta (5), pandita (5), many (5), search (4), this (4), was (4), dead (4), india (4), modern (4), other (4), integer (4), express (4), gaṇita (4), equations (4), treatise (4), hide (4), move (4), sidebar (4), toggle (3), view (3), about (3), text (3), 1356 (3), 1918 (3), series (3), continued (3), number (3), algorithm (3), numbers (3), given (3), such (3), are (3), tfrac (3), linear (3), problems (3), here (3), tools (3), main (3), languages (2), table (2), contact (2), privacy (2), policy (2), terms (2), categories (2), sanskrit (2), short (2), description (2), wikidata (2), works (2), ramanujan (2), advanced (2), harish (2), chandra (2), sciences (2), david (2), pingree (2), singh (2), new (2), infinite (2), śulba (2), sūtras (2), srinivasa (2), mahāvīra (2), bhāskara (2), āryabhaṭa (2), classical (2), ancient (2), permanent (2), link (2), part (2), 1936 (2), srinivas (2), sriram (2), vedic (2), period (2), kusuba (2), 2004 (2), knuth (2), donald (2), art (2), computer (2), programming (2), arithmetical (2), lecture (2), notes (2), references (2), volume (2), principal (2), editions (2), bhadragaṇita (2), book (2), permutations (2), objects (2), finding (2), permutation (2), that (2), describes (2), combinations (2), different (2), aṅka (2), pāśa (2), write (2), arbitrary (2), equivalent (2), kaumudī (2), give (2), few (2), more (2), rūpādyaṃśāvatāra (2), method (2), bhāgādāna (2), quadratic (2), includes (2), indeterminate (2), vargaprakṛti (2), kuṭṭaka (2), chāyā (2), rāśi (2), citi (2), khāta (2), special (2), kṣetra (2), śreḍhī (2), pertaining (2), miśraka (2), square (2), root (2), cube (2), prakīrṇaka (2), verses (2), appearance (2), upload (2), file (2), changes (2), read (2), article (2), log (2), create (2), account (2), donate (2), menu (2), add, topic, mobile, cookie, statement, statistics, developers, code, conduct, legal, safety, contacts, disclaimers, available, under, additional, may, apply, using, site, you, agree, registered, trademark, non, profit, organization, wikimedia, foundation, inc, use, creative, commons, attribution, sharealike, license, rendered, parsoid, last, edited, november, 2024, utc, hidden, permanently, december, 2019, all, containing, language, matches, 1350s, books, 14th, century, social, retrieved, https, org, index, php, title, ganita_kaumudi, oldid, 1255912355, tifr, study, homi, bhabha, centre, education, research, chennai, bhaskaracharya, pratishthana, statistical, institutions, europe, islamic, greece, china, babylon, regions, henry, thomas, colebrooke, walter, eugene, clark, translators, 1919, 2005, sarma, 2007, shukla, 1992, sen, 2000, saraswati, amma, 1903, 1978, rajagopal, 1901, 1954, 1892, 1953, krishnaswamy, ayyangar, hayashi, 1888, 1958, datta, 1876, 1962, sengupta, 1861, 1916, rangacarya, 1855, 1910, sudhakara, dvivedi, 1853, 1898, shankar, balakrishna, dikshit, 1821, 1900, bapudeva, sastri, historians, varanasi, ujjain, delhi, jaipur, jantar, mantar, kerala, school, astronomy, centres, expansions, trigonometric, functions, symbol, zero, hindu, arabic, numeral, system, brahmi, numerals, pioneering, innovations, yavanajataka, yuktibhāṣā, veṇvāroha, vasishtha, tantrasamgraha, surya, siddhānta, shiromani, sadratnamala, romaka, paitamaha, paulisa, pātīgaṇita, lokavibhaga, līlāvatī, karanapaddhati, kanakkusaram, grahalaghava, brāhmasphuṭasiddhānta, bijaganita, bakhshali, manuscript, aryabhatiya, treatises, shanti, swarup, bhatnagar, prize, recipients, kannan, soundararajan, ravi, vakil, akshay, venkatesh, manjul, bhargava, tilak, raj, prabhakar, subbayya, sivasankaranarayana, pillai, seshadri, narasimhan, parthasarathy, probabilist, varadhan, veeravalli, varadarajan, rao, subrahmanyan, chandrasekhar, mahalanobis, satyendra, nath, bose, virasena, sankara, variar, varāhamihira, gangesha, upadhyaya, sridhara, śrīpati, nilakantha, somayaji, jagannatha, samrat, achyuta, pisharati, parameshvara, munishvara, mahendra, sūri, mādhava, saṅgamagrāma, kamalakara, jyeṣṭhadeva, halayudha, govindasvāmi, brahmagupta, brahmadeva, melpathur, bhattathiri, yajnavalkya, pingala, pāṇini, manava, katyayana, baudhayana, apastamba, mathematicians, 1942, ramasubramanian, lectures, times, takanori, decomposition, charles, burnett, jan, hogendijk, eds, 0169, 8729, issn, 9004132023, isbn, brill, studies, exact, honour, kim, plofker, bibliography, 2006, addison, wesley, edwards, jhu, press, pascal, triangle, story, idea, 497, nārāyana, issue, princess, wales, abhinava, nibandhamālā, jyautishacharya, padmakara, dwivedi, sarasvati, bhavana, granthamala, translation, rationale, historical, college, haridwar, gurukul, kangri, vishwavidyalaya, magic, squares, determine, next, lexicographic, ordering, though, computational, methods, have, well, beyond, algorithms, dedicated, efficient, generation, discuss, their, his, noted, equivalence, formulae, things, taken, time, figurate, combinatorics, generating, including, multiset, binomial, coefficients, generalized, fibonacci, partitions, calculate, numerators, find, successive, denominators, same, way, operating, always, chosen, smallest, but, does, not, unique, procedure, instead, states, thus, there, ways, according, one, choices, evam, iṣṭavaśād, bahudhā, greedy, egyptian, pick, were, known, approximation, systematic, expressing, had, previously, been, nārāyaṇa, gave, section, twelfth, chapter, named, eight, first, aṃśāvatāra, bhāgajāti, 850, sāra, saṅgraha, writing, factorization, variant, results, used, knowledge, simple, recurring, solutions, type, chakravala, shadow, mounds, grain, stacks, excavations, geometry, 149, material, cyclic, quadratilerals, third, diagonal, arithmetic, geometric, progressions, sequences, generalization, crucial, sine, cosine, daily, life, mixture, materials, interest, payment, instalments, mixing, gold, purities, unknowns, weights, measures, length, area, etc, addition, subtraction, multiplication, division, described, complex, than, earlier, 475, 395, divided, into, chapters, udāharaṇa, sūtra, written, mathematician, alongside, algebraic, called, bijganita, vatamsa, pandit, गणितकौमदी, free, encyclopedia, item, projects, printable, version, download, pdf, print, export, switch, legacy, parser, get, shortened, url, cite, information, related, what, general, actions, english, talk, संस्कृतम्, हिन्दी, subsection, top, personal, pages, recent, community, portal, learn, help, contribute, random, current, events, navigation, jump, content,

Text of the page (random words):
ganita kaumudi wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 contents toggle contents subsection 1 1 1 prakīrṇaka vyavahāra 1 2 2 miśraka vyavahāra 1 3 3 śreḍhī vyavahāra 1 4 4 kṣetra vyavahāra 1 5 5 khāta vyavahāra 1 6 6 citi vyavahāra 1 7 7 rāśi vyavahāra 1 8 8 chāyā vyavahāra 1 9 9 kuṭṭaka 1 10 10 vargaprakṛti 1 11 11 bhāgādāna 1 12 12 rūpādyaṃśāvatāra 1 13 13 aṅka pāśa 1 14 14 bhadragaṇita 2 editions 3 references 4 external links toggle the table of contents ganita kaumudi 2 languages हिन्दी संस्कृतम् edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia 1356 mathematical treatise by narayana pandita ganita kaumudi sanskrit गणितकौमदी is a treatise on mathematics written by indian mathematician narayana pandita in 1356 it was an arithmetical treatise alongside the other algebraic treatise called bijganita vatamsa by narayana pandit contents edit gaṇita kaumudī contains about 475 verses of sūtra rules and 395 verses of udāharaṇa examples it is divided into 14 chapters vyavahāra 1 1 prakīrṇaka vyavahāra edit weights and measures length area volume etc it describes addition subtraction multiplication division square square root cube and cube root the problems of linear and quadratic equations described here are more complex than in earlier works 2 63 rules and 82 examples 1 2 miśraka vyavahāra edit mathematics pertaining to daily life mixture of materials interest on a principal payment in instalments mixing gold objects with different purities and other problems pertaining to linear indeterminate equations for many unknowns 2 42 rules and 49 examples 1 3 śreḍhī vyavahāra edit arithmetic and geometric progressions sequences and series the generalization here was crucial for finding the infinite series for sine and cosine 2 28 rules and 19 examples 1 4 kṣetra vyavahāra edit geometry 149 rules and 94 examples 1 includes special material on cyclic quadratilerals such as the third diagonal 2 5 khāta vyavahāra edit excavations 7 rules and 9 examples 1 6 citi vyavahāra edit stacks 2 rules and 2 examples 1 7 rāśi vyavahāra edit mounds of grain 2 rules and 3 examples 1 8 chāyā vyavahāra edit shadow problems 7 rules and 6 examples 1 9 kuṭṭaka edit linear integer equations 69 rules and 36 examples 1 10 vargaprakṛti edit quadratic 17 rules and 10 examples 1 includes a variant of the chakravala method 2 ganita kaumudi contains many results from continued fractions in the text narayana pandita used the knowledge of simple recurring continued fraction in the solutions of indeterminate equations of the type n x 2 k 2 y 2 displaystyle nx 2 k 2 y 2 11 bhāgādāna edit contains factorization method 1 11 rules and 7 examples 1 12 rūpādyaṃśāvatāra edit contains rules for writing a fraction as a sum of unit fractions 22 rules and 14 examples 1 unit fractions were known in indian mathematics in the vedic period 3 the śulba sūtras give an approximation of 2 equivalent to 1 1 3 1 3 4 1 3 4 34 displaystyle 1 tfrac 1 3 tfrac 1 3 cdot 4 tfrac 1 3 cdot 4 cdot 34 systematic rules for expressing a fraction as the sum of unit fractions had previously been given in the gaṇita sāra saṅgraha of mahāvīra c 850 3 nārāyaṇa s gaṇita kaumudi gave a few more rules the section bhāgajāti in the twelfth chapter named aṃśāvatāra vyavahāra contains eight rules 3 the first few are 3 rule 1 to express 1 as a sum of n unit fractions 3 1 1 1 2 1 2 3 1 3 4 1 n 1 n 1 n displaystyle 1 frac 1 1 cdot 2 frac 1 2 cdot 3 frac 1 3 cdot 4 dots frac 1 n 1 cdot n frac 1 n rule 2 to express 1 as a sum of n unit fractions 3 1 1 2 1 3 1 3 2 1 3 n 2 1 2 3 n 2 displaystyle 1 frac 1 2 frac 1 3 frac 1 3 2 dots frac 1 3 n 2 frac 1 2 cdot 3 n 2 rule 3 to express a fraction p q displaystyle p q as a sum of unit fractions 3 pick an arbitrary number i such that q i p displaystyle q i p is an integer r write p q 1 r i q r displaystyle frac p q frac 1 r frac i qr and find successive denominators in the same way by operating on the new fraction if i is always chosen to be the smallest such integer this is equivalent to the greedy algorithm for egyptian fractions but the gaṇita kaumudī s rule does not give a unique procedure and instead states evam iṣṭavaśād bahudhā thus there are many ways according to one s choices 3 rule 4 given n displaystyle n arbitrary numbers k 1 k 2 k n displaystyle k_ 1 k_ 2 dots k_ n 3 1 k 2 k 1 k 1 k 2 k 1 k 3 k 2 k 1 k 3 k 2 k n k n 1 k 1 k n k n 1 1 k 1 k n displaystyle 1 frac k_ 2 k_ 1 k_ 1 k_ 2 cdot k_ 1 frac k_ 3 k_ 2 k_ 1 k_ 3 cdot k_ 2 dots frac k_ n k_ n 1 k_ 1 k_ n cdot k_ n 1 frac 1 cdot k_ 1 k_ n rule 5 to express 1 as the sum of fractions with given numerators a 1 a 2 a n displaystyle a_ 1 a_ 2 dots a_ n 3 calculate i 1 i 2 i n displaystyle i_ 1 i_ 2 dots i_ n as i 1 a 1 1 displaystyle i_ 1 a_ 1 1 i 2 a 2 i 1 displaystyle i_ 2 a_ 2 i_ 1 i 3 a 3 i 2 displaystyle i_ 3 a_ 3 i_ 2 and so on and write 1 a 1 1 i 1 a 2 i 1 i 2 a 3 i 2 i 3 a n i n 1 i n 1 i n displaystyle 1 frac a_ 1 1 cdot i_ 1 frac a_ 2 i_ 1 cdot i_ 2 frac a_ 3 i_ 2 cdot i_ 3 dots frac a_ n i_ n 1 cdot i_ n frac 1 i_ n 13 aṅka pāśa edit combinatorics 97 rules and 45 examples 1 generating permutations including of a multiset combinations integer partitions binomial coefficients generalized fibonacci numbers 2 narayana pandita noted the equivalence of the figurate numbers and the formulae for the number of combinations of different things taken so many at a time 4 the book contains a rule to determine the number of permutations of n objects and a classical algorithm for finding the next permutation in lexicographic ordering though computational methods have advanced well beyond that ancient algorithm donald knuth describes many algorithms dedicated to efficient permutation generation and discuss their history in his book the art of computer programming 5 14 bhadragaṇita edit magic squares 60 rules and 17 examples 1 editions edit translation of ganita kaumudi with rationale in modern mathematics and historical notes by s l singh principal science college gurukul kangri vishwavidyalaya haridwar ganita kaumudi volume 1 2 nārāyana pandita issue 57 of princess of wales sarasvati bhavana granthamala abhinava nibandhamālā padmakara dwivedi jyautishacharya 1936 references edit notes 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 m d srinivas mathematics in india lecture 27 1 2 3 4 5 6 m s sriram mathematics in india lecture 25 1 2 3 4 5 6 7 8 9 10 kusuba 2004 p 497 edwards a w f pascal s arithmetical triangle the story of a mathematical idea jhu press p 16 knuth donald 2006 the art of computer programming addison wesley p 74 bibliography kusuba takanori 2004 indian rules for the decomposition of fractions in charles burnett jan p hogendijk kim plofker et al eds studies in the history of the exact sciences in honour of david pingree brill isbn 9004132023 issn 0169 8729 m d srinivas m s sriram k ramasubramanian mathematics in india from vedic period to modern times lectures 25 27 external links edit ganita kaumudi part 1 1936 ganita kaumudi part 2 1942 ganita kaumudi and the continued fraction permanent dead link v t e indian mathematics mathematicians ancient apastamba baudhayana katyayana manava pāṇini pingala yajnavalkya classical āryabhaṭa i āryabhaṭa ii bhāskara i bhāskara ii melpathur narayana bhattathiri brahmadeva brahmagupta govindasvāmi halayudha jyeṣṭhadeva kamalakara mādhava of saṅgamagrāma mahāvīra mahendra sūri munishvara narayana parameshvara achyuta pisharati jagannatha samrat nilakantha somayaji śrīpati sridhara gangesha upadhyaya varāhamihira sankara variar virasena modern srinivasa ramanujan satyendra nath bose p c mahalanobis subrahmanyan chandrasekhar c r rao veeravalli s varadarajan s r srinivasa varadhan k r parthasarathy probabilist m s narasimhan c s seshadri harish chandra subbayya sivasankaranarayana pillai tilak raj prabhakar manjul bhargava akshay venkatesh ravi vakil kannan soundararajan shanti swarup bhatnagar prize recipients in mathematical science treatises aryabhatiya bakhshali manuscript bijaganita brāhmasphuṭasiddhānta ganita kaumudi grahalaghava kanakkusaram karanapaddhati līlāvatī lokavibhaga pātīgaṇita paulisa siddhanta paitamaha siddhanta romaka siddhanta sadratnamala siddhānta shiromani śulba sūtras surya siddhanta tantrasamgraha vasishtha siddhanta veṇvāroha yuktibhāṣā yavanajataka pioneering innovations brahmi numerals hindu arabic numeral system symbol for zero 0 infinite series expansions for the trigonometric functions centres kerala school of astronomy and mathematics jantar mantar jaipur new delhi ujjain varanasi historians of mathematics bapudeva sastri 1821 1900 shankar balakrishna dikshit 1853 1898 sudhakara dvivedi 1855 1910 m rangacarya 1861 1916 p c sengupta 1876 1962 b b datta 1888 1958 t hayashi a a krishnaswamy ayyangar 1892 1953 a n singh 1901 1954 c t rajagopal 1903 1978 t a saraswati amma 1918 2000 s n sen 1918 1992 k s shukla 1918 2007 k v sarma 1919 2005 translators walter eugene clark henry thomas colebrooke david pingree other regions babylon china greece islamic mathematics europe modern institutions indian statistical institute bhaskaracharya pratishthana chennai mathematical institute institute of mathematical sciences indian institute of science harish chandra research institute homi bhabha centre for science education ramanujan institute for advanced study in mathematics tifr retrieved from https en wikipedia org w index php title ganita_kaumudi oldid 1255912355 categories indian mathematics social history of india 1356 works 14th century in science 1350s books hidden categories articles with short description short description matches wikidata articles containing sanskrit language text all articles with dead external links articles with dead external links from december 2019 articles with permanently dead external links this page was last edited on 7 november 2024 at 07 14 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents ganita kaumudi 2 languages add topic