Abhidharma-Kosa, 34–36 Abraham, George, 107 Acyuta, 154

Index

Abhidharma-ko´sa, 34–36 Babylonia, 76, 107 Abraham, George, 107 Bakhsh¯al¯ıManuscript,203 Acyuta, 154 Baudh¯ayana, 163 Agnicayana, 64, 65 Baudh¯ayana-´sulbas¯utra, 63, 65 Ahor¯atra, 80, 88 Bengal rule, 14 Aks.ara, 123 Bessarion, 136 al-Karkh¯ı, 142 Bhagan. a, 126 al-Tabari, 142 Bhagavadg¯ıt¯a, 55 Alaja bird, 71 Bharata Muni, 115 Alarkand, 188 Bh¯askara I, 38, 44, 141, 153, 204 Alcuin, 42, 136 Bh¯askara II, 112, 138, 153, 154, 206 Algorithm of extraction, 178 Bh¯askar¯ac¯arya II, 59, 104 Almagest, 154, 174, 175 Bh¯as.ya, 155, 158 Alp¯avayavatvam, 159 Bhatta, Hal¯ayudha, 121, 122 Ambu-Yantra, 103, 104 .. Bhattotpala, 153 Ancient China, 177 .. B¯ıjaganita, 138, 164, 168 Angulas, 40 . . B¯ıj¯a˙nkura, 164 Anustup, 124 .. Bloom of Thymaridas, 143 Anusv¯ara, 124 Boethius, 135 Apabhram. ´sa, 204 Apastamba-´¯ sulbas¯utra, 64, 68 Bombelli, Rafaello, 137 Apprenticeship Bombieri, 60 of a Mathematician, 56 Boole, George, 132 Archimedes, 58, 139 Bourbaki, 55 Ardhasamavr.tta, 125 Boyer, Carl, 136 Arithmos, 144 Brahma-sphuta-siddh¯anta, 185, 186 Artha´s¯astra, 84, 105 Brahmagupta, 2, 60, 92, 109, 138, 153, Aryabhat¯ .aI,140, 153, 157 204 Aryabhat¯ .¯ıya, 139, 158, 168, 204 Brahmaloka, 65 Asannah¯ . , 158 Brahmasphut.a Siddh¯anta, 92, 138 A´soka, 33 Br.hatsamhit¯ ˙ a, 90 Atharvaveda, 76 Buddhist works, 34, 43 Avyakta, 167 Buddhivil¯asini, 166 214 Index

Calendars, 1 Divy¯avad¯an, 100 Ahargan. a, 1, 4 Dron. a, 79, 80 Chinese, 16, 193, 199 Dv¯apara, 88, 90, 96 Chiuchi, 45, 47, 54 Dvivedi, Sudhakar, 93 Coptic, 4, 8 Diurnal, 1, 3 Easter, 16 French Revolutionary, 4 Epanthema, 138, 146–148 Gregorian, 4 Equation of time, 24 Hebrew, 2, 16 Ethnomathematics, 207 Indian, 52 Euclid’s Elements, 154, 171 Islamic, 2 Euler, 57, 58 Julian, 4, 8 Extraction, 180 Lunar, 2 Lunisolar, 2, 16 False position, 177 Madhyama, 2 Fermat, 57 Mainland Southeast Asian, 193 Fibonacci sequence, 112, 118 Modiﬁed Fibonacci, Leonardo, 142 Taichu, 198 Fleet, J. F., 100 Persian, 4 Saura, 1, 4 Gadya, 123 Solar, 1, 4, 11 Gan. e´sa’s, 167 Tai, 199 Gan. ita S¯ara Sangrha, ˙ 133 Tibetan, 2, 16 Gan. it¯aBh¯arati, 156 Vietnamese, 193 Gan. itakaumud¯ı, 154, 205 Cantor, Moritz, 138–140, 147 Gan. italat¯a, 204 Cartan, H., 55 Gan. itas¯ara, 154, 205 Caturacint¯aman. i, 203 Gan. itas¯arakaumud¯ı, 205 Cauchy–Stolz, 163 Gan. itas¯arap¯at.¯ıkaumud¯ı, 205 Chahal, J. S., 58, 59 Gan. itas¯arasam. graha, 141, 206 Chandas, 122, 123 Geber, 137 Chandas S¯´astram, 121, 127, 133 Gerard of Cremona, 136 Chandogya Upanishada, 56 Giridharabhat.t.a, 203 Chang, 39 Gnomon, 101, 105, 108 Chhih, 38, 39 Golap¯ada, 165 Chinese astronomy, 45 Golas¯ara, 154, 156 Chiu Chang Suan Shu, 37, 39, 43 Gop¯ala, 113 Chiu Chih Li, 37 Gou–Gu method, 53 Cocker, Edward, 209 Govindasv¯amin, 153, 155, 168 Colebrooke, 58, 138, 201 Colebrooke, H. T., 188 Hal¯ayudha, 113 Cossali, Pietro, 137 Hankel, Hermann, 138 Cycle of intercalation, 196, 198 Harappan Civilization, 66 Haridatta, 153 Dan. d.¯ı, 122 Hayashi, Takao, 203 Datta, B., 58 Hemacandra, 113 Dr.ggan. ita, 165 Hem¯adri, 208 Deligne, P., 60 Heron of Alexandria, 172 Diophantus, 137, 138, 148 Hindu astronomy, 195, 196 Dirichlet, 59 Hindu holidays, 22 Index 215

Høyrup, J., 71, 137, 149 Legendre, 57 Hui, Yang, 114 Leibniz, Gottfried, 132 Hunger, Hermann, 76 Levy, Sylvain, 55 L’huiller, 163 I-Hsing, 43, 44 L¯ıl¯avat¯ı, 133, 138, 159, 201 Iamblichus, 143, 145–148 L¯ıl¯avat¯ıvy¯akhy¯a, 163 Loyang monastery, 34 Jagan. a, 126 Lunis, Guglielmo de, 136 Jagann¯atha, 154 J¯ati, 125 Maceda, José, 111, 119 Jia Xian-Triangle, 180 M¯adhava, 154 Jñ¯anar¯aja, 154 Magic squares, 205 Josephus problem, 210 Mah¯abh¯arata, 55 Journal Asiatiques, 139 Mah¯abh¯askar¯ıya, 155 Jy¯a, 156 Mah¯abh¯askar¯ıya, 155 Jyes.t.hadeva, 154 Mah¯av¯ıra, 141, 142, 145, 153, 206 Jyotpatti, 154 Mah¯av¯ır¯ac¯arya, 108, 133 Mahidhara, 166 Kak, Subhash, 133 Malayali rule, 13 Kal¯a, 81, 82 Manusmr.ti, 86, 89 Kalid¯asa, 56 M¯atanga-Avad¯ ˙ ana, 35 Kamal¯akara, 154, 169 M¯atr¯a, 125 Kap¯alaka-Yantra, 103, 104 Meghad¯uta, 55 Karan. ams, 203 Meru-Prast¯ara, 112 Karan. apaddhati, 160, 169 Mesha Sam. kr¯anti, 15 K¯asth¯a, 81 Mesopotamia, 77 Kautilya, 84–86, 99, 106, 107, 109 Mount Meru, 112, 114, 116 K¯avy¯adar´sa, 122 Muh¯urta, 80 K¯ayasthas, 203 Mun¯ı´svara, 154, 168, 169 Kaye, George Rusby, 140 Muñj¯ala, 153 Ked¯ara, 113 Kerala rule, 13 N¯ad.¯ı, 76, 78, 88, 105 Kern, Hendrik, 139 Nagan. a, 126 Khan.d. a-Kh¯adyaka, 185, 188 N¯aland¯a, 34 Kr.s.n. aDaivajña, 164, 168 N¯ar¯ayan. a, 159, 205 Kriy¯akramakar¯ı, 163 N¯ar¯ayan. aPan. d. ita, 114, 154 Kriy¯akramakar¯ı, 159, 160 Nas.t.a, 127, 128 Ks.an. a, 84 Necklace numbers, 206 Kshaya, 22 Nemore, Jordanus de, 135 Kshemendra, 122 Nesselmann, Kudava, 79 Georg Heinrich Ferdinand, 145 Kusumapura, 87 Neufert, Ernst, 112 Nichomachus of Gerasa, 135, 143 Lagadha, 76, 77, 98 N¯ılakan. t.ha, 154, 156, 159 Laghu, 123 Nine Chapters on Lagrange, 57, 59 the Mathematical Art, 53 Lalla, 153, 168 Niravayavatvam, 159 Lank¯a, 90 Nirbhr¯anta, 167 Le Corbusier, 112 Nir¯ıks.an. aPar¯iks.an. am, 165 216 Index

Nity¯ananda, 154 Riemann hypothesis, 57, 60 Nr.simha Daivajña, 168 Riese, Adam, 209 Rodet, Léon, 139, 140, 147 Ohashi,ˆ Y., 90, 104 Rule of Three; Five, 204 Orissa rule, 13 Sadratnam¯al¯a, 159 P¯ada, 125 Sagan. a, 126 Padya, 123 Sam¯asa, 187 Padyak¯avya, 122 Samavr.tta, 125 Pali, 34 S¯amr¯at, 154 Pañcavim. ´satik¯a, 203 Sangamagr¯ ˙ ama, 154, 159 P¯an. ini, 121 Sangraha ˙ Sloka,´ 168 Parame´svara, 154, 163, 165 Sankalita, ˙ 163 Par¯ardha, 160 Sa´ nkara, ˙ 159, 168 Pascal, Blaise, 114 Sa´ nkara ˙ V¯ariyar, 154, 159 Patanjali, ˙ 83 Sa´ nkaran¯ ˙ ar¯ayan. a, 153 P¯at.¯ıgan. ita, 203 Sankhya, ˙ 163 Patna, 84, 87 Sanku-Yantra,´ 77, 105, 107 P¯avul¯uri Mallana, 206 Sarasvat¯ı, P¯avul¯urigan. itamu, 206 Svam¯ı Satya Prakash, 78 Pell’s equation, 58 Sarma, R. S., 133 Pell, John, 58 Satapatha-Br¯´ ahman. a, 66 Pher¯u, 204, 205 Savai R¯aj¯a Pheru, Thakkura, 154 Jai Singh, 108 Phulwari, Shar¯ıf , 87 Seidenberg, 67 Pingala, ˙ 112, 125, 127, 128, 130, 131 Serre, Jean-Pierre, 57 Pingree, David, 66, 72, 76, 109 Shukla, K. S., 93, 94 Plofker, Kim, 188 Siddha Gautama, 43, 45 Prakrits, 201 Siddh¯anta Pr¯an. a, 91, 94 -Sarva-Bhauma, 154, 169 Prastha, 78, 79 Siroman´ . i, 168 Proto-algebraic, 144 Tattva Viveka, 169 Protoalgebraic, 140, 145 D¯ıpika, 155 Pr.th¯ud. akasv¯amin, 153 R¯aja, 154 Ptolemy, 154, 172 sundara, 154 Putumana, 154, 160, 169 Tattva Viveka, 154 Singh, A. N., 58 Quadrivium, 135 Sis´ .yadhivr.ddhida Tantra, 168 Ragan. a, 126 Skandasena, 153 Ramchandra, Master, 211 Solar and lunar eclipses, 186 Ramus, 137 Square-Nature Realistic falcon, 68 (Varga-Prakrti), 58 Recreational mathematics, 207 Sr¯´ ıdhara, 153, 203 Rectangular falcon, 65 Srimala Jainas, 203 Regiomontanus, 136, 149 Sr¯´ ıpati, 153 Rekh¯agan. ita, 154 Stevin, Simon, 137 R. gjyotis.a, 77, 80, 81 Subha´ nkara, ˙ 208 Rhythmomachia, 136 Sulbas¯´ utras, 63, 64, 162 Index 217

Suri, Mahendra, 154 V¯asis.t.ha-Siddh¯anta, 105 S¯urya-Siddh¯anta, 2, 44, 79, 86, 95, 96 Vat.a´sren. i, 154, 165 S¯uryadeva, 153, 168 Vat.e´svara, 153, 155 Suvr.ttatilaka, 122 V¯ayu Pur¯ana, 100 Ved¯a˙nga Jyotis.a, 76, 107 Table R sin θ, 53 Ver Eecke, Paul, 144 Taittir¯ıya-sam. hit¯a, 64 Vi`ete, Fran¸cois, 137 Tamil rule, 13 Vin¯adi, 89, 91 Tang Dynasty, 47–50 Virah¯anka, 113 Tantrasangraha, ˙ 160, 168 Vossius, Isaac, 137 Tavernier, 208 Vr.tta, 125 Theon of Alexandria, 172 Vy¯akhya, 168 Thibaut, George, 93, 139 Vyakta, 167 Thymaridas, 148 Vy¯asa, 83, 84 Tithis, 20 Vyastavidhi, 165 Tret¯a, 90, 96 Tri´satik¯a, 203 Wallis, John, 137 Tr.kkut.t.aveli, 154 Weil, Andr´e, 55, 57, 58, 60 Wilson, Ervin, 112, 114, 116 Udayadiv¯akara, 153 Uddis.t.a, 131 Xing, Yi, 47, 50–53 Ujjain the centre of ancient Indian Yadav, B. S., 56 science, 185 Yagan. a, 126 Utpatti, 154 Yajus.jyotis.a, 77, 82 Yantrar¯aja, 154 Vallabha Gan. aka, 204 Yoga-Sutra, 83 Varah. mihira, 43, 102, 104, 153 Yuan Chwang, 34 Varasankalita, ˙ 163 Yuga, 81–83, 89 ´ Varman, Sankara, ˙ 154, 159–161 Yuktibh¯as.¯a, 156, 160, 163 Varn.ic, 125 Yuktid¯ıpika, 160, 168 expansion, 128 Meru, 132 Zeising, Adolf , 112 Prast¯ara, 127 Zero (Pujyam), 211 Vr.itta, 126 Zhou Bi Suanjing, 178