Index

abacus 427-8 see also counting grid

abstract number system, Egypt 121-2 AbU Kamil 146,148-50 Abil'I-Jild 153 Abil'I-Wara' al-BilzjanI 157, 161 abundant numbers 158-9 Abusir (Egypt) 118 accounting

ancient Iraq 100-4 Egypt 119-32 West Africa 345-72

addition fractions, Egypt 128-31 Yoruba number name formation 349 see also arithmetic

administration Egypt 116-18 see also bureaucracy

Africa Central 313-43 sources 313-14 Southern 313-43 West 345-72

African Americans 5 afterworld, sand patterns 267-268 aha (Egyptian mathematical unit) 122 Aida Yasuaki 429 Akinyele, A. B. 366-7 Akkadian 93 al-'AmilI, Baha' aI-Din 145 al-AntakI 162 aI-BaghdadI 159 al-BIrilnI, Abil Rayhan 153 al-FarabI 172 al-KarajI, Abil Bakr 141, 144, 160 al-KashI, Ghiyath aI-Din 140-1,158 al-Khazin 160

al-KhwarizmI, MuJ:tammad 9-10,139, 143-8

al-Ma'mun 157 al-Tilsl, Na~Ir aI-Din 157 al-UqlIdisl 139-40 algebra

ancient Iraq 108,111 geometric illustration 146-8, 175-7,

186 Hebrew tradition 173-87 identities 183-4 Islamic mathematics 143-50 Japan 429, 433-5 Madagascar 315 Mahavlra 417 word origin 145

algorithms algebraic 315 geometric 332-3 problem solving 123-5 word origin 139

Alhazen see Ibn al-Haytham alienation, mathematics education 19 Americas

colonization 87, 90 Inca 189-203 Sioux people 239-52 see also Mesoamerica

amicable numbers 158-9 angles

measurement 264-6 see also right angles

anthropology, mathematics and culture 13-22

Appollonius 138, 172 approximation formulas, Chinese

mathematical astronomy 401 Archimedes 138, 152, 158

467

468

architecture 104-6, 239-52 see also building

arctan series 420 area 236-7, 246-8 arithmetic

Egypt 125-7 India 138 Islamic mathematics 138, 139-43 Mahavira 416-17

arithmetic progressions 413 arithmology, Ibn Ezra 167-171 art

Asian influence 33 Australian aborigine 5-6, 7 mathematical intent 16-17 see also decorative arts; patterns

Aryabha!a 8,413-14 Aryabhatfya (Indian text) 414, 416 Asian influence, Western

civilization 23-35 astrolabes 157 astrology, China 379-380 astronomical tables

Chinese 399-400 Islamic 385 Maya 221

astronomy Babylonia 383 Chinese 373-407 epicyclic 401 geometry link 171 Inca 190 India 138, 384 Iraq 111 Kiribati 276 Mesopotamia 137-8 Pacific cultures 264-6 Portugal 86-7

asymptotes 172 Australia

colonization 290 education 55-8 see also Yolngu people

Australian aborigine art 5-6,7 mathematics 289-311

Aymara people (South America) 192 Aztec (Mesoamerican people) 87,231-7

Babylonia 93, 383 Baghdad 137 Bakshalf manuscript (Indian

text) 412-13 Banks Islands 258, 283 Baruya people, Papua New Guinea 4-5

base see number base basin metaphor, knowledge

production 82,88-9 basket weaving, Central and Southern

Africa 316-21 bayt al-l,1ikma (House of Wisdom) 137 Bernoulli numbers 435 betting 278 Bhaskara II 417-20 bias, history 83-4 biblical commentaries 167-9 Bfjagal}ita (Indian text) 417, 419 binary system 315, 462-3 binomial expansion 141-2 biological determinism, learning 19 bisexagesimal number systems 103 board game 278-81 body counting 258-9, 351 body painting 316 bones 313-14 Borneo

designs 272 Iban people 272,278-81 maps 274 straightening 261-2 sun elevation 264-5

bosho-ho (Japan) 434 botany 30, 32 Boyle, Robert 41 Brahmagupta 414-16,419-20 Briihmasphutasiddhanta (Indian

text) 414, 416 bricks 106 Buddhism 383 building

ancient Iraq 105-6 Pacific cultures 260-4 see also architecture

Bunge, Mario 46 bureaucracy

ancient Iraq 100-4 Inca 198 see also administration

burial sites 115-18

calculations, Maya 221-3 calculus 418 Calendar Round 208,210,214,233 calendars

Aztec 232 China 379, 380-1, 384-6, 388-99 Iraq 103 Korea 458,461-2 Maya 224 Muslim 385

calendars (continued.) Sacred Round 205-10,221,232 Zapotec 205-8 see also chronology

canoes 262-3 capacity 107 cardinal numbers 353 Caroline Islands 262-3, 274, 276 categorization, mathematics 431, 455-6 cat's cradle 266 census 366-7 centers of civilization 23, 29 Central America see Mesoamerica centroids 244 ceques (Inca lines) 190 ceremony 305-6

see also rites and rituals chance 278 charts 274-6 Chen Meidong 375 Chilam Balam (Maya books) 225 China

civilization 23,24-5 cultural contacts 383-8 education 425 history 31 literature translations 30 magic squares 446-7 Marco Polo 24-5 mathematical astronomy 373-407

calendar 388-99 historical and epistemological context 379-83 historiographical context 373-6 sources 376-9

mathematics 433 technology 25-6, 32

Chinese remainder theorem 395 Chokwe people (Africa) 332-9 Chouren zhuan (Chinese text) 378-9 Christianity 29, 32, 385-8 chronology

Chinese 373 epi-Olmec 210-12 Maya 213-14,218-25 Zapotec 207-8 see also calendars

chu (counting rods) 425 Chusok 458 Cieza de Leon, Pedro 192 cipher 139 circles

Ibn Ezra 169 Pacific cultures 262 Plains peoples 239-52

circumference, Earth 157 civilizations 23, 29 classification

Chinese mathematical works 433 concept 63 Japanese mathematics 431

clay tablets, Iraq 94-5, 102, 105, 107 climate 189-90 Closs, Michael P. 205-38 Codex Nuttall (Mesoamerican

text) 230-1 codices

Hebrew mathematics 172-3 Maya 212-13,215,217-18,221-4 Mesoamerican 230-1, 234-5

colonialism 64, 66, 359-65 colonization 90, 290 combinations see permutations and

combinations communication

experimental knowledge 41-2 Inca 192 mathematics 1-12

comparison, concept 63 compasses 25-26,461 Composition, Principle of 416 computistics 377 computus 381 Comteano, Mordecai 169 Conant, Levi 361-3 concepts, universal logic 63 cones 242-8 conic sections 156 construction, geometric 150-2, 410 constructivism see relativism context, indigenous systems 357 Cook Islands 272 cosine 138 counters, ancient Iraq 102 counting

body use 258-9,351 grid 199-202 rods 425 sticks 457 systems 4 see also accounting; number

cowrie shells 345 craft

Asia 32 experimental knowledge 42 see also decorative arts

cross-cultural comparisons 14-15, 19 cross-cultural contacts 79-80, 383-8 cube roots 140-141, 180-182 cubic equations 154-156

469

470

cubit 122 cuneiform 94-5 curriculum

Maya scribes 228-30 Yirrkala (Australia) 57-8 Yolngu people 74,293 see also education

curves, Pacific cultures 266-8 Cuzco 190 cylinder seals 97-100

D'Ambrosio, Ubiratan 79-92 dates see calendars; chronology Dayak people (Borneo) 265 Da;:an computus 393, 399 decImal system

India 409-10 Japan 427 Kiribati 255

decorative arts Chokwe people 332-9 Inca 190-1 Iraq 95-101 Pacific cultures 262, 271-4 Sotho people 324-33 Yombe people 322-9 see also patterns

dedecupling 127 defective numbers 158-9 deities

Aztec 232 Maya 214,225-7

Delambre, Joseph 374 Dhuwa (Australian aborigine

concept) 296 dibuinu see mabuinu dice 278, 456-7 differential calculus, Bhaskara II 418 ~iophantus 138, 143, 414 dIscourse, mathematical 1-9 divination 79

China 380 Iraq 109-11 Madagascar 315 see also magic squares· omens

divinity, Hebrew names ' 167-9 division

Rhind mathematical papyrus 126-7 see also arithmetic

divisor sum 158-9 doubling 126, 128-30 Dresden Codex 212-13, 215 217-18

221-4 "

East, Western knowledge 23-35 eclipses

China 380,382-3 Maya 221

economy, Inca 190 Edo period 427, 432 education

Egyptian scribes 119-20 ethnomathematics 19-20, 455-65 Iraq 106-9 Japan 425-6, 428 logic approaches 64 Yolngu people (Australia) 55-8 Yoruba people (Africa) 59-62 see also curriculum

Eglash, Ron 13-22 Egypt

mathematical sources 115-36 Rhind mathematical papyrus 120-31

endan-jutsu see tenzanjutsu endecagon 153-4 Endo Toshisada 447-8 engineering, Inca 189-90 environment 43,45, 189-90 epi-Olmec (Mesoamerican

people) 210-12 epicyclic astronomy 401 epistemology

Chinese astronomy 379-83 indigenous mathematics 15-17

equation solving geometrical illustration 146-8 India 412-13, 416, 419-20 Islamic mathematics 138, 144-8

154-6 ' Japan 428,433-4 Sumer 137

errors, Chinese astronomy 380 ethnomathematics 80 83

anthropological pers~ectives 13-22 Central and Southern African

decorative arts 339-40 Incas 190 Korea 455-65 Native American people 239-52

ethnoscience 80-3 etymology

algebra 145 algorithm 139 Yoruba number names 349-50,

354-5 zero 139

Euclid 138, 156-7, 158, 172 Europe

Asian knowledge 30-1 Chinese astronomy influence 385-8

experiment 41-2,47, 51

factors 349-50 false position 124 Fibonacci, Leonardo 9-10 Fiji 258, 285 flags 462, 464 floor patterns 100-1 Foucquet, Jean-Fran~ois 387-8 foundationism 66-8, 363-5 fractions

dimidiated 118 Egypt 128-31 Horus-eye 118 Mahavira 417 Pacific cultures 259 see also arithmetic

Freyle, Juan Diaz 87 Fujita Sadasuke 429, 436 funerary sources, Egypt 115-18

games Central and Southern Africa 315 counting sticks 457 dice 278, 456-7 Korean ethnomathematics 456-8 Pacific cultures 276-82 tangram 458

Ga~itasara Sa/igraha (Indian text) 416 ga!!ma (Australian aborigine

concept) 294 garland numbers 416-17 garma (Australia aboriginal

concept) 57-8 Gaubil, Antoine 373-4 Geertz, Clifford 43 gematriah (Hebrew hermeneutical

exercise) 168 geography, mathematics

influence 189-90 geomancy 461 geometry

algebraic problem illustration 146-8, 175-7,186

angle trisection 152 astronomy link 171 circles 169, 239-52, 262 cones 242-8 conic sections 156 cyclic quadrilaterals 415-16 Hebrew tradition 171-3 India 410-12 Islamic mathematics 138, 150-8 Maha vIra 417 Pacific cultures 260-76 patterns 96-101, 315-21 Sioux tipi 243-8

spheres 418 spherical 157,172-3 triangles 244-5, 415

Gerdes, Paulus 313-43 Gilbert Islands see Kiribati Gilsdorf, Thomas E, 189-203 glyphs

epi-Olmec 210-13

471

Maya number representation 213-16 Zapotec 207, 210 see also hieroglyph; petroglyph

gnomons 264,376 gods see deities Goladhyaya (Indian text) 417-18 Gomileroi people (Australia) 4 Grahaganita (Indian text) 418 Greek'heritage, Islamic

mathematics 138-9 Gregory Series 420 Gregory's Series 420 grid, counting 199-202 ground writing 267-8, 269 Guadalcanal (Melanesia) 283 Guaman Poma de Ayala, Felipe 192 gunpowder 25-6 gurru!u (Australian aboriginal

concept) 56-7,74,295-303

Halaf ware (Iraqi pottery) 96-7 halving 128 Han dynasty (China) 376, 379 Hauri people (South America) 192 Hawaii

designs 272 games 278,279,281-2 kinship terms 283 number system 255-6 string records 260 strip pattern symmetry 270

heavens 111 see also astrology; astronomy

Hebrew mathematics tradition 167-88 heptagon 152 heqat (Egyptian measurement unit) 118 Heron's formula 412 hexadecimal system 428 hexagrams 463 hieratic script 116-18 hieroglyphic 116-18 higher degree equations 428 Hindu-Arabic mathematics 26 Hinduism 31 Hipparchus 137 Hippocrates 173

472

historiography Chinese mathematical

astronomy 373-6 non-western mathematics 79-92

history Chinese astronomy 379-83 seventeenth century studies 30

Hobbes, Thomas 41-2 holography 368 horary characters 458,461-2 Horus (Egyptian mythological

figure) 118 huacas (Inca markers) 190 Huang Yilong 375 Huihui Ii (Chinese text) 385 hypotheses, science 49-50

I Ching (Yijing; Book of Changes) 401, 462-3

Iban people (Borneo) 272, 278-81 Ibn al-Haytham, al-I:Iasan 156-7, 172 Ibn Ezra, Abraham 167-71, 185-7 iconography, Maya 225-7 idai keisho 428 identities

algebraic 183-4 combinatorial 184-5

imagery, philosophy 69 Inca

empire 192-3 mathematics 189-203

India 409-22 Aryabhata I 413-14 astronomy 384 BakshiilI manuscript 412-13 Bhaskara II 417-20 Brahmagupta 414-16 civilization 23-4 early mathematics 26 influence on Islamic mathematics 138 MahiivIra 415,416-17 Sulbasfitras 410-12

indigenous societies, ethnomathematics 15-17

Industrial Revolution 33, 447 infinity 418 inheritance 104, 426 Initial Series (Maya chronolgical

statements) 213-15, 218-21, 224 institutions, scientific 42-3 integral calculus 418 interest rates 104 inversion 127 investment, science and technology 88 Iraq

anCient 93-113 bureaucracy and accountancy 100-4 decorative arts 95-101 divination 109-11 education 106-9 quantity surveying and

architecture 104-6 irrational numbers 148, 411-12 Ishango bone 313-14 Islam

mathematics 137-65 algebra 143-50 arithmetic 139-43 geometry 150-8 Greek heritage 138-9 Indian heritage 138 magic squares 160-2 Mesopotamian heritage 137-8 number theory 158-60

society 47 island metaphor 69-74 Israeli, Isaac 169

JabIr ibn Aflah 173 Japanese mathematics 423-55

classification 431 magic squares 435-47 Ritsuryo-Kakushiki age 424-7 Seki Takakazu 429-35 wasan age 427-47

Jesuits 30, 32, 385-8 Jiuzhang Suanshu (Chinese text) 430 Jochi, Shigeru 423-55 Juizhi Ii (Chinese text) 383-4 Jye~tadeva 420

Kant, Immanuel 58, 69-74 Kapingamarangi (Polynesia) 263 Karavindaswami 415 Kayan people (Borneo) 261-2,264-5 Kenyah people (Borneo) 264-5 Keraki people (Papua New

Guinea) 259 Kewa people (New Guinea) 257, 259 khar (Egyptian mathematical unit) 122 khipu see quipu Kim, Soo Hwan 455-65 kinship

Korea 458, 460 Pacific cultures 282-6 Yolngu people 56-7,295-303

Kiribati 255, 258, 276 knots and knotting

count recording 260 Inca quipus 194-5 Pacific cultures 266-7

knowledge basin metaphor 82, 88-9 creation 84-5 cycle 81, 85 indigenous societies 15-17 local 37-45 objectivity 48-50 rationality 45-8 scientific 82, 84-5 sources 48 traditions 291-2 transfer 88-9

konane 278 Korea 455-65 Kuhn, Thomas 42, 49 kuttaka (Hindu mathematics) 395,414

labor, ancient Iraq 103, 105 land

measurement 104-5,235-7 ownership, Australia 289-311 quantification 303-5 sacred sites 305-6

Langermann, Y. Tzvi 167-73 language

communication resource 2 logic 65 systems 359-60 Yoruba numeral use 353-5

Laplace, Pierre-Simon 374 lashing 267 Latour, Bruno 40-1 Le Dreuff, Michele 68-9, 71 leap months 396 Levi ben Gershon 171, 174-85 Liber abaci 9-10 lifa (Chinese texts) 377-8, 399-400 Liliivati (Indian text) 417 litema (African mathematics) 324-33 literacy, ancient Iraq 108-9 literature 29-30, 33 liver divination 109-10 loans 104 local knowledge 37-45 logic

disparate systems 293 kinship systems 296 and mathematics 55-78 objectification 68-74 relativism 62-3, 64-8 universalism 62-4, 66-8

Long Count epi-Olmec 210-12 Maya 213-14,218,225

Luba people (Africa) 5

lukasa (African geometry) 5 lunar parallax, tables 389-90 luni-solar calendars, Chinese 396 lunule 173 lusona see sona

Maaseh Hashev 174-85

473

mabuinu (African mathematics) 322-4 Madang people (Borneo) 274 Maenge people (Melanesia) 256 magic squares

bordered 160 China 446-7 composite 160-1 doubly even degree 441-2 Islamic mathematics 160-2 Japan 435-46 odd number degree 440-1 oddly-even degree 442-4 pandiagonal 160 stratiform pair method 437-8, 440

magnetic compass 25-6 Mahavlra 415,416-17 Maimonides 172 main mach an 278-81 Mangbetu people (Africa) 315-17 Mann, Adolphus 345, 358-9 Maori people 255, 269-71, 272 maps, Pacific cultures 274-6 marine technology 27, 32 Mariner, William 257-8 maritime power 28 Marquesas (Polynesia) 258 marriage customs, Pacific

cultures 283-5 marriage patterns 298, 302 Marshall Islands 274, 277 Martzloff, Jean-Claude 373-407 materials, ethnomathematics 455-65 Matsunaga Yoshisuke 429,434 Maya 212-30 measurement

angles 264-6 land 104-5,235-7

medicine 30, 32 Melanesia see Pacific cultures memory board 5 mensuration, Egypt 120-2 Mesoamerica 205-38

Aztec 231-7 epi-Olmec 210-12 Maya 212-30 Mixtec 230-1 Olmec 205 Zapotec 205-10

474

Mesopotamia 93, 137-8 metaphor

basin 82, 88-9 island 69-74 logic system basis 293-4

methodologies, scientific 50 metonic cycle 393-4 metrology 103-4, 107, 116-18 Mexico see Mesoamerica Micronesia see Pacific cultures migration, knowledge 25-7,40-2 minority groups 19-20 Mixtec (Mesoamerican people) 230-1 Moche people (South America) 191-2 modernism 45 Mokil people (Caroline Islands) 262-3 Mongol empire 24-5,384 monolinear designs 332-5, 338 month, Chinese calendar 393 Mota people (Banks Islands) 258, 283 multicultural education 20, 82 multiplication

Rhind mathematical papyrus 126-7 Yoruba number name formation 349 see also arithmetic

murals 324-33 Muslims 28, 385 mysticism 168 myth 79

Nakayama Shigeru 375 Native Americans, Sioux 239-52 natural language 2 natural number 360 navigation

Pacific cultures 274-6 Portuguese 86

Nazca lines (Peru) 192 Near Eastern civilization 23 Needham, Joseph 375 Negrito people (Philippines) 278 New Britain Island 256 New Guinea see Papua New Guinea New Zealand see Maori people Newton-Gregory formula 399 Nichomachus of Gerasa 138, 168 Nigeria see Yoruba people notation, additive system, Egypt 116 number, numeral distinction 356 number bases

two 315,462-3 four 257 five 257 ten

India 409-10

Japan 427 Kiribati 255

thirteen 221 sixteen 428 twenty 61

epi-Olmec 210 Maya 221 Polynesia 255 Yoruba people 346 Zapotec 207

forty 255-6 sixty 103 one hundred and twenty 103

number signs and symbols ancient Iraq 102 Aztec 233-4 Egypt 116 Maya 212-20 Mixtec 230 Zapotec 207 see also numerals

number systems abstract, Egypt 121-2 kinship system analogy 300-3 translation 357, 364, 367

number theory Hebrew tradition 167-71 Islamic mathematics 158-60

number words Baruya people 5 Gomileroi people 4 Inca 193-4 Kiribati 225 Polynesia 255-6 Yagwoia people 5 Yoruba 346-51

numbers abundant 158-9 amicable 158-9 Bernoulli 425 defective 158-9 garland 416-17 irrational 148, 411-12 perfect 158-9 ring 224

numeracy, ancient Iraq 108-9 numerals

number distinction 356 see also number signs and symbols

numerical speculation, Hebrew tradition 167-71

Nunes, Pedro 86

Oaxaca 205 objectification, Yoruba numeral

system 358, 363-4

objectivity, knowledge 48-50 Olmec (Mesoamerican people) 205 Omar Khayyam see 'Vmar Khayyam omens 109-10

see also divination opposites, Chinese texts 401 oral tradition, numeration 353 ordinal numbers 353, 354 Orey, Daniel Clark 239-52 outriggers 262-3

Pacific cultures 253-87 games 276-82 geometry 260-76 numeration 254-60 relations 282-6

Papua New Guinea 272, 273 counting systems 4-5 Kewa number words 257 tallying 259

papyri, Rhind mathematical papyrus 120-31

parallel lines, Pacific cultures 262-3 Pascal triangle 141-2,435 patterns

body painting 316 geometric 96-101, 315-21 Inca 190-1 marriage 298, 302 Pacific cultures 271-4 weaving 317-29 see also decorative arts; strip patterns;

symmetry pedagogy 18-21 Pell's equation 416,418-20 Pentecost Island (Vanuatu) 283-5 perfect numbers 158-9 perimeter, tipi base 247 permutations and combinations 184-5

Bhaskara II 418 Mahavlra 417

petroglyphs 314 philosophy, imagery 69 pi

ancient India 413 Chinese approximation 377 determination

Hebrew mathematics 169-70 Islamic mathematics 158

piecewise functions 400 place value

epi-Olmec 211 Inca quipu 195-7 Iraq 103-4 Islamic mathematics 139

zero 352-3 Plains Indian people 239-52 plurality 367-70 politics 289-92 Polo, Marco 24 polygons 150-4 Polynesia see Pacific cultures Popper, Karl 49 porcelain 27 Portugal 86 postcolonialism 66 pottery

Iraq 95-7 Maya 227-9

power maritime 28 Western science 43

practice, science 51

475

prediction, astronomical events 380-3 pRhind see Rhind mathematical papyrus Principle of Composition 416 printing 25-6 problem solving

Egypt 124-7 Iraqi education 108 science 42

problems of the birds 149-50 problems of the tens 145 proofs 8 Ptolemy 137-8, 399 Puttaswamy, T.K. 409-22 puzzles 281 Pythagorean theorem 376, 410-11

Qin liushao 395 Qing dynasty (China) 379 Qiyao ranzai jue (Chinese text) 384 quadratic equations 413 quadripod 243-5 quantification

concept 63 land 303-5 Yoruba people 356

Quechua (Inca language) 194 quilt making 5 quipu (Inca mathematical

device) 194-199

Ramanujan, Srinivasa 420 rationality

assumptions 52 desiderata 46 and disunity of sciences 37-54 science 45-8

realism see universalism reciprocity 302-3

476

record keeping Inca quipu 194-8 Pacific cultures 259-60

recursion kinship and number systems 300-2 numeration systems 351, 370

relations one-to-many 368 Pacific cultures 282-6 Yolngu people 295-303 see also kinship

relativism 363-5 logic 62-3, 64-8

religion 30, 167-9 see also Buddhism; Christianity;

Hinduism; Islam Rhind mathematical papyrus

(pRhind) 120-31 right angles 263-4, 415 ring numbers, Maya 224 ri tes and rituals

crop counting 259-60 Inca 190 Yolngu people 291,305-6

Ritsuryo-Kakushiki age (Japan) 424-7 Ritter, James 115-36 Robson, Eleanor 93-113 rock carving 6, 7 root extraction

ancient India 411-13 Islamic mathematics 140-1 Levi ben Gershon 175-83

Ruan Yuan 378

Sacred Round 205-10,221,232 sacred sites 305-6, 309 Sacrobosco, Johannes de 86 Sahagun, Fray Bernardino de 87 Samarra ware (Iraqi pottery) 96 samasa (Indian mathematical

principle) 416 Samoa 258, 272, 282-3 sand drawings 267-8, 269, 332-9 Sangaku Hono (Japanese mathematical

tablets) 429 Sanskrit literature 30 Saqqara (Egypt) 118 Schall von Bell, Adam 387 science 45-51

Asian 26-7, 32 disunity 37-54 knowledge categories 82 knowledge creation 84-5, 88 local knowledge 37-45

scribes Egypt 118-20 Iraq 107-9 Maya 227-30

sea trade 28-9 seasons 264-6 Sefer ha-El:zad (Book of the One) 167,

170-1 Sefer ha-Mispar (Book of the

Number) 167,171,185-7 Sefer ha-Shem (Book of the Name) 167,

169 Seki Kowa see Seki Takakazu Seki Takakazu 428,429-35,438-40 Seki-ryu school (Japan) 431 series 142 Sesake people (Vanuatu) 257 Sesiano, Jacques 137-65 sexagenary cycle

Chinese calendar 38893 Korean calendar 458-62

sexagesimal place value system (SPVS) 103-4

sexagesimal systems ancient Iraq 103 Mesopotamia 138

Short Count, Maya 225-6 Shoushi Ii (Chinese text) 373-4, 379,

393, 398 Shu Shu Jiu Zhang (Chinese text) 424,

433 Shushu jiuzhang (Chinese text) 395 Siddhiinta Sironmm:li (Indian text) 417 silk 27 Simonson, Shai 173-87 sine 138, 157,414 singularity 367-70 Sioux people (North America) 239-52 Sizer, Walter S. 253-87 social foundation, logic 64-74 social status, sand patterns 267 Society Islands 272 Society of Jesus see Jesuits sociology, scientific knowledge 37-45 sociopolitics, cthnomathematics 17-18 solar calendar, China 384 Solomon Islands see Vanuatu sona (African geometry) 332-9 Song dynasty (China) 381,433 Sotho people (Africa) 324-33 sources

Africa 313-14 Chinese mathematical

astronomy 376-9 Egyptian 115-36

sources (continued.) ethnomathematical materials 462-4 knowledge 48

South America, Incas 189-203 spears 261 sphaerics see spherical geometry spheres, Bhaskara II 418 spherical geometry

Hebrew mathematics 172-3 Islamic mathematics 157

spirituality, Sioux people 241 SPVS see sexagesimal place value system square root

ancient India 411-13 Babylonian method 175-7 Ibn Ezra 185-6 Islamic mathematics 140-1 Levi ben Gershon 177-80

star charts 276 status

Egyptian scribes 118-19 mathematicians

Inca 197, 198 Japan 426 Maya 228

straight lines 260-2 strategy

Egyptian problem solving 124-5 games 278-81

string figures 266 string records

Hawaii 260 Inca 194-8

strip patterns Central and Southern Africa 317-19 Inca 191 Maori people 269-70 symmetries 268-70

structure, Inca quipu 197-8 subtraction

Yoruba number name formation 349 see also arithmetic

sugaku (Japanese mathematics) 423-4, 447

Sulbasiitras 410-12 Sumer 93, 137 summation 142,413 sun, angle of elevation 264-5, 376 Sunzi suanjing 395 Superior Epoch (Chinese mathematical

astronomy) 395-6 surveying 104-6 Swazi people 319-20 symbolic language 2, 8-9 symmetry

ancient Iraq 97-101 Chokwe sona designs 332-4 Inca patterns 191 Pacific cultures 268-71 rotational 319-20 Sotho litema patterns 327-8 Yombe designs 323-4

tables astronomical 221, 385, 399-400 fractions 128-31

Tahau people (Pentecost Island) 285 Tahiti 258 Tahuatinsuyu 192 Takahara Yoshitane 430 Takebe Katahiro 379, 429, 445-6 tallying

number origins 297 Pacific cultures 259-60

Tami people (Melanesia) 271, 272 Tanaka Y oshizane 444 Tang dynasty (China) 383 tangram 458-9 Tanzania 317 Tasmania 6, 7 taxation 198, 260 technology

Asian 26-7, 32 early Chinese 25 migration from East 25-7

teepee see tipi tema see litema temples

ancient Iraq 102, 105 Aztec 235 Egypt 118

tengenjutsu (Japanese mathematical system) 424, 428

tenzanjutsu (Japanese mathematical system) 431, 433-4, 439

tetragrammaton 167-9 textbooks

Egypt 119-32 Japan 425

Thiibit ibn Qurra 158-9, 172 theology, geometry link 171 theorems 8-9,410 theories, scientific 49-50 tianyuanshu (Japanese mathematical

system) 428, 434 time

Chinese calendrical calculations 391-4

see also chronology tipis 239,241-8

477

478

tombs 115-19 Tonga 257-8,316-18 Torah 167-9 Torres Straights 274 Toy, C.H. 359 trade, east/west 28-9 translation

interpretations 8 metaphors 294 number systems 357, 364, 367 singularity/plurality 367-8

travel 24-5, 28-30 tree structure, quipu 198 triangles

right angled 415 Sioux tipi 244-5

trigonometry Bhaskara II 418-19 India 138 Islamic mathematics 138, 157

trigrams 462 tripods 243-5 trisection, angle 152 Turnbull, David 37-54 Tuvalu 258

Uganda 317-19 (Umar Khayyam 154-6, 157 unilineal development model 13-15 units

Chinese time measurement 393 Egyptian metrology 122

universalism 362-5 logic 62, 63-4, 66-8

universality, science 37-40

Vague Year 207-8 values

Aboriginal 240 Egyptian number signs 116

Van Kley, Edwin J. 23-35 Vanuatu 257, 267-9, 283-5 vargaprakriti (Pell's equation) 416,

418-20 vectors 306, 308 Venus 224 Verran, Helen 55-78,289-311,345-72 vigesimal number systems 61

epi-Olmec 210 Maya 221 Polynesia 255 Yoruba people 346 Zapotec 207

votive tablets 429 voyages of discovery 27-8, 86

wall decoration 316, 324-33 wasan (Japanese mathematics) 423-55 weather 189-90 weaving

Central and Southern Africa 316-29 hexagonal 321 Yombe people 322-9

Weber, Max 47 weights and measures, ancient Iraq 107 West, Asian influence 23-35 West Africa, Yoruba number

system 345-72 wigwams 241 winter solstice 396-8, 401 Wittgenstein, Ludwig 46 Wood, Leigh 1-12 work rates 103, 105 world views 240 writing

Egypt 116 epi-Olmec 210 Oaxaca 205 Olmec 205

Wuxing zhan (Chinese manuscript) 376

Yabuuchi Kiyoshi 375 Yagwoia people (Papua New

Guinea) 4-5 Yang Hui Suan Fa (Japanses text) 435 year bearers (Mesoamerican chronologic

reckoning) Aztec 232-3 Mixtec 230 Zapotec 207-8

Yijing (I Ching; Book of Changes) 401, 462-3

yin-yang (Chinese theory) 396-7 Yirritja (Australian aborigine

concept) 296 Yirrkala (Australia) 55-8, 292-3 Yolngu people (Australia) 55, 292-3

art 5-6 curriculum 74 kinship patterns 295-303 sacred sites 305-6

Yombe people (Africa), mabuinu designs 322-9

Yoruba people (Africa) 75 education 59-62 number system 61, 345-72

language use 353-5 number names 346-51

Yoshida Mitsuyoshi 428 Yuan dynasty (China) 433 yupana (Inca mathematics) 199-202

Zambales people (Philippines), game of chance 278

Zanzibar, weaving 319 Zapotec (Mesoamerican people) 205~ 10 zero

ancient India 409 Bhaskara II 418 Hebrew mathematics 170 Incas 195

Maya 217~18

origin 139, 352~3 Yoruba number system 352

Zhang Peiyu 375 Zhoubi suanjing (Chinese text) 376 Zhu Zaiyu 381, 398 Zoquean 210 Zu Chongzhi 377

479