Knowledge (XXG)

Egyptian numerals

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script used a different numeral system, using individual signs for the numbers 1 to 9, multiples of 10 from 10 to 90, the hundreds from 100 to 900, and the thousands from 1000 to 9000. A large number like 9999 could thus be written with only four signs—combining the signs for 9000, 900, 90, and 9—as
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opposed to 36 hieroglyphs. Boyer saw the new hieratic numerals as ciphered, mapping one number onto one Egyptian letter for the first time in human history. Greeks adopted the new system, mapping their counting numbers onto two of their alphabets, the Doric and Ionian.
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In the oldest hieratic texts the individual numerals were clearly written in a ciphered relationship to the Egyptian alphabet. But during the Old Kingdom a series of standardized writings had developed for sign-groups containing more than one numeral, repeated as
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practiced. However, repetition of the same numeral for each place-value was not allowed in the hieratic script. As the hieratic writing system developed over time, these sign-groups were further simplified for quick writing; this process continued into
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of the original Egyptian numbers. A breve (˘) in some reconstructed forms indicates a short vowel whose quality remains uncertain; the letter 'e' represents a vowel that was originally u or i (exact quality uncertain) but became e by Late Egyptian.
1099:(and even vertically). In this example the symbols decrease in value from top to bottom and from left to right. On the original stone carving, it is right-to-left, and the signs are thus reversed. 3244: 1602: 1541: 1488: 1435: 1346: 753:
from around 3000 BC until the early first millennium AD. It was a system of numeration based on multiples of ten, often rounded off to the higher power, written in
2824: 2850: 1717:, rather than being carved into hard stone (as were hieroglyphic texts), the vast majority of texts employing the Egyptian numeral system utilize the 3237: 2922: 710: 3303: 3151: 2979: 430: 3211: 2738: 2717: 3384: 3230: 3097: 1175:(and at other sites), nefer is used to indicate a ground level: height and depths are measured "above nefer" or "below nefer" respectively. 3315: 2969: 2964: 2845: 2817: 263: 2787: 1777:
The following table shows the reconstructed Middle Egyptian forms of the numerals (which are indicated by a preceding asterisk), the
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Hieratische Paläographie: Die Ägyptische Buchschrift in ihrer Entwicklung von der Fünften Dynastie bis zur römischen Kaiserzeit.
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Multiples of these values were expressed by repeating the symbol as many times as needed. For instance, a stone carving from
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Hoffmann, Friedhelm (2024-03-11). "Aspects of Zero in Ancient Egypt". In Gobets, Peter; Lawrence Kuhn, Robert (eds.).
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This was, however, uncommon for most numbers other than one and two and the signs were used most of the time.
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3 vols. 2nd ed. Leipzig: J. C. Hinrichs Schen Buchhandlungen. (Reprinted Osnabrück: Otto Zeller Verlag, 1965)
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form of numerals stressed an exact finite series notation, ciphered one-to-one onto the Egyptian alphabet.
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If the denominator became too large, the "mouth" was just placed over the beginning of the "denominator":
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as a placeholder in Egyptian numeration and zero was not used in calculations. However, the symbol
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script. Instances of numerals written in hieratic can be found as far back as the
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are a particularly important corpus of texts that utilize hieratic numerals.
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could also write out numerals as words phonetically, just like one can write
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The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition)
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Middle Egyptian: An Introduction to the Language and Culture of Hieroglyphs
2497: 2263: 2165: 3013: 2682:. Cambridge: Cambridge University Press. Numerals discussed in §§9.1–9.6. 1741: 1718: 1714: 766: 1839: 1736:
A comparative chart of Egyptian numerals, including hieratic and demotic
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The Origin and Significance of Zero: An Interdisciplinary Perspective
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Egyptian Grammar; Being an Introduction to the Study of Hieroglyphs
2689:. 3rd ed. Oxford: Griffith Institute. For numerals, see §§259–266. 2286: 1987: 1794: 1731: 1147: 390: 352: 313: 1187:
contained a "zero concept" replacing the magnitude in geometry.
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Two famous mathematical papyri using hieratic script are the
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As administrative and accounting texts were written on
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The Egyptians had no concept of a 3207: 2774: (archived September 29, 2007) 1142:There was no symbol or concept of 14: 2935:Ancient Egyptian race controversy 2685:Gardiner, Alan Henderson (1957). 2204:mḏwtt, ḏwtt, or ḏbꜥtt (?) (fem.) 1597:{\displaystyle ={\frac {1}{100}}} 1216:of positive integers, except for 3206: 3196: 3186: 3177: 3176: 3165: 3128: 2794: (archived January 12, 2004) 1630:), for instance, was written as 3197: 1740:Boyer proved 50 years ago that 1669: 1632: 1550: 1536:{\displaystyle ={\frac {3}{4}}} 1483:{\displaystyle ={\frac {2}{3}}} 1430:{\displaystyle ={\frac {1}{2}}} 1385: 1363:and for the non-unit fractions 1341:{\displaystyle ={\frac {1}{3}}} 1292: 1238: 1027: 2733:. Princeton University Press. 1353:Special symbols were used for 1168:, it indicated a zero balance; 16:Numerals used in Ancient Egypt 1: 3396:Category:Egyptian hieroglyphs 2784: (archived March 4, 2001) 1159: 3380:List of Egyptian hieroglyphs 2202:, ḏwtj, or ḏbꜥty (?) (masc.) 813: 3120:Egypt–Mesopotamia relations 2940:Population history of Egypt 2574:. University of St. Andrews 1812:Reconstructed vocalization 1763:Moscow Mathematical Papyrus 1025:shows the number 4,622 as: 3447: 2678:Allen, James Paul (2000). 2649:Callender, John B. (1975) 1773:Egyptian words for numbers 1767:Rhind Mathematical Papyrus 1194: 1117:beautiful, pleasant, good 431:Non-standard radices/bases 3393: 3160: 3137: 3126: 2864: 2841: 2710:10.1163/9789004691568_007 2704:. Brill. pp. 64–81. 2662:Loprieno, Antonio (1995) 1822: 1814: 1811: 1803: 3172:Ancient Egypt portal 2696:. Baltimore: Halgo, Inc. 2694:Old Hieratic Paleography 2692:Goedicke, Hans (1988). 2030:sjst or jst (?) (fem.) 687:List of numeral systems 3364:Category:Egyptologists 2753:Möller, Georg (1927). 2360:, ḫmnw, or ḫmnwjw (?) 2336:, sfḫw, or sfḫwjw (?) 2210:*(mu)ḏawā́taj (masc.) 1737: 1598: 1537: 1484: 1431: 1373:and, less frequently, 1342: 745:The system of ancient 726:This article contains 3359:List of Egyptologists 2846:Glossary of artifacts 2798:Egyptian Math History 2727:Joseph, G.G. (2011). 2506:one hundred thousand 2312:, sjsw, or jswjw (?) 1735: 1723:Early Dynastic Period 1599: 1538: 1485: 1432: 1343: 55:Hindu–Arabic numerals 3431:Egyptian mathematics 3416:Egyptian hieroglyphs 3332:Gardiner's sign list 3254:Egyptian hieroglyphs 2549:Egyptian mathematics 2207:*ḏubā́ꜥataj (masc.) 1578: 1517: 1464: 1411: 1322: 1276:1, and the positive 1004:(also called lotus) 954:Gardiner's sign list 584:Prehistoric counting 360:Common radices/bases 42:Place-value notation 2992:Cursive hieroglyphs 2568:"Egyptian numerals" 1831:per Callender 1975 1663:while the numeral ( 1622:instead of "30" in 759:positional notation 531:Sign-value notation 2965:Funerary practices 2144:*pisī́ḏaw (masc.) 2110:*ḫamā́naw (masc.) 2028:or jsw (?) (masc.) 1894:*sinúwwaj (masc.) 1834:per Loprieno 1995 1826:(Sahidic dialect) 1738: 1725:. The Old Kingdom 1594: 1533: 1480: 1427: 1338: 1115:heart with trachea 773:Digits and numbers 728:special characters 187:East Asian systems 3403: 3402: 3220: 3219: 2975:Great Royal Wives 2945:Prehistoric Egypt 2778:Numbers and dates 2740:978-0-691-13526-7 2719:978-90-04-69156-8 2544:Egyptian language 2535: 2534: 2141:*p˘sī́ḏat (fem.) 2139:*p˘sī́ḏaw (masc.) 2107:*ḫ˘mā́nat (fem.) 2105:*ḫ˘mā́naw (masc.) 1857:*wiꜥī́yat (fem.) 1705:Hieratic numerals 1699: 1698: 1695: 1694: 1691: 1690: 1661: 1660: 1657: 1656: 1653: 1652: 1616:Egyptian language 1607: 1606: 1592: 1572: 1571: 1568: 1567: 1546: 1545: 1531: 1511: 1510: 1507: 1506: 1478: 1458: 1457: 1454: 1453: 1425: 1405: 1404: 1401: 1400: 1351: 1350: 1336: 1316: 1315: 1312: 1311: 1262: 1261: 1258: 1257: 1254: 1253: 1197:Egyptian fraction 1171:in a drawing for 1140: 1139: 1136: 1135: 1132: 1131: 1093: 1092: 1089: 1088: 1085: 1084: 1067: 1066: 1052: 1051: 1019: 1018: 948: 947: 944: 943: 929: 928: 925: 924: 910: 909: 906: 905: 891: 890: 887: 886: 872: 871: 868: 867: 853: 852: 849: 848: 834: 833: 830: 829: 747:Egyptian numerals 734:rendering support 721: 720: 520: 519: 3438: 3344: 3340:Manuel de Codage 3336: 3247: 3240: 3233: 3224: 3210: 3209: 3200: 3199: 3190: 3189: 3180: 3179: 3170: 3169: 3168: 3132: 2827: 2820: 2813: 2804: 2788:Egyptian Numbers 2750: 2748: 2747: 2723: 2667: 2660: 2654: 2647: 2641: 2635: 2629: 2623: 2617: 2611: 2605: 2602:Merzbach, Uta C. 2599: 2593: 2590: 2584: 2583: 2581: 2579: 2564: 2242:*máꜥb˘ꜣ (masc.) 2239:*máꜥb˘ꜣ (masc.) 2178:*mū́ḏaw (masc.) 2076:*sáfḫaw (masc.) 2038:*sáʾsaw (masc.) 2000:*dī́jaw (masc.) 1962:*jifdáw (masc.) 1928:*ḫámtaw (masc.) 1860:*wúꜥꜥuw (masc.) 1801: 1793:clues as to the 1678: 1674: 1670: 1641: 1637: 1633: 1603: 1601: 1600: 1595: 1593: 1585: 1559: 1555: 1551: 1542: 1540: 1539: 1534: 1532: 1524: 1500: 1496: 1489: 1487: 1486: 1481: 1479: 1471: 1447: 1443: 1436: 1434: 1433: 1428: 1426: 1418: 1394: 1390: 1386: 1382: 1381: 1377: 1372: 1371: 1367: 1362: 1361: 1357: 1347: 1345: 1344: 1339: 1337: 1329: 1301: 1297: 1293: 1290:was written as: 1289: 1288: 1284: 1247: 1243: 1239: 1235: 1234: 1230: 1225: 1224: 1220: 1202:Rational numbers 1167: 1161: 1125: 1121: 1107: 1069: 1054: 1036: 1032: 1028: 937: 933: 918: 914: 899: 895: 880: 876: 861: 857: 842: 838: 823: 819: 784: 713: 706: 699: 502: 486: 468: 458:balanced ternary 455: 442: 48: 19: 3446: 3445: 3441: 3440: 3439: 3437: 3436: 3435: 3421:Numeral systems 3406: 3405: 3404: 3399: 3389: 3368: 3347: 3342: 3334: 3320: 3316:Transliteration 3292: 3261:Characteristics 3256: 3251: 3221: 3216: 3166: 3164: 3156: 3133: 3124: 2860: 2837: 2831: 2792:Wayback Machine 2782:Wayback Machine 2772:Wayback Machine 2764: 2745: 2743: 2741: 2726: 2720: 2699: 2675: 2670: 2661: 2657: 2651:Middle Egyptian 2648: 2644: 2636: 2632: 2624: 2620: 2612: 2608: 2600: 2596: 2591: 2587: 2577: 2575: 2566: 2565: 2561: 2557: 2540: 2253: 2235: 2221: 2203: 2189: 2175:*mū́ḏat (fem.) 2174: 2173:*mū́ḏaw (masc.) 2169: 2155: 2140: 2135: 2121: 2106: 2101: 2087: 2073:*sáfḫat (fem.) 2072: 2071:*sáfḫaw (masc.) 2067: 2049: 2035:*j˘ssát (fem.) 2034: 2033:*j˘ssáw (masc.) 2029: 2011: 1997:*dī́jat (fem.) 1996: 1995:*dī́jaw (masc.) 1991: 1973: 1959:*j˘fdát (fem.) 1958: 1957:*j˘fdáw (masc.) 1953: 1939: 1925:*ḫámtat (fem.) 1924: 1923:*ḫámtaw (masc.) 1919: 1905: 1891:*síntaj (fem.) 1890: 1889:*sínwaj (masc.) 1885: 1871: 1856: 1855:*wíꜥyaw (masc.) 1847: 1808:transliteration 1779:transliteration 1775: 1707: 1645: 1612: 1610:Written numbers 1576: 1575: 1563: 1515: 1514: 1462: 1461: 1409: 1408: 1379: 1375: 1374: 1369: 1365: 1364: 1359: 1355: 1354: 1320: 1319: 1305: 1286: 1282: 1281: 1232: 1228: 1227: 1222: 1218: 1217: 1199: 1193: 1162: 1116: 1111: 1105: 1097:both directions 1060: 1003: 809: 775: 743: 742: 741: 732:Without proper 717: 681: 680: 603: 589:Proto-cuneiform 534: 533: 522: 521: 516: 515: 500: 484: 466: 453: 440: 427: 356: 355: 343: 342: 323: 283: 268: 259: 258: 249: 248: 230: 189: 188: 179: 178: 130: 72: 58: 57: 45: 44: 32:Numeral systems 17: 12: 11: 5: 3444: 3442: 3434: 3433: 3428: 3423: 3418: 3408: 3407: 3401: 3400: 3394: 3391: 3390: 3388: 3387: 3382: 3376: 3374: 3370: 3369: 3367: 3366: 3361: 3355: 3353: 3349: 3348: 3346: 3345: 3337: 3328: 3326: 3322: 3321: 3319: 3318: 3313: 3312: 3311: 3300: 3298: 3294: 3293: 3291: 3290: 3285: 3280: 3275: 3270: 3264: 3262: 3258: 3257: 3252: 3250: 3249: 3242: 3235: 3227: 3218: 3217: 3215: 3214: 3204: 3194: 3184: 3174: 3161: 3158: 3157: 3155: 3154: 3149: 3144: 3138: 3135: 3134: 3127: 3125: 3123: 3122: 3117: 3112: 3107: 3106: 3105: 3100: 3090: 3085: 3080: 3075: 3070: 3069: 3068: 3063: 3053: 3048: 3043: 3038: 3033: 3028: 3023: 3018: 3017: 3016: 3011: 3001: 2996: 2995: 2994: 2984: 2983: 2982: 2972: 2967: 2962: 2957: 2952: 2947: 2942: 2937: 2932: 2927: 2926: 2925: 2915: 2910: 2905: 2904: 2903: 2893: 2892: 2891: 2886: 2881: 2871: 2865: 2862: 2861: 2859: 2858: 2853: 2848: 2842: 2839: 2838: 2832: 2830: 2829: 2822: 2815: 2807: 2801: 2800: 2795: 2785: 2775: 2763: 2762:External links 2760: 2759: 2758: 2751: 2739: 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1877: 1864: 1861: 1858: 1853: 1836: 1835: 1832: 1828: 1827: 1821: 1813: 1810: 1774: 1771: 1751:Roman numerals 1706: 1703: 1697: 1696: 1693: 1692: 1689: 1688: 1685: 1682: 1659: 1658: 1655: 1654: 1651: 1650: 1647: 1611: 1608: 1605: 1604: 1591: 1588: 1583: 1573: 1570: 1569: 1566: 1565: 1544: 1543: 1530: 1527: 1522: 1512: 1509: 1508: 1505: 1504: 1493: 1490: 1477: 1474: 1469: 1459: 1456: 1455: 1452: 1451: 1440: 1437: 1424: 1421: 1416: 1406: 1403: 1402: 1399: 1398: 1349: 1348: 1335: 1332: 1327: 1317: 1314: 1313: 1310: 1309: 1260: 1259: 1256: 1255: 1252: 1251: 1206:unit fractions 1195:Main article: 1192: 1189: 1183:, a deed from 1177: 1176: 1173:Meidum Pyramid 1169: 1138: 1137: 1134: 1133: 1130: 1129: 1118: 1113: 1104: 1101: 1091: 1090: 1087: 1086: 1083: 1082: 1079: 1076: 1073: 1065: 1064: 1050: 1049: 1046: 1043: 1040: 1017: 1016: 1011: 1008: 1005: 998: 992: 986: 985:Single stroke 983: 979: 978: 975: 972: 969: 966: 963: 960: 957: 950: 949: 946: 945: 942: 941: 930: 927: 926: 923: 922: 911: 908: 907: 904: 903: 892: 889: 888: 885: 884: 873: 870: 869: 866: 865: 854: 851: 850: 847: 846: 835: 832: 831: 828: 827: 816: 812: 811: 806: 803: 800: 797: 794: 791: 788: 774: 771: 763:decimal system 736:, you may see 724: 723: 722: 719: 718: 716: 715: 708: 701: 693: 690: 689: 683: 682: 679: 678: 673: 668: 663: 658: 653: 648: 643: 642: 641: 636: 631: 621: 616: 610: 609: 602: 601: 596: 591: 586: 581: 576: 571: 566: 561: 556: 551: 546: 540: 539: 538:Non-alphabetic 535: 529: 528: 527: 524: 523: 518: 517: 514: 513: 508: 495: 479: 474: 461: 448: 434: 433: 426: 425: 418: 413: 408: 403: 398: 393: 388: 383: 378: 373: 368: 362: 361: 357: 350: 349: 348: 345: 344: 341: 340: 334: 328: 327: 322: 321: 316: 311: 306: 301: 296: 290: 289: 287:Post-classical 282: 281: 275: 274: 267: 266: 260: 256: 255: 254: 251: 250: 247: 246: 241: 235: 234: 229: 228: 223: 218: 213: 208: 207: 206: 195: 194: 190: 186: 185: 184: 181: 180: 177: 176: 171: 166: 161: 156: 151: 146: 141: 136: 129: 128: 123: 118: 113: 108: 103: 98: 93: 88: 83: 78: 71: 70: 68:Eastern Arabic 65: 63:Western Arabic 59: 53: 52: 51: 46: 40: 39: 38: 35: 34: 28: 27: 15: 13: 10: 9: 6: 4: 3: 2: 3443: 3432: 3429: 3427: 3424: 3422: 3419: 3417: 3414: 3413: 3411: 3397: 3392: 3386: 3383: 3381: 3378: 3377: 3375: 3371: 3365: 3362: 3360: 3357: 3356: 3354: 3350: 3341: 3338: 3333: 3330: 3329: 3327: 3323: 3317: 3314: 3310: 3309:Rosetta Stone 3307: 3306: 3305: 3302: 3301: 3299: 3295: 3289: 3286: 3284: 3281: 3279: 3276: 3274: 3271: 3269: 3268:Determinative 3266: 3265: 3263: 3259: 3255: 3248: 3243: 3241: 3236: 3234: 3229: 3228: 3225: 3213: 3205: 3203: 3195: 3193: 3185: 3183: 3175: 3173: 3163: 3162: 3159: 3153: 3150: 3148: 3147:Egyptologists 3145: 3143: 3140: 3139: 3136: 3131: 3121: 3118: 3116: 3113: 3111: 3108: 3104: 3101: 3099: 3096: 3095: 3094: 3091: 3089: 3086: 3084: 3081: 3079: 3076: 3074: 3071: 3067: 3064: 3062: 3059: 3058: 3057: 3054: 3052: 3049: 3047: 3044: 3042: 3039: 3037: 3034: 3032: 3029: 3027: 3024: 3022: 3019: 3015: 3012: 3010: 3007: 3006: 3005: 3002: 3000: 2997: 2993: 2990: 2989: 2988: 2985: 2981: 2978: 2977: 2976: 2973: 2971: 2968: 2966: 2963: 2961: 2958: 2956: 2953: 2951: 2948: 2946: 2943: 2941: 2938: 2936: 2933: 2931: 2928: 2924: 2921: 2920: 2919: 2916: 2914: 2911: 2909: 2906: 2902: 2899: 2898: 2897: 2894: 2890: 2887: 2885: 2882: 2880: 2877: 2876: 2875: 2872: 2870: 2867: 2866: 2863: 2857: 2854: 2852: 2849: 2847: 2844: 2843: 2840: 2835: 2834:Ancient Egypt 2828: 2823: 2821: 2816: 2814: 2809: 2808: 2805: 2799: 2796: 2793: 2789: 2786: 2783: 2779: 2776: 2773: 2769: 2766: 2765: 2761: 2756: 2752: 2742: 2736: 2732: 2731: 2725: 2721: 2715: 2711: 2707: 2703: 2698: 2695: 2691: 2688: 2684: 2681: 2677: 2676: 2672: 2665: 2659: 2656: 2652: 2646: 2643: 2640:, p. 87. 2639: 2634: 2631: 2628:, p. 86. 2627: 2622: 2619: 2615: 2614:Hoffmann 2024 2610: 2607: 2603: 2598: 2595: 2589: 2586: 2573: 2569: 2563: 2560: 2554: 2550: 2547: 2545: 2542: 2541: 2537: 2530: 2526: 2523: 2520: 2517: 2515: 2512: 2511: 2508: 2505: 2503: 2501: 2499: 2496: 2495: 2491: 2487: 2485:ten thousand 2484: 2481: 2478: 2476: 2473: 2472: 2468: 2464: 2462:one thousand 2461: 2458: 2455: 2453: 2450: 2449: 2445: 2441: 2438: 2435: 2432: 2430: 2427: 2426: 2422: 2418: 2415: 2412: 2409: 2407: 2404: 2403: 2399: 2395: 2392: 2389: 2386: 2383: 2380: 2379: 2375: 2371: 2368: 2365: 2362: 2359: 2356: 2355: 2351: 2347: 2344: 2341: 2338: 2335: 2332: 2331: 2327: 2323: 2320: 2317: 2314: 2311: 2308: 2307: 2303: 2299: 2296: 2293: 2290: 2288: 2285: 2284: 2280: 2276: 2273: 2270: 2267: 2265: 2262: 2261: 2257: 2251: 2247: 2244: 2241: 2238: 2236:mꜥbꜣt (fem.) 2233: 2230: 2229: 2225: 2219: 2215: 2212: 2209: 2206: 2201: 2198: 2197: 2193: 2187: 2183: 2180: 2177: 2172: 2167: 2164: 2163: 2159: 2153: 2149: 2146: 2143: 2138: 2133: 2130: 2129: 2125: 2119: 2115: 2112: 2109: 2104: 2099: 2096: 2095: 2091: 2085: 2081: 2078: 2075: 2070: 2065: 2062: 2061: 2057: 2053: 2047: 2043: 2040: 2037: 2032: 2027: 2024: 2023: 2019: 2015: 2009: 2005: 2002: 1999: 1994: 1989: 1986: 1985: 1981: 1977: 1971: 1967: 1964: 1961: 1956: 1951: 1948: 1947: 1943: 1937: 1933: 1930: 1927: 1922: 1917: 1914: 1913: 1909: 1903: 1899: 1896: 1893: 1888: 1883: 1880: 1879: 1875: 1869: 1865: 1862: 1859: 1854: 1851: 1845: 1841: 1838: 1837: 1833: 1830: 1829: 1825: 1820: 1817: 1809: 1806: 1802: 1799: 1796: 1792: 1791:Egyptologists 1788: 1784: 1780: 1772: 1770: 1768: 1764: 1759: 1757: 1752: 1746: 1743: 1734: 1730: 1728: 1727:Abusir Papyri 1724: 1720: 1716: 1712: 1704: 1702: 1686: 1683: 1680: 1679: 1676: 1675: 1672: 1671: 1668: 1666: 1648: 1643: 1642: 1639: 1638: 1635: 1634: 1631: 1629: 1625: 1621: 1617: 1609: 1589: 1586: 1581: 1574: 1561: 1560: 1557: 1556: 1553: 1552: 1549: 1528: 1525: 1520: 1513: 1502: 1501: 1498: 1497: 1494: 1491: 1475: 1472: 1467: 1460: 1449: 1448: 1445: 1444: 1441: 1438: 1422: 1419: 1414: 1407: 1396: 1395: 1392: 1391: 1388: 1387: 1384: 1333: 1330: 1325: 1318: 1303: 1302: 1299: 1298: 1295: 1294: 1291: 1280:below. Thus, 1279: 1275: 1271: 1267: 1249: 1248: 1245: 1244: 1241: 1240: 1237: 1215: 1211: 1207: 1203: 1198: 1190: 1188: 1186: 1182: 1179:According to 1174: 1170: 1166: 1157: 1156: 1155: 1153: 1149: 1145: 1127: 1126: 1123: 1122: 1119: 1114: 1109: 1108: 1102: 1100: 1098: 1080: 1077: 1074: 1071: 1070: 1056: 1055: 1047: 1044: 1041: 1038: 1037: 1034: 1033: 1030: 1029: 1026: 1024: 1015: 1012: 1009: 1006: 1002: 999: 997: 993: 991: 987: 984: 981: 980: 976: 973: 970: 967: 964: 961: 958: 955: 952: 951: 939: 938: 935: 934: 931: 920: 919: 916: 915: 912: 901: 900: 897: 896: 893: 882: 881: 878: 877: 874: 863: 862: 859: 858: 855: 844: 843: 840: 839: 836: 825: 824: 821: 820: 817: 814: 808:1 million, or 807: 804: 801: 798: 795: 792: 789: 786: 785: 782: 780: 772: 770: 768: 764: 760: 756: 752: 751:Ancient Egypt 748: 739: 735: 731: 729: 714: 709: 707: 702: 700: 695: 694: 692: 691: 688: 685: 684: 677: 674: 672: 669: 667: 664: 662: 659: 657: 654: 652: 649: 647: 644: 640: 637: 635: 632: 630: 627: 626: 625: 624:Alphasyllabic 622: 620: 617: 615: 612: 611: 608: 605: 604: 600: 597: 595: 592: 590: 587: 585: 582: 580: 577: 575: 572: 570: 567: 565: 562: 560: 557: 555: 552: 550: 547: 545: 542: 541: 537: 536: 532: 526: 525: 512: 509: 506: 499: 496: 493: 492: 483: 480: 478: 475: 472: 465: 462: 459: 452: 449: 446: 439: 436: 435: 432: 429: 428: 423: 419: 417: 414: 412: 409: 407: 404: 402: 399: 397: 394: 392: 389: 387: 384: 382: 379: 377: 374: 372: 369: 367: 364: 363: 359: 358: 354: 347: 346: 338: 335: 333: 330: 329: 325: 324: 320: 317: 315: 312: 310: 307: 305: 302: 300: 297: 295: 292: 291: 288: 285: 284: 280: 277: 276: 273: 270: 269: 265: 262: 261: 257:Other systems 253: 252: 245: 242: 240: 239:Counting rods 237: 236: 232: 231: 227: 224: 222: 219: 217: 214: 212: 209: 205: 202: 201: 200: 197: 196: 192: 191: 183: 182: 175: 172: 170: 167: 165: 162: 160: 157: 155: 152: 150: 147: 145: 142: 140: 137: 135: 132: 131: 127: 124: 122: 119: 117: 114: 112: 109: 107: 104: 102: 99: 97: 94: 92: 89: 87: 84: 82: 79: 77: 74: 73: 69: 66: 64: 61: 60: 56: 50: 49: 43: 37: 36: 33: 29: 25: 21: 20: 3304:Decipherment 3287: 2874:Architecture 2754: 2744:. Retrieved 2729: 2701: 2693: 2686: 2679: 2673:Bibliography 2663: 2658: 2650: 2645: 2633: 2621: 2609: 2597: 2588: 2576:. Retrieved 2571: 2562: 2528: 2524:one million 2489: 2466: 2443: 2439:two hundred 2420: 2416:one hundred 2397: 2373: 2349: 2325: 2301: 2278: 2255: 2249: 2223: 2217: 2191: 2185: 2157: 2151: 2136:psḏt (fem.) 2123: 2117: 2102:ḫmnt (fem.) 2089: 2083: 2068:sfḫt (fem.) 2055: 2051: 2045: 2017: 2013: 2007: 1979: 1975: 1969: 1954:jfdt (fem.) 1941: 1935: 1920:ḫmtt (fem.) 1907: 1901: 1886:sntj (fem.) 1873: 1867: 1776: 1760: 1747: 1739: 1708: 1700: 1664: 1662: 1627: 1626:. The word ( 1619: 1613: 1547: 1352: 1269: 1263: 1209: 1200: 1178: 1163: 1740 1151: 1141: 1094: 1020: 1007:Bent finger 982:Description 776: 761:such as the 749:was used in 746: 744: 725: 568: 490: 451:Signed-digit 326:Contemporary 193:Contemporary 3212:WikiProject 3026:Mathematics 2987:Hieroglyphs 2901:Portraiture 2869:Agriculture 2856:Main topics 2638:Joseph 2011 2626:Joseph 2011 2578:January 12, 2436:*šinjū́taj 2390:*pisḏíjjaw 2387:*p˘siḏáwju 2363:*ḫamanáwju 2170:mḏt (fem.) 1992:djt (fem.) 1978:) or ϥⲧⲟⲉ ( 1819:translation 1783:hieroglyphs 1758:, as well. 1278:denominator 1214:reciprocals 815:Hieroglyph 755:hieroglyphs 629:Akṣarapallī 599:Tally marks 498:Non-integer 3410:Categories 3398: (40) 3283:Triliteral 3273:Uniliteral 3142:Egyptology 3110:Technology 3073:Philosophy 3021:Literature 2913:Chronology 2746:2024-05-03 2555:References 2413:*ší(nju)t 2339:*safḫáwju 2315:*j˘ssáwju 2268:*ḥ˘mí (?) 2054:) or ⲥⲟⲉ ( 1212:, sums of 1181:Carl Boyer 1001:Water lily 666:Glagolitic 639:Kaṭapayādi 607:Alphabetic 511:Asymmetric 353:radix/base 294:Cistercian 279:Babylonian 226:Vietnamese 81:Devanagari 3278:Biliteral 3046:Mythology 2970:Geography 2960:Dynasties 2908:Astronomy 2531:) "many" 2396:ⲡⲥⲧⲁⲓⲟⲩ ( 2258:) (fem.) 2252:) (masc.) 2226:) (fem.) 2220:) (masc.) 2194:) (fem.) 2188:) (masc.) 2160:) (fem.) 2154:) (masc.) 2126:) (fem.) 2120:) (masc.) 2092:) (fem.) 2086:) (masc.) 2058:) (fem.) 2048:) (masc.) 2020:) (fem.) 2016:) or ϯⲉ ( 2010:) (masc.) 1982:) (fem.) 1972:) (masc.) 1944:) (fem.) 1938:) (masc.) 1910:) (fem.) 1904:) (masc.) 1876:) (fem.) 1870:) (masc.) 1274:numerator 1191:Fractions 634:Āryabhaṭa 579:Kharosthi 471:factorial 438:Bijective 339:(Iñupiaq) 169:Sundanese 164:Mongolian 111:Malayalam 3426:Numerals 3325:Research 3288:Numerals 3182:Category 3103:District 3098:Capitals 3083:Religion 3066:Titulary 3056:Pharaohs 3036:Military 3031:Medicine 3014:Hieratic 3004:Language 2930:Clothing 2884:Obelisks 2538:See also 2433:*šū́taj 2366:*ḫamnéw 2345:seventy 2342:*safḫéw 2318:*saʾséw 2300:ⲧⲁⲉⲓⲟⲩ ( 2294:*díjjaw 2222:ϫⲟⲩⲱⲧⲉ ( 2122:ϣⲙⲟⲩⲛⲉ ( 1934:ϣⲟⲙⲛ̄ⲧ ( 1805:Egyptian 1795:vocalism 1765:and the 1742:hieratic 1719:hieratic 1010:Tadpole 994:Coil of 805:100,000 781:of ten: 767:hieratic 661:Georgian 651:Cyrillic 619:Armenian 574:Etruscan 569:Egyptian 477:Negative 337:Kaktovik 332:Cherokee 309:Pentadic 233:Historic 216:Japanese 149:Javanese 139:Balinese 126:Dzongkha 91:Gurmukhi 86:Gujarati 24:a series 22:Part of 3202:Outline 3192:Commons 3152:Museums 3088:Scribes 3078:Pottery 3009:Demotic 2999:History 2950:Cuisine 2879:Revival 2790:at the 2780:at the 2770:at the 2482:*ḏ˘báꜥ 2479:*ḏubáꜥ 2410:*šúwat 2398:pstaiou 2393:ninety 2372:ϩⲙⲉⲛⲉ ( 2369:eighty 2291:*díjwu 2271:*ḥ˘méw 2254:ⲙⲁⲁⲃⲉ ( 2245:thirty 2234:(masc.) 2216:ϫⲟⲩⲱⲧ ( 2213:twenty 2168:(masc.) 2134:(masc.) 2116:ϣⲙⲟⲩⲛ ( 2100:(masc.) 2088:ϣⲁϣϥⲉ ( 2082:ϣⲁϣϥ̄ ( 2066:(masc.) 1990:(masc.) 1968:ϥⲧⲟⲟⲩ ( 1952:(masc.) 1940:ϣⲟⲙⲧⲉ ( 1918:(masc.) 1906:ⲥⲛ̄ⲧⲉ ( 1884:(masc.) 1816:English 1781:of the 1756:Demotic 1715:ostraca 1711:papyrus 1624:English 1492:  1439:  1378:⁄ 1368:⁄ 1358:⁄ 1285:⁄ 1266:solidus 1231:⁄ 1221:⁄ 1112:  988:Cattle 802:10,000 564:Chuvash 482:Complex 272:Ancient 264:History 211:Hokkien 199:Chinese 144:Burmese 134:Tibetan 121:Kannada 101:Sinhala 76:Bengali 3352:People 3343:(1988) 3335:(1927) 3297:Topics 3051:People 2918:Cities 2836:topics 2737:  2716:  2653:, 1975 2321:sixty 2302:taeiou 2297:fifty 2274:forty 2248:ⲙⲁⲁⲃ ( 2224:jouōte 2190:ⲙⲏⲧⲉ ( 2156:ⲯⲓⲧⲉ ( 2124:šmoune 2113:eight 2079:seven 2044:ⲥⲟⲟⲩ ( 1931:three 1900:ⲥⲛⲁⲩ ( 1872:ⲟⲩⲉⲓ ( 1824:Coptic 1787:Coptic 1667:) was 1628:thirty 1620:thirty 1272:, the 1023:Karnak 990:hobble 799:1,000 787:Value 779:powers 765:. The 676:Hebrew 646:Coptic 559:Brahmi 544:Aegean 501:  485:  467:  454:  441:  304:Muisca 244:Tangut 221:Korean 204:Suzhou 116:Telugu 3373:Lists 3115:Trade 3093:Sites 3041:Music 2955:Dance 2889:Pylon 2851:Index 2527:ϩⲁϩ ( 2521:*ḥaḥ 2518:*ḥaḥ 2488:ⲧⲃⲁ ( 2459:*ḫaꜣ 2456:*ḫaꜣ 2442:ϣⲏⲧ ( 2382:psḏjw 2374:hmene 2358:ḫmnjw 2348:ϣϥⲉ ( 2334:sfḫjw 2310:sjsjw 2277:ϩⲙⲉ ( 2256:maabe 2218:jouōt 2200:mḏwtj 2184:ⲙⲏⲧ ( 2158:psite 2150:ⲯⲓⲥ ( 2147:nine 2118:šmoun 2090:šašfe 2006:ϯⲟⲩ ( 2003:five 1974:ϥⲧⲟ ( 1970:ftoou 1965:four 1942:šomte 1936:šomnt 1866:ⲟⲩⲁ ( 1848:wꜥt ( 1844:masc. 1840:wꜥ(w) 1148:nefer 810:many 671:Greek 656:Geʽez 614:Abjad 594:Roman 554:Aztec 549:Attic 464:Mixed 422:table 314:Quipu 299:Mayan 154:Khmer 106:Tamil 3061:List 2980:List 2923:List 2735:ISBN 2714:ISBN 2580:2023 2465:ϣⲟ ( 2419:ϣⲉ ( 2324:ⲥⲉ ( 2250:maab 2232:mꜥbꜣ 2192:mēte 2181:ten 2152:psis 2132:psḏw 2098:ḫmnw 2084:šašf 2064:sfḫw 2050:ⲥⲟ ( 2046:soou 2041:six 2026:sjsw 2008:tiou 1980:ftoe 1950:jfdw 1916:ḫmtw 1908:snte 1902:snau 1897:two 1882:snwj 1874:ouei 1863:one 1850:fem. 1713:or 1270:i.e. 1226:and 1210:i.e. 1185:Edfu 1144:zero 1103:Zero 996:rope 977:C11 971:D50 968:M12 962:V20 796:100 319:Rumi 174:Thai 96:Odia 2896:Art 2706:doi 2529:hah 2498:ḥfn 2490:tba 2475:ḏbꜥ 2444:šēt 2429:štj 2350:šfe 2287:dyw 2279:hme 2264:ḥmw 2186:mēt 2166:mḏw 2056:soe 2018:tie 2012:ϯ ( 1988:djw 1976:fto 1868:oua 1590:100 1152:nfr 1110:nfr 1014:Heh 974:I8 965:V1 959:Z1 956:ID 793:10 351:By 159:Lao 3412:: 2712:. 2570:. 2514:ḥḥ 2492:) 2469:) 2467:šo 2452:ḫꜣ 2446:) 2423:) 2421:še 2406:št 2400:) 2376:) 2352:) 2328:) 2326:se 2304:) 2281:) 2052:so 2014:ti 1852:) 1769:. 1665:30 1383:: 1268:, 1208:, 1165:BC 1160:c. 790:1 416:60 411:20 406:16 401:12 396:10 26:on 3246:e 3239:t 3232:v 2826:e 2819:t 2812:v 2749:. 2722:. 2708:: 2616:. 2582:. 1846:) 1842:( 1587:1 1582:= 1529:4 1526:3 1521:= 1476:3 1473:2 1468:= 1423:2 1420:1 1415:= 1380:4 1376:3 1370:3 1366:2 1360:2 1356:1 1334:3 1331:1 1326:= 1287:3 1283:1 1233:4 1229:3 1223:3 1219:2 1150:( 740:. 730:. 712:e 705:t 698:v 507:) 505:φ 503:( 494:) 491:i 489:2 487:( 473:) 469:( 460:) 456:( 447:) 445:1 443:( 424:) 420:( 391:8 386:6 381:5 376:4 371:3 366:2

Index

a series
Numeral systems
Place-value notation
Hindu–Arabic numerals
Western Arabic
Eastern Arabic
Bengali
Devanagari
Gujarati
Gurmukhi
Odia
Sinhala
Tamil
Malayalam
Telugu
Kannada
Dzongkha
Tibetan
Balinese
Burmese
Javanese
Khmer
Lao
Mongolian
Sundanese
Thai
Chinese
Suzhou
Hokkien
Japanese

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