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Harold Scott MacDonald Coxeter

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1691: 1677: 597:. He attributed his longevity to his vegetarian diet, daily exercise such as fifty press-ups and standing on his head for fifteen minutes each morning, and consuming a nightly cocktail made from 426:). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with 59: 1859: 472:, where the standard of mathematics was higher. Coxeter won an entrance scholarship and went to Trinity in 1926 to read mathematics. There he earned his BA (as 1834: 1103: 1849: 396: 145: 1249: 729: 430:), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the 1799: 1864: 662:, was published in 1982. It contained 41 essays on geometry, based on a symposium for Coxeter held at Toronto in 1979. A second such volume, 1829: 1475: 1819: 356:
in Canada, from 1936 until his retirement in 1996, becoming a full professor there in 1948. His many honours included membership in the
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in 1954 and the two became lifelong friends; his work on geometric figures helped inspire some of Escher's works, particularly the
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In his youth, Coxeter composed music and was an accomplished pianist at the age of 10. He felt that
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were intimately related, outlining his ideas in a 1962 article on "Music and Mathematics" in the
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H. S. M. Coxeter (1907–2003), Erich W. Ellers, Branko Grünbaum, Peter McMullen, Asia Ivic Weiss
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1995: F. Arthur Sherk, Peter McMullen, Anthony C. Thompson and Asia Ivić Weiss, editors:
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and mathematician. He is regarded as one of the greatest geometers of the 20th century.
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University of Toronto Archives & Records Management Services 
1747: 534: 508: 1563: 938: 598: 504:. In 1934 he spent a further year at Princeton as a Procter Fellow. 602: 507:
In 1936 Coxeter moved to the University of Toronto. In 1938 he and
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King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry
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King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry
58: 1209:, 11th edition, by W. W. Rouse Ball; revised by H. S. M. Coxeter" 337:(9 February 1907 – 31 March 2003) was a British-Canadian 79: 1728:
University of Toronto Archives and Records Management Services
1352:. Providence, Rhode Island: American Mathematical Society. 476:) in 1928, and his doctorate in 1931. In 1932 he went to 1766:
video of a lecture by H.S.M. Coxeter, April 28, 2000.
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Kaleidoscopes — Selected Writings of H. S. M. Coxeter
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Biographical Memoirs of Fellows of the Royal Society
1596:. Providence, R.I.: American Mathematical Society. 1301:. Queen's Printer for Canada. Retrieved 26 May 2010 1623: 1458: 1107:(online ed.). Oxford University Press. 2004. 1096: 1372: 1321:Proceedings of the Edinburgh Mathematical Society 1250:Philosophical Transactions of the Royal Society A 1174: 1012: 951:2011: The Fifty-Nine Icosahedra, Tarquin Group, 730:Philosophical Transactions of the Royal Society A 525:. In 1940 Coxeter edited the eleventh edition of 1771: 1748:www.donaldcoxeter.com www.math.yorku.ca/dcoxeter 397:Coxeter's loxodromic sequence of tangent circles 344:Coxeter was born in England and educated at the 146:Coxeter's loxodromic sequence of tangent circles 1860:Presidents of the Canadian Mathematical Society 1594:The Coxeter Legacy: Reflections and Projections 1499: 496:. Returning to Trinity for a year, he attended 1724:Harold Scott MacDonald Coxeter archival papers 1415: 562:. He also inspired some of the innovations of 419:, England, to Harold Samuel Coxeter and Lucy ( 1476:Bulletin of the American Mathematical Society 1348:Davis, Chandler; Ellers, Erich, eds. (2006). 632:. In 1990, he became a Foreign Member of the 1466:Generators and relations for discrete groups 1202: 750:Generators and Relations for Discrete Groups 1835:Academic staff of the University of Toronto 1588: 1347: 1850:Academics of the University of East Anglia 1750:webpages dedicated to him (in development) 1689: 1675: 1170: 1168: 1166: 1164: 1162: 1160: 434:. A maternal cousin was the architect Sir 196:a daughter, Susan Thomas, and a son, Edgar 1764:The Mathematics in the Art of M.C. Escher 1754:Jaron's World: Shapes in Other Dimensions 1744:Notices of the AMS: Volume 50, Number 10. 1527: 1484: 1443: 1400: 1332: 1136: 1134: 1132: 1130: 1098:"Oxford Dictionary of National Biography" 1037: 853:1981: (with R. Frucht and D. L. Powers), 628:in 1950 and in 1997 he was awarded their 1542: 1295:Office of the Governor General of Canada 1008: 1006: 1004: 901:"Regular and Semi-Regular Polytopes III" 537:in 1948. He was elected a Fellow of the 371:He was an author of 12 books, including 1618: 1468:by H. S. M. Coxeter and W. O. J. Moser" 1276:. American Academy of Arts and Sciences 1186:MacTutor History of Mathematics Archive 1157: 1104:Oxford Dictionary of National Biography 874:"Regular and Semi-Regular Polytopes II" 14: 1800:Fellows of the Royal Society of Canada 1772: 1127: 1091: 1089: 752:1980: Second edition, Springer-Verlag 677:"Regular and Semi-Regular Polytopes I" 383:(1947). Many concepts in geometry and 1865:Canadian fellows of the Royal Society 1001: 931:The Beauty of Geometry: Twelve Essays 634:American Academy of Arts and Sciences 420: 1830:Alumni of Trinity College, Cambridge 1703:Harold Scott MacDonald Coxeter fonds 1310: 1820:20th-century English mathematicians 1207:Mathematical Recreations and Essays 1086: 1067:Mathematical Association of America 574:were the first to publish the full 527:Mathematical Recreations and Essays 387:are named after him, including the 24: 1630:. New York: Walker & Company. 1582: 25: 1876: 1790:Companions of the Order of Canada 1653: 1592:; Ellers, Erich W, eds. (2006). 1270:"Harold Scott MacDonald Coxeter" 1181:"Harold Scott MacDonald Coxeter" 817:, (3rd edition), Dover edition, 781:(2nd edition), Macmillan Company 588: 352:. He worked for 60 years at the 57: 1536: 1529:10.1090/s0002-9904-1962-10714-9 1493: 1486:10.1090/S0002-9904-1958-10178-0 1452: 1445:10.1090/s0002-9904-1950-09414-2 1409: 1402:10.1090/s0002-9904-1943-07977-3 1366: 1341: 1304: 1288: 1228:10.1090/S0002-9904-1940-07170-8 766:, (2nd paperback edition 1989, 464:were named. He was accepted at 1733:Harold Scott MacDonald Coxeter 1262: 1234: 1196: 1147:, Walker & Company, 2006, 1054: 993:Harold Scott MacDonald Coxeter 986: 581:He worked for 60 years at the 36:Harold Scott MacDonald Coxeter 13: 1: 1737:Mathematics Genealogy Project 997:Mathematics Genealogy Project 979: 615:Canadian Mathematical Society 458:St George's School, Harpenden 162:Goldberg–Coxeter construction 27:Canadian geometer (1907–2003) 1795:Fellows of the Royal Society 1715:How to use archival material 1121:UK public library membership 748:1957: (with W. O. J. Moser) 585:and published twelve books. 533:in 1892. He was elevated to 410: 7: 1825:Recreational mathematicians 1479:. 64, Part 1 (3): 106–108. 1016:; Ivić Weiss, Asia (2006). 962: 703:University of Toronto Press 626:Fellow of the Royal Society 543:Fellow of the Royal Society 523:University of Toronto Press 10: 1881: 1242:Michael S. Longuet-Higgins 840:Cambridge University Press 722:Michael S. Longuet-Higgins 529:, originally published by 454:King Alfred School, London 1697: 1684: 1669: 1552:The Journal of Philosophy 1423:The real projective plane 1334:10.1017/s0013091500017016 1311:Edge, W. L. (June 1983). 905:Mathematische Zeitschrift 878:Mathematische Zeitschrift 836:Regular Complex Polytopes 744:The Real Projective Plane 682:Mathematische Zeitschrift 608: 576:list of uniform polyhedra 518:The Fifty-Nine Icosahedra 502:philosophy of mathematics 466:King's College, Cambridge 374:The Fifty-Nine Icosahedra 348:, with student visits to 307: 286: 274: 264: 254: 247: 214:Henry Marshall Tory Medal 200: 192: 184: 117: 113:(B.A., 1929; Ph.D., 1931) 106: 87: 65: 56: 34: 1548:Introduction to Geometry 1507:Introduction to geometry 1299:Order of Canada citation 1191:University of St Andrews 764:Introduction to Geometry 669: 647:In 1973 he received the 179:Regular skew apeirohedra 1840:Canadian mathematicians 1248:. "Uniform Polyhedra", 728:) "Uniform Polyhedra", 636:and in 1997 was made a 539:Royal Society of Canada 484:, where he worked with 401:Coxeter–Dynkin diagrams 358:Royal Society of Canada 346:University of Cambridge 111:University of Cambridge 1550:by H. S. M. Coxeter". 1380:Non-euclidean geometry 1258:10.1098/rsta.1954.0003 1113:10.1093/ref:odnb/89876 1039:10.1098/rsbm.2006.0004 933:, Dover Publications, 738:10.1098/rsta.1954.0003 698:Non-Euclidean Geometry 649:Jeffery–Williams Prize 601:, peach schnapps, and 447:Canadian Music Journal 405:Todd–Coxeter algorithm 314:Harold Scott MacDonald 226:Jeffery–Williams Prize 188:Hendrina, died in 1999 166:Todd–Coxeter algorithm 158:Boerdijk–Coxeter helix 150:Coxeter–Dynkin diagram 1845:People from Harpenden 1516:Bull. Amer. Math. Soc 1432:Bull. Amer. Math. Soc 1389:Bull. Amer. Math. Soc 1216:Bull. Amer. Math. Soc 1203:Frame, J. S. (1940). 855:Zero-Symmetric Graphs 685:46: 380–407, MR 2,10 583:University of Toronto 568:M. S. Longuet-Higgins 511:, H. T. Flather, and 443:mathematics and music 432:Royal Academy of Arts 354:University of Toronto 269:University of Toronto 232:CRM-Fields-PIMS prize 1509:by H. S. M. Coxeter" 1425:by H. S. M. Coxeter" 1382:by H. S. M. Coxeter" 1177:Robertson, Edmund F. 1062:"Geometry Revisited" 513:John Flinders Petrie 478:Princeton University 415:Coxeter was born in 350:Princeton University 154:Coxeter–Todd lattice 1175:O'Connor, John J.; 1074:on 25 December 2018 969:Coxeter–James Prize 916:John Wiley and Sons 886:Projective Geometry 829:Projective Geometry 619:Coxeter–James Prize 500:'s seminars on the 498:Ludwig Wittgenstein 452:He was educated at 436:Giles Gilbert Scott 171:Tutte–Coxeter graph 1460:Hall Jr., Marshall 1350:The Coxeter Legacy 1315:The Geometric Vein 797:Twisted honeycombs 790:Geometry Revisited 691:10.1007/BF01181449 664:The Coxeter Legacy 660:The Geometric Vein 564:Buckminster Fuller 482:Rockefeller Fellow 1805:British geometers 1720: 1719: 1709: 1708: 1637:978-0-8027-1499-2 1603:978-0-8218-3722-1 1546:(1963). "Review: 1374:Blumenthal, L. M. 1119:(Subscription or 974:Spiral similarity 957:978-1-907550-08-9 895:978-0-387-40623-7 867:978-0-12-194580-0 848:978-0-521-20125-4 814:Regular Polytopes 779:Regular Polytopes 772:978-0-471-50458-0 715:978-0-88385-522-5 617:have awarded the 494:Solomon Lefschetz 380:Regular Polytopes 311: 310: 287:Doctoral students 249:Scientific career 16:(Redirected from 1872: 1855:Senior Wranglers 1705: 1693: 1680: 1679: 1667: 1666: 1658: 1657: 1649: 1629: 1620:Roberts, Siobhan 1615: 1576: 1575: 1540: 1534: 1533: 1531: 1513: 1497: 1491: 1490: 1488: 1472: 1456: 1450: 1449: 1447: 1429: 1413: 1407: 1406: 1404: 1386: 1370: 1364: 1363: 1345: 1339: 1338: 1336: 1308: 1302: 1292: 1286: 1285: 1283: 1281: 1274:Member directory 1266: 1260: 1240:Harold Coxeter, 1238: 1232: 1231: 1213: 1200: 1194: 1193: 1172: 1155: 1141:Roberts, Siobhan 1138: 1125: 1124: 1116: 1100: 1093: 1084: 1083: 1081: 1079: 1070:. Archived from 1058: 1052: 1051: 1041: 1018:Longair, Malcolm 1014:Roberts, Siobhan 1010: 999: 990: 705:(6th ed, 1998), 613:Since 1978, the 555:series based on 545:in 1950. He met 531:W. W. Rouse Ball 480:for a year as a 425: 336: 276:Doctoral advisor 142:Coxeter notation 99:Toronto, Ontario 94: 75: 73: 61: 51: 32: 31: 21: 1880: 1879: 1875: 1874: 1873: 1871: 1870: 1869: 1770: 1769: 1701: 1674: 1656: 1638: 1604: 1590:Davis, Chandler 1585: 1583:Further reading 1580: 1579: 1564:10.2307/2023059 1541: 1537: 1511: 1501:Freudenthal, H. 1498: 1494: 1470: 1457: 1453: 1427: 1414: 1410: 1384: 1371: 1367: 1360: 1346: 1342: 1309: 1305: 1293: 1289: 1279: 1277: 1268: 1267: 1263: 1246:J. C. P. Miller 1239: 1235: 1211: 1201: 1197: 1173: 1158: 1139: 1128: 1118: 1095: 1094: 1087: 1077: 1075: 1060: 1059: 1055: 1011: 1002: 991: 987: 982: 965: 726:J. C. P. Miller 672: 658:in his honour, 642:Order of Canada 630:Sylvester Medal 611: 591: 572:J. C. P. Miller 474:Senior Wrangler 470:Trinity College 462:Petrie polygons 413: 366:Order of Canada 324: 303: 243: 238:Sylvester Medal 177: 173: 169: 164: 160: 156: 152: 148: 144: 140: 138:Coxeter matroid 136: 132: 128: 126:Coxeter functor 124: 122:Coxeter element 107:Alma mater 102: 96: 92: 83: 77: 76:9 February 1907 71: 69: 52: 39: 37: 28: 23: 22: 15: 12: 11: 5: 1878: 1868: 1867: 1862: 1857: 1852: 1847: 1842: 1837: 1832: 1827: 1822: 1817: 1812: 1807: 1802: 1797: 1792: 1787: 1782: 1768: 1767: 1761: 1751: 1745: 1739: 1730: 1718: 1717: 1711: 1710: 1707: 1706: 1699: 1695: 1694: 1686: 1682: 1681: 1671: 1663: 1662: 1655: 1654:External links 1652: 1651: 1650: 1636: 1616: 1602: 1584: 1581: 1578: 1577: 1535: 1492: 1451: 1438:(4): 376–378. 1417:DuVal, Patrick 1408: 1395:(9): 679–680. 1365: 1359:978-0821837221 1358: 1340: 1327:(2): 284–285. 1303: 1287: 1261: 1233: 1222:(3): 211–213. 1195: 1156: 1126: 1085: 1053: 1000: 984: 983: 981: 978: 977: 976: 971: 964: 961: 960: 959: 949: 927: 908: 897: 881: 870: 859:Academic Press 851: 832: 825: 809: 792: 786:S. L. Greitzer 782: 775: 760: 746: 740: 718: 693: 671: 668: 624:He was made a 621:in his honor. 610: 607: 593:Coxeter was a 590: 587: 541:in 1948 and a 412: 409: 393:Coxeter groups 309: 308: 305: 304: 302: 301: 299:Norman Johnson 296: 290: 288: 284: 283: 278: 272: 271: 266: 262: 261: 256: 252: 251: 245: 244: 242: 241: 235: 229: 223: 217: 211: 204: 202: 198: 197: 194: 190: 189: 186: 182: 181: 119: 118:Known for 115: 114: 108: 104: 103: 97: 95:(aged 96) 89: 85: 84: 78: 67: 63: 62: 54: 53: 38: 35: 26: 18:Donald Coxeter 9: 6: 4: 3: 2: 1877: 1866: 1863: 1861: 1858: 1856: 1853: 1851: 1848: 1846: 1843: 1841: 1838: 1836: 1833: 1831: 1828: 1826: 1823: 1821: 1818: 1816: 1813: 1811: 1808: 1806: 1803: 1801: 1798: 1796: 1793: 1791: 1788: 1786: 1783: 1781: 1778: 1777: 1775: 1765: 1762: 1759: 1758:Discover mag. 1755: 1752: 1749: 1746: 1743: 1740: 1738: 1734: 1731: 1729: 1725: 1722: 1721: 1716: 1713: 1712: 1704: 1700: 1696: 1692: 1687: 1683: 1678: 1672: 1668: 1665: 1664: 1660: 1659: 1647: 1643: 1639: 1633: 1628: 1627: 1621: 1617: 1613: 1609: 1605: 1599: 1595: 1591: 1587: 1586: 1573: 1569: 1565: 1561: 1557: 1553: 1549: 1545: 1539: 1530: 1525: 1521: 1517: 1510: 1508: 1502: 1496: 1487: 1482: 1478: 1477: 1469: 1467: 1461: 1455: 1446: 1441: 1437: 1433: 1426: 1424: 1418: 1412: 1403: 1398: 1394: 1390: 1383: 1381: 1375: 1369: 1361: 1355: 1351: 1344: 1335: 1330: 1326: 1322: 1318: 1316: 1307: 1300: 1296: 1291: 1275: 1271: 1265: 1259: 1255: 1251: 1247: 1243: 1237: 1229: 1225: 1221: 1217: 1210: 1208: 1199: 1192: 1188: 1187: 1182: 1178: 1171: 1169: 1167: 1165: 1163: 1161: 1154: 1153:0-8027-1499-4 1150: 1146: 1142: 1137: 1135: 1133: 1131: 1122: 1114: 1110: 1106: 1105: 1099: 1092: 1090: 1073: 1069: 1068: 1063: 1057: 1049: 1045: 1040: 1035: 1031: 1027: 1023: 1019: 1015: 1009: 1007: 1005: 998: 994: 989: 985: 975: 972: 970: 967: 966: 958: 954: 950: 948: 947:0-486-40919-8 944: 940: 936: 932: 928: 925: 924:0-471-01003-0 921: 917: 913: 909: 906: 902: 898: 896: 892: 888: 887: 882: 879: 875: 871: 868: 864: 860: 856: 852: 849: 845: 841: 837: 833: 831:(2nd edition) 830: 826: 824: 823:0-486-61480-8 820: 816: 815: 810: 807: 806:0-8218-1653-5 803: 799: 798: 793: 791: 787: 783: 780: 776: 773: 769: 765: 761: 759: 758:0-387-09212-9 755: 751: 747: 745: 741: 739: 735: 731: 727: 723: 719: 716: 712: 708: 704: 700: 699: 694: 692: 688: 684: 683: 678: 674: 673: 667: 665: 661: 657: 652: 650: 645: 643: 639: 635: 631: 627: 622: 620: 616: 606: 604: 600: 596: 589:Personal life 586: 584: 579: 577: 573: 569: 565: 561: 560:tessellations 558: 554: 553: 548: 544: 540: 536: 532: 528: 524: 520: 519: 514: 510: 505: 503: 499: 495: 491: 490:Oswald Veblen 487: 483: 479: 475: 471: 467: 463: 459: 455: 450: 448: 444: 439: 437: 433: 429: 428:nitrous oxide 423: 418: 408: 406: 402: 398: 394: 390: 389:Coxeter graph 386: 382: 381: 376: 375: 369: 367: 363: 362:Royal Society 359: 355: 351: 347: 342: 340: 335: 331: 327: 323: 319: 315: 306: 300: 297: 295: 292: 291: 289: 285: 282: 279: 277: 273: 270: 267: 263: 260: 257: 253: 250: 246: 239: 236: 233: 230: 227: 224: 221: 218: 215: 212: 209: 208:Smith's Prize 206: 205: 203: 199: 195: 191: 187: 183: 180: 176: 172: 167: 163: 159: 155: 151: 147: 143: 139: 135: 134:Coxeter group 131: 130:Coxeter graph 127: 123: 120: 116: 112: 109: 105: 100: 91:31 March 2003 90: 86: 81: 68: 64: 60: 55: 50: 46: 42: 33: 30: 19: 1726:held at the 1625: 1593: 1558:(1): 19–21. 1555: 1551: 1547: 1538: 1522:(2): 55–59. 1519: 1515: 1506: 1495: 1474: 1465: 1454: 1435: 1431: 1422: 1411: 1392: 1388: 1379: 1368: 1349: 1343: 1324: 1320: 1314: 1306: 1290: 1278:. 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Baker 1774:Categories 1760:, Apr 2007 1688:1183  1123:required.) 980:References 595:vegetarian 557:hyperbolic 515:published 417:Kensington 403:, and the 364:, and the 72:1907-02-09 1815:Polytopes 1810:Chirality 1505:"Review: 1464:"Review: 1421:"Review: 1378:"Review: 1205:"Review: 1048:1748-8494 1032:: 45–66. 907:200: 3–45 638:Companion 535:professor 509:P. 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Index

Donald Coxeter
CC
FRS
FRSC

London
Toronto, Ontario
University of Cambridge
Coxeter element
Coxeter functor
Coxeter graph
Coxeter group
Coxeter matroid
Coxeter notation
Coxeter's loxodromic sequence of tangent circles
Coxeter–Dynkin diagram
Coxeter–Todd lattice
Boerdijk–Coxeter helix
Goldberg–Coxeter construction
Todd–Coxeter algorithm
Tutte–Coxeter graph
LCF notation
Regular skew apeirohedra
Smith's Prize
Henry Marshall Tory Medal
FPS
Jeffery–Williams Prize
CRM-Fields-PIMS prize
Sylvester Medal
Geometry

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