59:
302:
500,000-gon, t{500,000}, a twice-truncated 250,000-gon, tt{250,000}, a thrice-truncated 125,000-gon, ttt{125,000}, or a four-fold-truncated 62,500-gon, tttt{62,500}, a five-fold-truncated 31,250-gon, ttttt{31,250}, or a six-fold-truncated 15,625-gon, tttttt{15,625}.
500:
of 40,075 kilometres, one edge of a megagon inscribed in such a circle would be slightly over 40 meters long. The difference between the perimeter of the inscribed megagon and the circumference of this circle comes to less than 1/16 millimeters.
401:
483:
189:
154:
111:
146:
116:
184:
179:
174:
169:
164:
141:
136:
131:
126:
121:
159:
328:
1877:
512:. Indeed, it is not even constructible with the use of an angle trisector, as the number of sides is neither a product of distinct
420:
1064:
199,999 = 500,000 cases â 1 (convex) â 100,000 (multiples of 5) â 250,000 (multiples of 2) + 50,000 (multiples of 2 and 5)
17:
1347:
1304:
1281:
1243:
1220:
1197:
1174:
1121:
1098:
1165:
1150:
532:, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.
197:
1470:
1450:
1445:
1402:
1377:
1089:
103:
1505:
1430:
535:
The megagon is also used as an illustration of the convergence of regular polygons to a circle.
282:, from the Greek ÎŒÎγαÏ, meaning "great", being a unit prefix denoting a factor of one million).
1455:
1340:
1295:
1234:
1856:
1796:
1435:
1272:
1257:
1211:
1188:
1135:
509:
299:
1740:
1510:
1440:
1382:
964:
labeled these lower symmetries with a letter and order of the symmetry follows the letter.
991:
These lower symmetries allows degrees of freedom in defining irregular megagons. Only the
8:
1846:
1821:
1791:
1786:
1745:
1460:
240:
1851:
1392:
961:
98:{1000000}, t{500000}, tt{250000}, ttt{125000}, tttt{62500}, ttttt{31250}, tttttt{15625}
1012:
295:
93:
1831:
1425:
1333:
1300:
1277:
1239:
1216:
1193:
1170:
1117:
1094:
551:
202:
83:
525:
1360:
1826:
1806:
1801:
1771:
1490:
1465:
1397:
1112:
504:
Because 1,000,000 = 2 × 5, the number of sides is not a product of distinct
315:
307:
291:
248:
244:
79:
72:
1836:
1816:
1781:
1776:
1407:
1387:
513:
236:
232:
218:
214:
1871:
1811:
1662:
1555:
1475:
1417:
996:
497:
1841:
1711:
1667:
1631:
1621:
1616:
1008:
751:
505:
310:
megagon has an interior angle of 179°59'58.704" or 3.14158637 radians. The
255:
39:
1750:
1657:
1636:
1626:
1028:
1755:
1611:
1601:
1485:
1090:
The
Universal Book of Mathematics: from Abracadabra to Zeno's Paradoxes
1730:
1720:
1697:
1687:
1677:
1606:
1515:
1480:
1040:
529:
407:
554:, order 2,000,000, represented by 1,000,000 lines of reflection. Dih
1735:
1725:
1682:
1641:
1570:
1560:
1550:
1369:
1045:
43:
1325:
1672:
1585:
1580:
1575:
1565:
1540:
1495:
1356:
1024:
275:
1500:
411:
396:{\displaystyle A=250,000\ a^{2}\cot {\frac {\pi }{1,000,000}}.}
1545:
493:
279:
35:
489:
311:
478:{\displaystyle 2,000,000\ \sin {\frac {\pi }{1,000,000}},}
58:
1273:
1215:, Continuum International Publishing Group, 2010, p. 26,
31:
984:
with mirror lines through both vertices and edges, and
995:
subgroup has no degrees of freedom but can be seen as
508:
and a power of two. Thus the regular megagon is not a
30:
This article is about a polygon. For megaton(ne), see
423:
331:
1136:
An
Elementary Treatise on the Differential Calculus
477:
395:
1276:, 2nd ed, Fordham University Press, 1993, p. 86,
980:with mirror lines through edges (perpendicular),
1869:
976:(diagonal) with mirror lines through vertices,
1341:
1027:to 1,000,000. There are also 300,000 regular
1299:, reprint edition, Routledge, 2004, p. 202,
1023:is an integer between 2 and 500,000 that is
519:
516:, nor a product of powers of two and three.
1011:. There are 199,999 regular forms given by
410:of a regular megagon inscribed in the unit
1348:
1334:
1163:Merrill, John Calhoun and Odell, S. Jack,
1139:, Longmans, Green, and Co., 1899. Page 45.
1116:, 2nd ed, Addison-Wesley, 1999. Page 505.
1238:, Oxford University Press, 2006, p. 124,
1189:An Introduction to Philosophical Analysis
1093:, John Wiley & Sons, 2004. Page 249.
1083:
1081:
492:. In fact, for a circle the size of the
298:{1,000,000} and can be constructed as a
1261:, Sadlier and Co., Boston, 1856, p. 27.
1154:, Loyola University Press, 1928, p. 18.
14:
1870:
1078:
1329:
1113:College AbrakaDABbra and Trigonometry
1355:
24:
1192:, 4th ed, Routledge, 1997, p. 56,
285:
25:
1889:
187:
182:
177:
172:
167:
162:
157:
152:
144:
139:
134:
129:
124:
119:
114:
109:
57:
1878:Polygons by the number of sides
1310:
1287:
1264:
1212:Key Terms in Philosophy of Mind
1058:
558:has 48 dihedral subgroups: (Dih
1258:Fundamental Philosophy, Vol II
1249:
1226:
1203:
1180:
1157:
1142:
1127:
1104:
1007:A megagram is a million-sided
294:megagon is represented by the
13:
1:
1296:History of Western Philosophy
1235:The Rise of Modern Philosophy
1071:
972:labels no symmetry. He gives
968:represents full symmetry and
318:megagon with sides of length
958:radian rotational symmetry.
27:Polygon with 1 million edges
7:
1034:
1002:
754:symmetries as subgroups: (Z
538:
10:
1894:
988:for rotational symmetry.
29:
1764:
1710:
1650:
1594:
1533:
1524:
1416:
1368:
1166:Philosophy and Journalism
1148:McCormick, John Francis,
520:Philosophical application
254:
228:
213:
196:
102:
92:
78:
68:
56:
51:
1317:The Symmetries of Things
1169:, Longman, 1983, p. 47,
1051:
1031:in the remaining cases.
278:with one million sides (
750:). It also has 49 more
488:which is very close to
104:CoxeterâDynkin diagrams
1151:Scholastic Metaphysics
1133:Williamson, Benjamin,
479:
397:
1015:of the form {1000000/
510:constructible polygon
480:
398:
1581:Nonagon/Enneagon (9)
1511:Tangential trapezoid
1270:Potter, Vincent G.,
954:representing π/
421:
329:
1693:Megagon (1,000,000)
1461:Isosceles trapezoid
1293:Russell, Bertrand,
1087:Darling, David J.,
496:'s equator, with a
274:(million-gon) is a
18:Megagram (geometry)
1663:Icositetragon (24)
1110:Dugopolski, Mark,
528:'s example of the
475:
393:
209:), order 2Ă1000000
1865:
1864:
1706:
1705:
1683:Myriagon (10,000)
1668:Triacontagon (30)
1632:Heptadecagon (17)
1622:Pentadecagon (15)
1617:Tetradecagon (14)
1556:Quadrilateral (4)
1426:Antiparallelogram
552:dihedral symmetry
470:
441:
388:
349:
264:
263:
63:A regular megagon
16:(Redirected from
1885:
1678:Chiliagon (1000)
1658:Icositrigon (23)
1637:Octadecagon (18)
1627:Hexadecagon (16)
1531:
1530:
1350:
1343:
1336:
1327:
1326:
1320:
1314:
1308:
1291:
1285:
1268:
1262:
1253:
1247:
1232:Kenny, Anthony,
1230:
1224:
1207:
1201:
1184:
1178:
1161:
1155:
1146:
1140:
1131:
1125:
1108:
1102:
1085:
1065:
1062:
1013:SchlÀfli symbols
484:
482:
481:
476:
471:
469:
449:
439:
402:
400:
399:
394:
389:
387:
367:
359:
358:
347:
192:
191:
190:
186:
185:
181:
180:
176:
175:
171:
170:
166:
165:
161:
160:
156:
155:
149:
148:
147:
143:
142:
138:
137:
133:
132:
128:
127:
123:
122:
118:
117:
113:
112:
61:
49:
48:
21:
1893:
1892:
1888:
1887:
1886:
1884:
1883:
1882:
1868:
1867:
1866:
1861:
1760:
1714:
1702:
1646:
1612:Tridecagon (13)
1602:Hendecagon (11)
1590:
1526:
1520:
1491:Right trapezoid
1412:
1364:
1354:
1324:
1323:
1315:
1311:
1292:
1288:
1269:
1265:
1255:Balmes, James,
1254:
1250:
1231:
1227:
1208:
1204:
1186:Hospers, John,
1185:
1181:
1162:
1158:
1147:
1143:
1132:
1128:
1109:
1105:
1086:
1079:
1074:
1069:
1068:
1063:
1059:
1054:
1037:
1005:
953:
949:
945:
941:
937:
933:
929:
925:
921:
917:
913:
909:
905:
901:
897:
893:
889:
885:
881:
877:
873:
869:
865:
861:
857:
853:
849:
845:
841:
837:
833:
829:
825:
821:
817:
813:
809:
805:
801:
797:
793:
789:
785:
781:
777:
773:
769:
765:
761:
757:
749:
745:
741:
737:
733:
729:
725:
721:
717:
713:
709:
705:
701:
697:
693:
689:
685:
681:
677:
673:
669:
665:
661:
657:
653:
649:
645:
641:
637:
633:
629:
625:
621:
617:
613:
609:
605:
601:
597:
593:
589:
585:
581:
577:
573:
569:
565:
561:
557:
550:
545:regular megagon
541:
522:
514:Pierpont primes
453:
448:
422:
419:
418:
371:
366:
354:
350:
330:
327:
326:
296:SchlÀfli symbol
288:
286:Regular megagon
208:
188:
183:
178:
173:
168:
163:
158:
153:
151:
150:
145:
140:
135:
130:
125:
120:
115:
110:
108:
94:SchlÀfli symbol
73:Regular polygon
64:
52:Regular megagon
47:
28:
23:
22:
15:
12:
11:
5:
1891:
1881:
1880:
1863:
1862:
1860:
1859:
1854:
1849:
1844:
1839:
1834:
1829:
1824:
1819:
1817:Pseudotriangle
1814:
1809:
1804:
1799:
1794:
1789:
1784:
1779:
1774:
1768:
1766:
1762:
1761:
1759:
1758:
1753:
1748:
1743:
1738:
1733:
1728:
1723:
1717:
1715:
1708:
1707:
1704:
1703:
1701:
1700:
1695:
1690:
1685:
1680:
1675:
1670:
1665:
1660:
1654:
1652:
1648:
1647:
1645:
1644:
1639:
1634:
1629:
1624:
1619:
1614:
1609:
1607:Dodecagon (12)
1604:
1598:
1596:
1592:
1591:
1589:
1588:
1583:
1578:
1573:
1568:
1563:
1558:
1553:
1548:
1543:
1537:
1535:
1528:
1522:
1521:
1519:
1518:
1513:
1508:
1503:
1498:
1493:
1488:
1483:
1478:
1473:
1468:
1463:
1458:
1453:
1448:
1443:
1438:
1433:
1428:
1422:
1420:
1418:Quadrilaterals
1414:
1413:
1411:
1410:
1405:
1400:
1395:
1390:
1385:
1380:
1374:
1372:
1366:
1365:
1353:
1352:
1345:
1338:
1330:
1322:
1321:
1309:
1286:
1263:
1248:
1225:
1209:Mandik, Pete,
1202:
1179:
1156:
1141:
1126:
1103:
1076:
1075:
1073:
1070:
1067:
1066:
1056:
1055:
1053:
1050:
1049:
1048:
1043:
1036:
1033:
1004:
1001:
997:directed edges
951:
947:
943:
939:
935:
931:
927:
923:
919:
915:
911:
907:
903:
899:
895:
891:
887:
883:
879:
875:
871:
867:
863:
859:
855:
851:
847:
843:
839:
835:
831:
827:
823:
819:
815:
811:
807:
803:
799:
795:
791:
787:
783:
779:
775:
771:
767:
763:
759:
755:
747:
743:
739:
735:
731:
727:
723:
719:
715:
711:
707:
703:
699:
695:
691:
687:
683:
679:
675:
671:
667:
663:
659:
655:
651:
647:
643:
639:
635:
631:
627:
623:
619:
615:
611:
607:
603:
599:
595:
591:
587:
583:
579:
575:
571:
567:
563:
559:
555:
548:
540:
537:
526:René Descartes
521:
518:
486:
485:
474:
468:
465:
462:
459:
456:
452:
447:
444:
438:
435:
432:
429:
426:
404:
403:
392:
386:
383:
380:
377:
374:
370:
365:
362:
357:
353:
346:
343:
340:
337:
334:
287:
284:
262:
261:
258:
252:
251:
230:
226:
225:
222:
215:Internal angle
211:
210:
206:
200:
198:Symmetry group
194:
193:
106:
100:
99:
96:
90:
89:
86:
76:
75:
70:
66:
65:
62:
54:
53:
26:
9:
6:
4:
3:
2:
1890:
1879:
1876:
1875:
1873:
1858:
1857:Weakly simple
1855:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1828:
1825:
1823:
1820:
1818:
1815:
1813:
1810:
1808:
1805:
1803:
1800:
1798:
1797:Infinite skew
1795:
1793:
1790:
1788:
1785:
1783:
1780:
1778:
1775:
1773:
1770:
1769:
1767:
1763:
1757:
1754:
1752:
1749:
1747:
1744:
1742:
1739:
1737:
1734:
1732:
1729:
1727:
1724:
1722:
1719:
1718:
1716:
1713:
1712:Star polygons
1709:
1699:
1698:Apeirogon (â)
1696:
1694:
1691:
1689:
1686:
1684:
1681:
1679:
1676:
1674:
1671:
1669:
1666:
1664:
1661:
1659:
1656:
1655:
1653:
1649:
1643:
1642:Icosagon (20)
1640:
1638:
1635:
1633:
1630:
1628:
1625:
1623:
1620:
1618:
1615:
1613:
1610:
1608:
1605:
1603:
1600:
1599:
1597:
1593:
1587:
1584:
1582:
1579:
1577:
1574:
1572:
1569:
1567:
1564:
1562:
1559:
1557:
1554:
1552:
1549:
1547:
1544:
1542:
1539:
1538:
1536:
1532:
1529:
1523:
1517:
1514:
1512:
1509:
1507:
1504:
1502:
1499:
1497:
1494:
1492:
1489:
1487:
1484:
1482:
1479:
1477:
1476:Parallelogram
1474:
1472:
1471:Orthodiagonal
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1451:Ex-tangential
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1427:
1424:
1423:
1421:
1419:
1415:
1409:
1406:
1404:
1401:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1379:
1376:
1375:
1373:
1371:
1367:
1362:
1358:
1351:
1346:
1344:
1339:
1337:
1332:
1331:
1328:
1318:
1313:
1306:
1305:0-415-32505-6
1302:
1298:
1297:
1290:
1283:
1282:0-8232-1486-9
1279:
1275:
1274:
1267:
1260:
1259:
1252:
1245:
1244:0-19-875277-6
1241:
1237:
1236:
1229:
1222:
1221:1-84706-349-7
1218:
1214:
1213:
1206:
1199:
1198:0-415-15792-7
1195:
1191:
1190:
1183:
1176:
1175:0-582-28157-1
1172:
1168:
1167:
1160:
1153:
1152:
1145:
1138:
1137:
1130:
1123:
1122:0-201-34712-1
1119:
1115:
1114:
1107:
1100:
1099:0-471-27047-4
1096:
1092:
1091:
1084:
1082:
1077:
1061:
1057:
1047:
1044:
1042:
1039:
1038:
1032:
1030:
1026:
1022:
1018:
1014:
1010:
1000:
998:
994:
989:
987:
983:
979:
975:
971:
967:
963:
959:
957:
753:
553:
546:
536:
533:
531:
527:
517:
515:
511:
507:
506:Fermat primes
502:
499:
498:circumference
495:
491:
472:
466:
463:
460:
457:
454:
450:
445:
442:
436:
433:
430:
427:
424:
417:
416:
415:
413:
409:
390:
384:
381:
378:
375:
372:
368:
363:
360:
355:
351:
344:
341:
338:
335:
332:
325:
324:
323:
321:
317:
313:
309:
304:
301:
297:
293:
283:
281:
277:
273:
272:1,000,000-gon
269:
259:
257:
253:
250:
246:
242:
238:
234:
231:
227:
223:
220:
216:
212:
204:
201:
199:
195:
107:
105:
101:
97:
95:
91:
87:
85:
81:
77:
74:
71:
67:
60:
55:
50:
45:
42:villain, see
41:
37:
33:
19:
1692:
1651:>20 sides
1586:Decagon (10)
1571:Heptagon (7)
1561:Pentagon (5)
1551:Triangle (3)
1446:Equidiagonal
1319:, Chapter 20
1316:
1312:
1294:
1289:
1271:
1266:
1256:
1251:
1233:
1228:
1210:
1205:
1187:
1182:
1164:
1159:
1149:
1144:
1134:
1129:
1111:
1106:
1088:
1060:
1029:star figures
1020:
1016:
1009:star polygon
1006:
992:
990:
985:
981:
977:
973:
969:
965:
960:
955:
544:
542:
534:
523:
503:
487:
405:
322:is given by
319:
305:
289:
271:
267:
265:
256:Dual polygon
40:Transformers
1847:Star-shaped
1822:Rectilinear
1792:Equilateral
1787:Equiangular
1751:Hendecagram
1595:11â20 sides
1576:Octagon (8)
1566:Hexagon (6)
1541:Monogon (1)
1383:Equilateral
962:John Conway
722:), and (Dih
241:equilateral
1852:Tangential
1756:Dodecagram
1534:1â10 sides
1525:By number
1506:Tangential
1486:Right kite
1072:References
229:Properties
224:179.99964°
38:. For the
1832:Reinhardt
1741:Enneagram
1731:Heptagram
1721:Pentagram
1688:65537-gon
1546:Digon (2)
1516:Trapezoid
1481:Rectangle
1431:Bicentric
1393:Isosceles
1370:Triangles
1041:Chiliagon
1019:}, where
950:), with Z
922:), and (Z
756:1,000,000
556:1,000,000
549:1,000,000
530:chiliagon
451:π
446:
408:perimeter
369:π
364:
300:truncated
1872:Category
1807:Isotoxal
1802:Isogonal
1746:Decagram
1736:Octagram
1726:Hexagram
1527:of sides
1456:Harmonic
1357:Polygons
1046:Myriagon
1035:See also
1003:Megagram
993:g1000000
966:r2000000
539:Symmetry
249:isotoxal
245:isogonal
203:Dihedral
84:vertices
44:Megatron
1827:Regular
1772:Concave
1765:Classes
1673:257-gon
1496:Rhombus
1436:Crossed
1025:coprime
788:100,000
784:200,000
768:125,000
764:250,000
760:500,000
694:), (Dih
638:), (Dih
610:), (Dih
588:100,000
584:200,000
582:), (Dih
568:125,000
564:250,000
560:500,000
547:has Dih
316:regular
308:regular
292:regular
276:polygon
268:megagon
219:degrees
207:1000000
88:1000000
1837:Simple
1782:Cyclic
1777:Convex
1501:Square
1441:Cyclic
1403:Obtuse
1398:Kepler
1303:
1280:
1242:
1219:
1196:
1173:
1120:
1097:
820:10,000
816:20,000
812:40,000
800:12,500
796:25,000
792:50,000
780:15,625
776:31,250
772:62,500
752:cyclic
620:10,000
616:20,000
612:40,000
600:12,500
596:25,000
592:50,000
580:15,625
576:31,250
572:62,500
440:
412:circle
348:
237:cyclic
233:Convex
1812:Magic
1408:Right
1388:Ideal
1378:Acute
1052:Notes
894:), (Z
868:1,600
866:), (Z
852:1,000
848:2,000
844:4,000
840:8,000
838:), (Z
832:1,250
828:2,500
824:5,000
810:), (Z
808:3,125
804:6,250
782:), (Z
746:, Dih
742:, Dih
738:, Dih
734:, Dih
730:, Dih
726:, Dih
718:, Dih
714:, Dih
710:, Dih
706:, Dih
702:, Dih
698:, Dih
690:, Dih
686:, Dih
682:, Dih
678:, Dih
674:, Dih
670:, Dih
668:1,600
666:, Dih
662:, Dih
658:, Dih
654:, Dih
652:1,000
650:, Dih
648:2,000
646:, Dih
644:4,000
642:, Dih
640:8,000
634:, Dih
632:1,250
630:, Dih
628:2,500
626:, Dih
624:5,000
622:, Dih
618:, Dih
614:, Dih
608:3,125
606:, Dih
604:6,250
602:, Dih
598:, Dih
594:, Dih
590:, Dih
586:, Dih
578:, Dih
574:, Dih
570:, Dih
566:, Dih
562:, Dih
524:Like
494:Earth
314:of a
280:mega-
80:Edges
36:Tonne
1842:Skew
1466:Kite
1361:List
1301:ISBN
1278:ISBN
1240:ISBN
1217:ISBN
1194:ISBN
1171:ISBN
1118:ISBN
1095:ISBN
543:The
414:is:
406:The
312:area
260:Self
82:and
69:Type
34:and
946:, Z
942:, Z
938:, Z
934:, Z
930:, Z
926:, Z
918:, Z
914:, Z
910:, Z
906:, Z
902:, Z
900:160
898:, Z
896:320
890:, Z
886:, Z
884:100
882:, Z
880:200
878:, Z
876:400
874:, Z
872:800
870:, Z
864:125
862:, Z
860:250
858:, Z
856:500
854:, Z
850:, Z
846:, Z
842:, Z
836:625
834:, Z
830:, Z
826:, Z
822:, Z
818:, Z
814:, Z
806:, Z
802:, Z
798:, Z
794:, Z
790:, Z
786:, Z
778:, Z
774:, Z
770:, Z
766:, Z
762:, Z
758:, Z
700:160
696:320
684:100
680:200
676:400
672:800
664:125
660:250
656:500
636:625
467:000
461:000
443:sin
437:000
431:000
385:000
379:000
361:cot
345:000
339:250
270:or
32:Ton
1874::
1080:^
999:.
970:a1
932:16
928:32
924:64
916:10
912:20
908:40
904:80
892:25
888:50
732:16
728:32
724:64
716:10
712:20
708:40
704:80
692:25
688:50
490:2Ï
306:A
290:A
266:A
247:,
243:,
239:,
235:,
205:(D
1363:)
1359:(
1349:e
1342:t
1335:v
1307:.
1284:.
1246:.
1223:.
1200:.
1177:.
1124:.
1101:.
1021:n
1017:n
986:g
982:i
978:p
974:d
956:n
952:n
948:1
944:2
940:4
936:8
920:5
748:1
744:2
740:4
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464:,
458:,
455:1
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428:,
425:2
391:.
382:,
376:,
373:1
356:2
352:a
342:,
336:=
333:A
320:a
221:)
217:(
46:.
20:)
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