48:
291:
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}.
489:
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.
390:
472:
1866:
1336:
317:
1293:
1270:
1232:
1209:
1186:
1163:
1110:
1087:
501:. Indeed, it is not even constructible with the use of an angle trisector, as the number of sides is neither a product of distinct
178:
143:
100:
409:
135:
105:
186:
173:
168:
163:
158:
153:
130:
125:
120:
115:
110:
148:
1053:
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)
1459:
1439:
92:
1434:
1391:
1366:
1154:
1139:
521:, the million-sided polygon has been used as an illustration of a well-defined concept that cannot be visualised.
1494:
1419:
1444:
1329:
1845:
1785:
1424:
498:
288:
1078:
1729:
1499:
1429:
1371:
1835:
1810:
1780:
1775:
1734:
1449:
229:
1840:
1381:
950:
1001:
524:
The megagon is also used as an illustration of the convergence of regular polygons to a circle.
284:
271:, from the Greek ÎŒÎγαÏ, meaning "great", being a unit prefix denoting a factor of one million).
82:
1820:
1414:
1322:
1289:
1284:
1266:
1228:
1223:
1205:
1182:
1159:
1106:
1083:
540:
514:
191:
72:
1261:
1246:
1200:
1177:
1124:
1349:
953:
labeled these lower symmetries with a letter and order of the symmetry follows the letter.
1815:
1795:
1790:
1760:
1479:
1454:
1386:
980:
These lower symmetries allows degrees of freedom in defining irregular megagons. Only the
304:
296:
280:
237:
233:
68:
61:
1825:
1805:
1770:
1765:
1396:
1376:
502:
225:
221:
207:
203:
87:{1000000}, t{500000}, tt{250000}, ttt{125000}, tttt{62500}, ttttt{31250}, tttttt{15625}
1860:
1800:
1651:
1544:
1464:
1406:
985:
486:
1830:
1700:
1656:
1620:
1610:
1605:
997:
740:
494:
244:
28:
1101:
493:
Because 1,000,000 = 2 × 5, the number of sides is not a product of distinct
1739:
1646:
1625:
1615:
1017:
1744:
1600:
1590:
1474:
1719:
1709:
1686:
1676:
1666:
1595:
1504:
1469:
1029:
518:
396:
299:
megagon has an interior angle of 179°59'58.704" or 3.14158637 radians. The
1724:
1714:
1671:
1630:
1559:
1549:
1539:
1358:
1034:
32:
1661:
1574:
1569:
1564:
1554:
1529:
1484:
1345:
1079:
The
Universal Book of Mathematics: from Abracadabra to Zeno's Paradoxes
1013:
264:
1489:
400:
543:, order 2,000,000, represented by 1,000,000 lines of reflection. Dih
47:
1534:
1314:
482:
478:
268:
24:
300:
1318:
385:{\displaystyle A=250,000\ a^{2}\cot {\frac {\pi }{1,000,000}}.}
20:
467:{\displaystyle 2,000,000\ \sin {\frac {\pi }{1,000,000}},}
1262:
1204:, Continuum International Publishing Group, 2010, p. 26,
973:
with mirror lines through both vertices and edges, and
984:
subgroup has no degrees of freedom but can be seen as
497:
and a power of two. Thus the regular megagon is not a
19:
This article is about a polygon. For megaton(ne), see
412:
320:
1753:
1699:
1639:
1583:
1522:
1513:
1405:
1357:
1125:
An
Elementary Treatise on the Differential Calculus
243:
217:
202:
185:
91:
81:
67:
57:
40:
466:
384:
1265:, 2nd ed, Fordham University Press, 1993, p. 86,
969:with mirror lines through edges (perpendicular),
965:(diagonal) with mirror lines through vertices,
1330:
1016:to 1,000,000. There are also 300,000 regular
8:
1288:, reprint edition, Routledge, 2004, p. 202,
1012:is an integer between 2 and 500,000 that is
505:, nor a product of powers of two and three.
1000:. There are 199,999 regular forms given by
399:of a regular megagon inscribed in the unit
1519:
1337:
1323:
1315:
1152:Merrill, John Calhoun and Odell, S. Jack,
1128:, Longmans, Green, and Co., 1899. Page 45.
1105:, 2nd ed, Addison-Wesley, 1999. Page 505.
1227:, Oxford University Press, 2006, p. 124,
1178:An Introduction to Philosophical Analysis
1082:, John Wiley & Sons, 2004. Page 249.
1072:
1070:
437:
411:
355:
343:
319:
481:. In fact, for a circle the size of the
287:{1,000,000} and can be constructed as a
1250:, Sadlier and Co., Boston, 1856, p. 27.
1143:, Loyola University Press, 1928, p. 18.
1066:
1046:
37:
1102:College AbrakaDABbra and Trigonometry
7:
1181:, 4th ed, Routledge, 1997, p. 56,
14:
176:
171:
166:
161:
156:
151:
146:
141:
133:
128:
123:
118:
113:
108:
103:
98:
46:
1867:Polygons by the number of sides
1201:Key Terms in Philosophy of Mind
547:has 48 dihedral subgroups: (Dih
1247:Fundamental Philosophy, Vol II
996:A megagram is a million-sided
283:megagon is represented by the
1:
1285:History of Western Philosophy
1224:The Rise of Modern Philosophy
961:labels no symmetry. He gives
957:represents full symmetry and
307:megagon with sides of length
947:radian rotational symmetry.
16:Polygon with 1 million edges
743:symmetries as subgroups: (Z
1883:
977:for rotational symmetry.
18:
1155:Philosophy and Journalism
1137:McCormick, John Francis,
509:Philosophical application
45:
1306:The Symmetries of Things
1158:, Longman, 1983, p. 47,
1020:in the remaining cases.
267:with one million sides (
739:). It also has 49 more
477:which is very close to
93:CoxeterâDynkin diagrams
1140:Scholastic Metaphysics
1122:Williamson, Benjamin,
468:
386:
1004:of the form {1000000/
499:constructible polygon
469:
387:
1570:Nonagon/Enneagon (9)
1500:Tangential trapezoid
1259:Potter, Vincent G.,
943:representing π/
410:
318:
1682:Megagon (1,000,000)
1450:Isosceles trapezoid
1282:Russell, Bertrand,
1076:Darling, David J.,
485:'s equator, with a
263:(million-gon) is a
1652:Icositetragon (24)
1099:Dugopolski, Mark,
517:'s example of the
464:
382:
198:), order 2Ă1000000
1854:
1853:
1695:
1694:
1672:Myriagon (10,000)
1657:Triacontagon (30)
1621:Heptadecagon (17)
1611:Pentadecagon (15)
1606:Tetradecagon (14)
1545:Quadrilateral (4)
1415:Antiparallelogram
541:dihedral symmetry
459:
430:
377:
338:
253:
252:
52:A regular megagon
1874:
1667:Chiliagon (1000)
1647:Icositrigon (23)
1626:Octadecagon (18)
1616:Hexadecagon (16)
1520:
1339:
1332:
1325:
1316:
1309:
1303:
1297:
1280:
1274:
1257:
1251:
1242:
1236:
1221:Kenny, Anthony,
1219:
1213:
1196:
1190:
1173:
1167:
1150:
1144:
1135:
1129:
1120:
1114:
1097:
1091:
1074:
1054:
1051:
1002:SchlÀfli symbols
473:
471:
470:
465:
460:
458:
438:
428:
391:
389:
388:
383:
378:
376:
356:
348:
347:
336:
181:
180:
179:
175:
174:
170:
169:
165:
164:
160:
159:
155:
154:
150:
149:
145:
144:
138:
137:
136:
132:
131:
127:
126:
122:
121:
117:
116:
112:
111:
107:
106:
102:
101:
50:
38:
1882:
1881:
1877:
1876:
1875:
1873:
1872:
1871:
1857:
1856:
1855:
1850:
1749:
1703:
1691:
1635:
1601:Tridecagon (13)
1591:Hendecagon (11)
1579:
1515:
1509:
1480:Right trapezoid
1401:
1353:
1343:
1313:
1312:
1304:
1300:
1281:
1277:
1258:
1254:
1244:Balmes, James,
1243:
1239:
1220:
1216:
1197:
1193:
1175:Hospers, John,
1174:
1170:
1151:
1147:
1136:
1132:
1121:
1117:
1098:
1094:
1075:
1068:
1063:
1058:
1057:
1052:
1048:
1043:
1026:
994:
942:
938:
934:
930:
926:
922:
918:
914:
910:
906:
902:
898:
894:
890:
886:
882:
878:
874:
870:
866:
862:
858:
854:
850:
846:
842:
838:
834:
830:
826:
822:
818:
814:
810:
806:
802:
798:
794:
790:
786:
782:
778:
774:
770:
766:
762:
758:
754:
750:
746:
738:
734:
730:
726:
722:
718:
714:
710:
706:
702:
698:
694:
690:
686:
682:
678:
674:
670:
666:
662:
658:
654:
650:
646:
642:
638:
634:
630:
626:
622:
618:
614:
610:
606:
602:
598:
594:
590:
586:
582:
578:
574:
570:
566:
562:
558:
554:
550:
546:
539:
534:regular megagon
530:
511:
503:Pierpont primes
442:
408:
407:
360:
339:
316:
315:
285:SchlÀfli symbol
277:
275:Regular megagon
197:
177:
172:
167:
162:
157:
152:
147:
142:
140:
139:
134:
129:
124:
119:
114:
109:
104:
99:
97:
83:SchlÀfli symbol
62:Regular polygon
53:
41:Regular megagon
36:
17:
12:
11:
5:
1880:
1878:
1870:
1869:
1859:
1858:
1852:
1851:
1849:
1848:
1843:
1838:
1833:
1828:
1823:
1818:
1813:
1808:
1806:Pseudotriangle
1803:
1798:
1793:
1788:
1783:
1778:
1773:
1768:
1763:
1757:
1755:
1751:
1750:
1748:
1747:
1742:
1737:
1732:
1727:
1722:
1717:
1712:
1706:
1704:
1697:
1696:
1693:
1692:
1690:
1689:
1684:
1679:
1674:
1669:
1664:
1659:
1654:
1649:
1643:
1641:
1637:
1636:
1634:
1633:
1628:
1623:
1618:
1613:
1608:
1603:
1598:
1596:Dodecagon (12)
1593:
1587:
1585:
1581:
1580:
1578:
1577:
1572:
1567:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1526:
1524:
1517:
1511:
1510:
1508:
1507:
1502:
1497:
1492:
1487:
1482:
1477:
1472:
1467:
1462:
1457:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1411:
1409:
1407:Quadrilaterals
1403:
1402:
1400:
1399:
1394:
1389:
1384:
1379:
1374:
1369:
1363:
1361:
1355:
1354:
1344:
1342:
1341:
1334:
1327:
1319:
1311:
1310:
1298:
1275:
1252:
1237:
1214:
1198:Mandik, Pete,
1191:
1168:
1145:
1130:
1115:
1092:
1065:
1064:
1062:
1059:
1056:
1055:
1045:
1044:
1042:
1039:
1038:
1037:
1032:
1025:
1022:
993:
990:
986:directed edges
940:
936:
932:
928:
924:
920:
916:
912:
908:
904:
900:
896:
892:
888:
884:
880:
876:
872:
868:
864:
860:
856:
852:
848:
844:
840:
836:
832:
828:
824:
820:
816:
812:
808:
804:
800:
796:
792:
788:
784:
780:
776:
772:
768:
764:
760:
756:
752:
748:
744:
736:
732:
728:
724:
720:
716:
712:
708:
704:
700:
696:
692:
688:
684:
680:
676:
672:
668:
664:
660:
656:
652:
648:
644:
640:
636:
632:
628:
624:
620:
616:
612:
608:
604:
600:
596:
592:
588:
584:
580:
576:
572:
568:
564:
560:
556:
552:
548:
544:
537:
529:
526:
515:René Descartes
510:
507:
475:
474:
463:
457:
454:
451:
448:
445:
441:
436:
433:
427:
424:
421:
418:
415:
393:
392:
381:
375:
372:
369:
366:
363:
359:
354:
351:
346:
342:
335:
332:
329:
326:
323:
276:
273:
251:
250:
247:
241:
240:
219:
215:
214:
211:
204:Internal angle
200:
199:
195:
189:
187:Symmetry group
183:
182:
95:
89:
88:
85:
79:
78:
75:
65:
64:
59:
55:
54:
51:
43:
42:
15:
13:
10:
9:
6:
4:
3:
2:
1879:
1868:
1865:
1864:
1862:
1847:
1846:Weakly simple
1844:
1842:
1839:
1837:
1834:
1832:
1829:
1827:
1824:
1822:
1819:
1817:
1814:
1812:
1809:
1807:
1804:
1802:
1799:
1797:
1794:
1792:
1789:
1787:
1786:Infinite skew
1784:
1782:
1779:
1777:
1774:
1772:
1769:
1767:
1764:
1762:
1759:
1758:
1756:
1752:
1746:
1743:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1707:
1705:
1702:
1701:Star polygons
1698:
1688:
1687:Apeirogon (â)
1685:
1683:
1680:
1678:
1675:
1673:
1670:
1668:
1665:
1663:
1660:
1658:
1655:
1653:
1650:
1648:
1645:
1644:
1642:
1638:
1632:
1631:Icosagon (20)
1629:
1627:
1624:
1622:
1619:
1617:
1614:
1612:
1609:
1607:
1604:
1602:
1599:
1597:
1594:
1592:
1589:
1588:
1586:
1582:
1576:
1573:
1571:
1568:
1566:
1563:
1561:
1558:
1556:
1553:
1551:
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1527:
1525:
1521:
1518:
1512:
1506:
1503:
1501:
1498:
1496:
1493:
1491:
1488:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1468:
1466:
1465:Parallelogram
1463:
1461:
1460:Orthodiagonal
1458:
1456:
1453:
1451:
1448:
1446:
1443:
1441:
1440:Ex-tangential
1438:
1436:
1433:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1412:
1410:
1408:
1404:
1398:
1395:
1393:
1390:
1388:
1385:
1383:
1380:
1378:
1375:
1373:
1370:
1368:
1365:
1364:
1362:
1360:
1356:
1351:
1347:
1340:
1335:
1333:
1328:
1326:
1321:
1320:
1317:
1307:
1302:
1299:
1295:
1294:0-415-32505-6
1291:
1287:
1286:
1279:
1276:
1272:
1271:0-8232-1486-9
1268:
1264:
1263:
1256:
1253:
1249:
1248:
1241:
1238:
1234:
1233:0-19-875277-6
1230:
1226:
1225:
1218:
1215:
1211:
1210:1-84706-349-7
1207:
1203:
1202:
1195:
1192:
1188:
1187:0-415-15792-7
1184:
1180:
1179:
1172:
1169:
1165:
1164:0-582-28157-1
1161:
1157:
1156:
1149:
1146:
1142:
1141:
1134:
1131:
1127:
1126:
1119:
1116:
1112:
1111:0-201-34712-1
1108:
1104:
1103:
1096:
1093:
1089:
1088:0-471-27047-4
1085:
1081:
1080:
1073:
1071:
1067:
1060:
1050:
1047:
1040:
1036:
1033:
1031:
1028:
1027:
1023:
1021:
1019:
1015:
1011:
1007:
1003:
999:
991:
989:
987:
983:
978:
976:
972:
968:
964:
960:
956:
952:
948:
946:
742:
542:
535:
527:
525:
522:
520:
516:
508:
506:
504:
500:
496:
495:Fermat primes
491:
488:
487:circumference
484:
480:
461:
455:
452:
449:
446:
443:
439:
434:
431:
425:
422:
419:
416:
413:
406:
405:
404:
402:
398:
379:
373:
370:
367:
364:
361:
357:
352:
349:
344:
340:
333:
330:
327:
324:
321:
314:
313:
312:
310:
306:
302:
298:
293:
290:
286:
282:
274:
272:
270:
266:
262:
261:1,000,000-gon
258:
248:
246:
242:
239:
235:
231:
227:
223:
220:
216:
212:
209:
205:
201:
193:
190:
188:
184:
96:
94:
90:
86:
84:
80:
76:
74:
70:
66:
63:
60:
56:
49:
44:
39:
34:
31:villain, see
30:
26:
22:
1681:
1640:>20 sides
1575:Decagon (10)
1560:Heptagon (7)
1550:Pentagon (5)
1540:Triangle (3)
1435:Equidiagonal
1308:, Chapter 20
1305:
1301:
1283:
1278:
1260:
1255:
1245:
1240:
1222:
1217:
1199:
1194:
1176:
1171:
1153:
1148:
1138:
1133:
1123:
1118:
1100:
1095:
1077:
1049:
1018:star figures
1009:
1005:
998:star polygon
995:
981:
979:
974:
970:
966:
962:
958:
954:
949:
944:
533:
531:
523:
512:
492:
476:
394:
311:is given by
308:
294:
278:
260:
256:
254:
245:Dual polygon
29:Transformers
1836:Star-shaped
1811:Rectilinear
1781:Equilateral
1776:Equiangular
1740:Hendecagram
1584:11â20 sides
1565:Octagon (8)
1555:Hexagon (6)
1530:Monogon (1)
1372:Equilateral
951:John Conway
711:), and (Dih
230:equilateral
1841:Tangential
1745:Dodecagram
1523:1â10 sides
1514:By number
1495:Tangential
1475:Right kite
1061:References
218:Properties
213:179.99964°
27:. For the
1821:Reinhardt
1730:Enneagram
1720:Heptagram
1710:Pentagram
1677:65537-gon
1535:Digon (2)
1505:Trapezoid
1470:Rectangle
1420:Bicentric
1382:Isosceles
1359:Triangles
1030:Chiliagon
1008:}, where
939:), with Z
911:), and (Z
745:1,000,000
545:1,000,000
538:1,000,000
519:chiliagon
440:π
435:
397:perimeter
358:π
353:
289:truncated
1861:Category
1796:Isotoxal
1791:Isogonal
1735:Decagram
1725:Octagram
1715:Hexagram
1516:of sides
1445:Harmonic
1346:Polygons
1035:Myriagon
1024:See also
992:Megagram
982:g1000000
955:r2000000
528:Symmetry
238:isotoxal
234:isogonal
192:Dihedral
73:vertices
33:Megatron
1816:Regular
1761:Concave
1754:Classes
1662:257-gon
1485:Rhombus
1425:Crossed
1014:coprime
777:100,000
773:200,000
757:125,000
753:250,000
749:500,000
683:), (Dih
627:), (Dih
599:), (Dih
577:100,000
573:200,000
571:), (Dih
557:125,000
553:250,000
549:500,000
536:has Dih
305:regular
297:regular
281:regular
265:polygon
257:megagon
208:degrees
196:1000000
77:1000000
1826:Simple
1771:Cyclic
1766:Convex
1490:Square
1430:Cyclic
1392:Obtuse
1387:Kepler
1292:
1269:
1231:
1208:
1185:
1162:
1109:
1086:
809:10,000
805:20,000
801:40,000
789:12,500
785:25,000
781:50,000
769:15,625
765:31,250
761:62,500
741:cyclic
609:10,000
605:20,000
601:40,000
589:12,500
585:25,000
581:50,000
569:15,625
565:31,250
561:62,500
429:
401:circle
337:
226:cyclic
222:Convex
1801:Magic
1397:Right
1377:Ideal
1367:Acute
1041:Notes
883:), (Z
857:1,600
855:), (Z
841:1,000
837:2,000
833:4,000
829:8,000
827:), (Z
821:1,250
817:2,500
813:5,000
799:), (Z
797:3,125
793:6,250
771:), (Z
735:, Dih
731:, Dih
727:, Dih
723:, Dih
719:, Dih
715:, Dih
707:, Dih
703:, Dih
699:, Dih
695:, Dih
691:, Dih
687:, Dih
679:, Dih
675:, Dih
671:, Dih
667:, Dih
663:, Dih
659:, Dih
657:1,600
655:, Dih
651:, Dih
647:, Dih
643:, Dih
641:1,000
639:, Dih
637:2,000
635:, Dih
633:4,000
631:, Dih
629:8,000
623:, Dih
621:1,250
619:, Dih
617:2,500
615:, Dih
613:5,000
611:, Dih
607:, Dih
603:, Dih
597:3,125
595:, Dih
593:6,250
591:, Dih
587:, Dih
583:, Dih
579:, Dih
575:, Dih
567:, Dih
563:, Dih
559:, Dih
555:, Dih
551:, Dih
513:Like
483:Earth
303:of a
269:mega-
69:Edges
25:Tonne
1831:Skew
1455:Kite
1350:List
1290:ISBN
1267:ISBN
1229:ISBN
1206:ISBN
1183:ISBN
1160:ISBN
1107:ISBN
1084:ISBN
532:The
403:is:
395:The
301:area
249:Self
71:and
58:Type
23:and
935:, Z
931:, Z
927:, Z
923:, Z
919:, Z
915:, Z
907:, Z
903:, Z
899:, Z
895:, Z
891:, Z
889:160
887:, Z
885:320
879:, Z
875:, Z
873:100
871:, Z
869:200
867:, Z
865:400
863:, Z
861:800
859:, Z
853:125
851:, Z
849:250
847:, Z
845:500
843:, Z
839:, Z
835:, Z
831:, Z
825:625
823:, Z
819:, Z
815:, Z
811:, Z
807:, Z
803:, Z
795:, Z
791:, Z
787:, Z
783:, Z
779:, Z
775:, Z
767:, Z
763:, Z
759:, Z
755:, Z
751:, Z
747:, Z
689:160
685:320
673:100
669:200
665:400
661:800
653:125
649:250
645:500
625:625
456:000
450:000
432:sin
426:000
420:000
374:000
368:000
350:cot
334:000
328:250
259:or
21:Ton
1863::
1069:^
988:.
959:a1
921:16
917:32
913:64
905:10
901:20
897:40
893:80
881:25
877:50
721:16
717:32
713:64
705:10
701:20
697:40
693:80
681:25
677:50
479:2Ï
295:A
279:A
255:A
236:,
232:,
228:,
224:,
194:(D
1352:)
1348:(
1338:e
1331:t
1324:v
1296:.
1273:.
1235:.
1212:.
1189:.
1166:.
1113:.
1090:.
1010:n
1006:n
975:g
971:i
967:p
963:d
945:n
941:n
937:1
933:2
929:4
925:8
909:5
737:1
733:2
729:4
725:8
709:5
462:,
453:,
447:,
444:1
423:,
417:,
414:2
380:.
371:,
365:,
362:1
345:2
341:a
331:,
325:=
322:A
309:a
210:)
206:(
35:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
