206:
196:
175:
550:
able to make the people around you understand it, then you should not proceed any further before rewriting. It may involve several rounds of back and forth before your argument is polished enough to be understandable. Once that is done, you should submit it to a mathematics journal. Posting your own research onto a
Knowledge article is something that you should never do, even if the research is correct - that should be left to others. Best wishes,
32:
287:
144:
2338:
1151:
912:
1381:
As you have been repeatedly told, this is original research, which is forbidden by
Knowledge's core policies. You need to get your research published. After that, it needs to become notable. (Most research, including my own, is not.) After that, it can be incorporated into Knowledge. Until then, your
549:
If you want to contribute to mathematical research, the proper way to do it would be to do what all people do when they are starting out: First discuss your work with your friends and colleagues to make sure that your argument is written so clearly that no one could misunderstood it. If you are not
683:
r1=radius of the small circle; r3=radius of the larger circle; a=side of the small polygon; A1/P1=area/perimeter of the small circle; A2/P2=area/perimeter of the small polygon; A3/P3=area/perimeter of the larger circle; A4/P4=area/perimeter of the larger polygon; c=coefficient of the area/perimeter
2418:
the concentric circles to straight strips". But in this case it is even worse because the next paragraph (dividing up a circle into triangles) follows a completely different idea. It would be better to let the reader be aware of this difference, like adding another picture of "dividing up a circle
2234:
You've asked two digital superidiots. Please stop doing this. They may easily produce as long laudatory enunciations as you wish, based just on a statistical correlation of words you used in your question, but they have ZERO idea about abstract notions you use and their mathematical definitions.
2138:
You have been asked not to edit earlier posts in talk page threads. Again, please just post a new, corrected version at the bottom of the thread. If this process seems cumbersome, because you are revising a large block of text, then please instead post that text in your
546:, you do not explain how c follows from a and b. And in fact, c is false: the sum of the areas of the four quarter circles (centered at the vertices and passing through a point halfway between the square's center and a side) is strictly less than the area of the square.
423:
You seem to miss the fact the proportionality coefficient between the area of a circle and the square of its radius is the same as between the circumference of the circle and its diameter (which is known at least since
Archimedes). And that coefficient
2364:, you can remove the reference if you want. But I would leave the fact (that there is no better approximation with denominator <16604) there. The fact is routine to verify for anyone with computer literacy, so I would think it would fall under
926:
2290:
This is not a help page for mathematics. You might try asking on a site intended for that. Or you might read a calculus textbook section on integration in polar coordinates. There's a good chance that it will contain this exact example.
2215:
Most probably
Archimedes did not considered this approach, because he apparently understood, what he was trying to do. And if he tried it and then he left no notes about it, then it would mean the approach turned out counterproductive.
687:
1355:
1773:
1527:
2402:
of shell integration in turn depends on the formula of area of ring which apparently relies on the formula of area of circle. Without referring to shell integration, it is actually complicated to justify "one can
1181:
Problem #2: Despite of the difference decreases between the polygons' perimeter, as the number of their sides increases, the actual value of their perimeter can only be calculated with endless fractions. (See
674:
is based on the assumption, that the circumference of a circle can be calculated from the difference of the perimeters of an inscribed and a circumscribed polygon. To test this theory, I start with squares.
2023:
95:
1688:
262:
1901:
1212:
2263:
The first integral goes from - r to r, while the second goes from - π/2 to π/2, but when performing the trigonometric substitution, i got the integral from - x/sin θ to x/sin θ.
1948:
1835:
1585:
2061:
1204:
1452:
and to estimate (bound from both sides) its actual value. Additionally, the more sides of polygons, the better estimation (shorter interval in which the sought value is).
1146:{\displaystyle r1={\tfrac {\sqrt {3}}{2}}*a;r3=a;P1=2c*{\tfrac {\sqrt {3}}{2}}*a=c*{\sqrt {3}}*a;P2=6*a;P3=2c*a;P4=6*{\tfrac {2}{\sqrt {3}}}*a={\tfrac {12}{\sqrt {3}}}*a}
1359:
This proportion enables to exactly determine the area of the circle between the squares and vice versa: the square between the inscribed and the circumscribed circles.
1176:
672:
399:
1608:
907:{\displaystyle r1={\tfrac {a}{2}};r3={\tfrac {\sqrt {2}}{2}}*a;P1=2c*{\tfrac {a}{2}}=c*a;P2=4*a;P3=2c*{\tfrac {\sqrt {2}}{2}}*a=c*{\sqrt {2}}*a;P4=4*{\sqrt {2}}*a}
1219:
2452:
1545:
the actual value of their perimeter can only be calculated with endless fractions. (See {\sqrt {3}} above for instance.) That means decrease of accuracy.
252:
1362:
1694:
2184:
1478:
228:
2447:
2442:
2267:
58:
43:
53:
219:
180:
2067:
Honestly, not an impressive result. Especially today, in days of super-computers, compared to a twenty-two–centuries–old result by
1554:
And this has nothing to do with accuracy, because we can calculate values of roots as accurate (as many exact digits) as we want.
1959:
52:
at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be
2201:
Unfortunately, I can't ask Mr
Archimedes about it. I didn't find any notes about if he considered and dismissed this approach.
308:
304:
300:
49:
1382:
research should not be discussed on
Knowledge talk pages, because talk pages are for discussing impending edits to articles.
606:
381:
Thank you for thinking along. I've added some extra explanation to support my theorem. Please note, that I'm not calculating
2162:
1617:
155:
2167:
1396:
Your definition of c and value of P4 is wrong, but no serious math journal would publish your work even if you fix it.
338:
31:
1551:
One doesn't need a square root to get an 'endless fraction', a simple ordinary quotient is enough: 1/3 = 0.3333333...
919:
678:
1841:
317:
2271:
2424:
2373:
1178:
is based on calculating with 71 side polygons. Such determination is a rough guess between 4 and infinite.
555:
491:
487:
483:
114:
480:
Please indent your entries properly. This helps much in following the talk when it forks into sub-threads.
2319:
2420:
1401:
161:
205:
2140:
594:
143:
2202:
2170:
2117:
1912:
1367:
611:
598:
574:
537:
522:
475:
456:
418:
402:
2330:) a reliable source? I'm afraid it counts as a primary source and as such it should be considered
1784:
227:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
2369:
2312:
2206:
2174:
2121:
1563:
1371:
636:
615:
602:
578:
566:
551:
526:
460:
406:
356:
323:
211:
2034:
1185:
195:
174:
2399:
2395:
2192:
2411:
2407:
this ring by a rectangle". Anyway, it's still a good introduction paragraph to onion proof.
2391:
2348:
2296:
2240:
2221:
2148:
2095:
1397:
1387:
503:
437:
401:, what I'm doing, is comparing the circle directly to a square, instead of other polygons.
319:
286:
495:
1161:
657:
384:
2365:
2282:
1590:
1350:{\displaystyle A1=c*{\tfrac {a^{2}}{4}};A2=a^{2};A3=c*{\tfrac {a^{2}}{2}};A4=2*a^{2};}
2436:
2331:
2188:
17:
2281:
The text is correct as written. Citation would be nice, although this is arguably
2361:
2344:
2292:
2236:
2217:
2144:
2091:
1448:
The properties of two sequences of perimeters allow us to infer the coefficient
1383:
514:
499:
450:
433:
376:
224:
2068:
1768:{\displaystyle A3=c\cdot {\tfrac {a^{2}}{2}};\color {darkred}A4=2\cdot a^{2};}
201:
2114:
I don't know, if it was a 71, or a 96 side polygon, but that's not the point.
1462:
The mathematical constant \pi is based on calculating with 71 side polygons.
1522:{\displaystyle 3{\frac {10}{\color {darkred}71}}<\pi <3{\frac {1}{7}}}
1475:
appears in the well-known result of
Archimedes, who calculated the bounding
321:
2428:
2377:
2352:
2300:
2275:
2244:
2225:
2210:
2196:
2178:
2152:
2125:
2099:
1405:
1391:
1375:
619:
582:
559:
530:
507:
464:
441:
410:
2168:
Screenshot of discussing the area of a circle with a supercomputer (Bard)
2163:
Screenshot of discussing the area of a circle with a supercomputer (Bing)
1560:
There is a mistake in the first drawing: a side of the big square is
543:
2159:
I've asked two supercomputers about this. Here are their responses:
1363:
File:Find_the_area_of_a_circle_by_cutting_it_to_four_quarters.jpeg
482:
Compare the content and the visible results in these three edits:
1209:
Take the areas of the squares and the inscribed circles instead:
1612:
As a result, the fourth equation in the second set should read:
1431:, that the circumference of a circle can be calculated from the
1155:
The number of the polygons' sides can be increased to infinite.
324:
280:
137:
2084:: cease bragging about your mind-blowing results, and start
2018:{\displaystyle a^{2}<c\cdot {\frac {a^{2}}{2}}<2a^{2}}
1541:
Sentences #7 & 8 reveal an obvious misunderstanding.
1683:{\displaystyle A1=c\cdot {\tfrac {a^{2}}{4}};A2=a^{2};}
1441:
There is NO such assumption, and the coefficient named
107:
88:
1882:
1714:
1637:
1445:
is NOT calculated from a difference of any perimeters.
1298:
1239:
1206:
above for instance.) That means decrease of accuracy.
1124:
1101:
996:
940:
832:
766:
725:
701:
2037:
1962:
1915:
1844:
1787:
1697:
1620:
1593:
1566:
1481:
1222:
1188:
1164:
929:
690:
660:
387:
573:
Thank you. I've extended the proof on its talk page.
223:, a collaborative effort to improve the coverage of
62:
of the decision if they believe there was a mistake.
2386:First paragraphs of onion proof and triangle proof
2055:
2017:
1942:
1895:
1829:
1767:
1682:
1602:
1579:
1521:
1349:
1198:
1170:
1145:
906:
666:
393:
2266:How do I get the same bounds given in the proof?
2410:Similar problem lies in the first paragraph of
1427:The idea of the mathematical constant \pi is
1435:of an inscribed and a circumscribed polygon.
332:This page has archives. Sections older than
8:
1896:{\displaystyle A1:A2=A3:A4={\tfrac {c}{4}}}
1779:and all you can infer from this system is:
643:The following discussion has been closed.
632:
363:The following discussion has been closed.
352:
169:
67:
26:
2111:Thank you, the large square is corrected.
2036:
2009:
1988:
1982:
1967:
1961:
1914:
1881:
1843:
1786:
1755:
1720:
1713:
1696:
1671:
1643:
1636:
1619:
1592:
1570:
1565:
1509:
1485:
1480:
1338:
1304:
1297:
1273:
1245:
1238:
1221:
1189:
1187:
1163:
1123:
1100:
1024:
995:
939:
928:
891:
860:
831:
765:
724:
700:
689:
659:
629:Disproval of the mathematical constant pi
386:
455:Yeah. Yet, they're still proportional.
2326:Is the page linked there (published at
2259:Semicircle proof: bounds of integration
171:
141:
1158:Problem #1: The mathematical constant
654:The idea of the mathematical constant
342:when more than 5 sections are present.
1735:
1490:
7:
217:This article is within the scope of
2414:that it is complicated to justify "
160:It is of interest to the following
2185:LLMs cannot be relied on for facts
494:. Please find more description at
25:
2453:Mid-priority mathematics articles
2307:Can this ref be considered valid?
1458:Sentence #5 is clearly invented.
336:may be automatically archived by
237:Knowledge:WikiProject Mathematics
2336:
2335:
285:
240:Template:WikiProject Mathematics
204:
194:
173:
142:
30:
257:This article has been rated as
1943:{\displaystyle A2<A3<A4}
48:nominee, but did not meet the
1:
2245:17:34, 13 November 2023 (UTC)
2226:17:37, 13 November 2023 (UTC)
2211:16:03, 11 November 2023 (UTC)
2197:14:00, 10 November 2023 (UTC)
2179:13:25, 10 November 2023 (UTC)
1830:{\displaystyle A3:A1=A4:A2=2}
1423:Sentence #1 is false. Twice.
496:Help:Talk pages § Indentation
231:and see a list of open tasks.
2448:C-Class mathematics articles
2443:Former good article nominees
2378:23:23, 22 January 2023 (UTC)
2353:17:05, 18 January 2023 (UTC)
2311:Please see this addition by
2301:14:58, 16 October 2022 (UTC)
2276:14:44, 16 October 2022 (UTC)
1580:{\displaystyle a{\sqrt {2}}}
1433:difference of the perimeters
560:16:12, 20 January 2021 (UTC)
531:11:32, 20 January 2021 (UTC)
508:10:05, 20 January 2021 (UTC)
465:09:53, 20 January 2021 (UTC)
442:20:55, 19 January 2021 (UTC)
428:denoted by the Greek letter
411:20:42, 19 January 2021 (UTC)
2183:A wonderful example of why
2056:{\displaystyle 2<c<4}
1199:{\displaystyle {\sqrt {3}}}
916:I continue with hexagons.
131:Former good article nominee
2469:
2088:from old masters instead.
1468:No grounds for this claim.
609:) 08:00, 10 May 2021 (UTC)
583:20:58, 23 April 2021 (UTC)
96:WikiProject A-class review
56:. Editors may also seek a
256:
189:
168:
128:
70:
66:
44:Mathematics good articles
2429:05:17, 8 June 2024 (UTC)
2328:shreevatsa.wordpress.com
2153:12:03, 17 May 2021 (UTC)
2126:09:27, 17 May 2021 (UTC)
2100:21:20, 16 May 2021 (UTC)
2071:(who died circa 212 BC).
1406:13:00, 16 May 2021 (UTC)
1392:12:45, 16 May 2021 (UTC)
1376:09:27, 15 May 2023 (UTC)
646:Please do not modify it.
620:09:35, 15 May 2023 (UTC)
366:Please do not modify it.
263:project's priority scale
2390:The first paragraph of
1429:based on the assumption
492:Special:Diff/1001584067
488:Special:Diff/1001583999
484:Special:Diff/1001583645
220:WikiProject Mathematics
2320:Special:Diff/589555823
2057:
2019:
1944:
1897:
1831:
1769:
1684:
1604:
1581:
1523:
1351:
1200:
1172:
1147:
908:
668:
395:
339:Lowercase sigmabot III
150:This article is rated
2058:
2020:
1945:
1898:
1832:
1770:
1685:
1605:
1582:
1524:
1352:
1201:
1173:
1148:
909:
669:
396:
50:good article criteria
2035:
1960:
1913:
1842:
1785:
1695:
1618:
1591:
1564:
1479:
1220:
1186:
1171:{\displaystyle \pi }
1162:
927:
688:
667:{\displaystyle \pi }
658:
394:{\displaystyle \pi }
385:
243:mathematics articles
115:Good article nominee
2315:on 7 January 2014:
2143:and edit it there.
18:Talk:Area of a disk
2313:User:Ebony Jackson
2141:personal userspace
2108:{re|Mgnbar|CiaPan}
2053:
2015:
1940:
1893:
1891:
1827:
1765:
1764:
1730:
1680:
1653:
1603:{\displaystyle 2a}
1600:
1577:
1535:a number of sides!
1519:
1494:
1347:
1314:
1255:
1196:
1168:
1143:
1135:
1112:
1007:
951:
904:
843:
775:
736:
710:
664:
391:
212:Mathematics portal
156:content assessment
71:Article milestones
2419:into triangles".
2396:shell integration
2256:
2255:
1997:
1890:
1729:
1652:
1575:
1517:
1495:
1313:
1254:
1194:
1134:
1133:
1111:
1110:
1029:
1006:
1002:
950:
946:
896:
865:
842:
838:
774:
735:
731:
709:
626:
625:
597:comment added by
349:addition proposal
346:
345:
277:
276:
273:
272:
269:
268:
136:
135:
124:
123:
16:(Redirected from
2460:
2341:
2340:
2339:
2329:
2062:
2060:
2059:
2054:
2024:
2022:
2021:
2016:
2014:
2013:
1998:
1993:
1992:
1983:
1972:
1971:
1949:
1947:
1946:
1941:
1902:
1900:
1899:
1894:
1892:
1883:
1836:
1834:
1833:
1828:
1774:
1772:
1771:
1766:
1760:
1759:
1731:
1725:
1724:
1715:
1689:
1687:
1686:
1681:
1676:
1675:
1654:
1648:
1647:
1638:
1609:
1607:
1606:
1601:
1586:
1584:
1583:
1578:
1576:
1571:
1528:
1526:
1525:
1520:
1518:
1510:
1496:
1486:
1356:
1354:
1353:
1348:
1343:
1342:
1315:
1309:
1308:
1299:
1278:
1277:
1256:
1250:
1249:
1240:
1205:
1203:
1202:
1197:
1195:
1190:
1177:
1175:
1174:
1169:
1152:
1150:
1149:
1144:
1136:
1129:
1125:
1113:
1106:
1102:
1030:
1025:
1008:
998:
997:
952:
942:
941:
913:
911:
910:
905:
897:
892:
866:
861:
844:
834:
833:
776:
767:
737:
727:
726:
711:
702:
673:
671:
670:
665:
648:
633:
610:
570:
541:
518:
479:
454:
422:
400:
398:
397:
392:
380:
368:
353:
341:
325:
289:
281:
245:
244:
241:
238:
235:
214:
209:
208:
198:
191:
190:
185:
177:
170:
153:
147:
146:
138:
129:Current status:
110:
108:December 7, 2009
91:
68:
38:Area of a circle
34:
27:
21:
2468:
2467:
2463:
2462:
2461:
2459:
2458:
2457:
2433:
2432:
2388:
2337:
2327:
2309:
2261:
2033:
2032:
2005:
1984:
1963:
1958:
1957:
1911:
1910:
1840:
1839:
1783:
1782:
1751:
1716:
1693:
1692:
1667:
1639:
1616:
1615:
1589:
1588:
1562:
1561:
1477:
1476:
1334:
1300:
1269:
1241:
1218:
1217:
1184:
1183:
1160:
1159:
925:
924:
686:
685:
656:
655:
644:
631:
622:
592:
564:
535:
512:
473:
448:
416:
383:
382:
374:
364:
351:
337:
326:
320:
294:
242:
239:
236:
233:
232:
210:
203:
183:
154:on Knowledge's
151:
106:
87:
23:
22:
15:
12:
11:
5:
2466:
2464:
2456:
2455:
2450:
2445:
2435:
2434:
2412:triangle proof
2387:
2384:
2383:
2382:
2381:
2380:
2342:
2324:
2323:
2308:
2305:
2304:
2303:
2287:
2286:
2268:138.255.106.16
2260:
2257:
2254:
2253:
2252:
2251:
2250:
2249:
2248:
2247:
2232:
2231:
2230:
2229:
2228:
2165:
2160:
2157:
2156:
2155:
2131:
2130:
2129:
2128:
2115:
2112:
2109:
2103:
2102:
2089:
2072:
2065:
2064:
2063:
2052:
2049:
2046:
2043:
2040:
2027:
2026:
2025:
2012:
2008:
2004:
2001:
1996:
1991:
1987:
1981:
1978:
1975:
1970:
1966:
1952:
1951:
1950:
1939:
1936:
1933:
1930:
1927:
1924:
1921:
1918:
1905:
1904:
1903:
1889:
1886:
1880:
1877:
1874:
1871:
1868:
1865:
1862:
1859:
1856:
1853:
1850:
1847:
1837:
1826:
1823:
1820:
1817:
1814:
1811:
1808:
1805:
1802:
1799:
1796:
1793:
1790:
1777:
1776:
1775:
1763:
1758:
1754:
1750:
1747:
1744:
1741:
1738:
1734:
1728:
1723:
1719:
1712:
1709:
1706:
1703:
1700:
1690:
1679:
1674:
1670:
1666:
1663:
1660:
1657:
1651:
1646:
1642:
1635:
1632:
1629:
1626:
1623:
1611:
1599:
1596:
1574:
1569:
1555:
1552:
1549:
1548:
1547:
1536:
1516:
1513:
1508:
1505:
1502:
1499:
1493:
1489:
1484:
1469:
1466:
1465:
1464:
1453:
1446:
1439:
1438:
1437:
1418:
1413:
1411:
1410:
1409:
1408:
1346:
1341:
1337:
1333:
1330:
1327:
1324:
1321:
1318:
1312:
1307:
1303:
1296:
1293:
1290:
1287:
1284:
1281:
1276:
1272:
1268:
1265:
1262:
1259:
1253:
1248:
1244:
1237:
1234:
1231:
1228:
1225:
1193:
1167:
1142:
1139:
1132:
1128:
1122:
1119:
1116:
1109:
1105:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1057:
1054:
1051:
1048:
1045:
1042:
1039:
1036:
1033:
1028:
1023:
1020:
1017:
1014:
1011:
1005:
1001:
994:
991:
988:
985:
982:
979:
976:
973:
970:
967:
964:
961:
958:
955:
949:
945:
938:
935:
932:
903:
900:
895:
890:
887:
884:
881:
878:
875:
872:
869:
864:
859:
856:
853:
850:
847:
841:
837:
830:
827:
824:
821:
818:
815:
812:
809:
806:
803:
800:
797:
794:
791:
788:
785:
782:
779:
773:
770:
764:
761:
758:
755:
752:
749:
746:
743:
740:
734:
730:
723:
720:
717:
714:
708:
705:
699:
696:
693:
684:of the circle
663:
650:
649:
640:
639:
630:
627:
624:
623:
591:
590:
589:
588:
587:
586:
585:
571:
562:
547:
519:
510:
481:
468:
467:
445:
444:
390:
370:
369:
360:
359:
350:
347:
344:
343:
331:
328:
327:
322:
318:
316:
313:
312:
296:
295:
290:
284:
275:
274:
271:
270:
267:
266:
255:
249:
248:
246:
229:the discussion
216:
215:
199:
187:
186:
178:
166:
165:
159:
148:
134:
133:
126:
125:
122:
121:
118:
111:
103:
102:
99:
92:
84:
83:
80:
77:
73:
72:
64:
63:
35:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2465:
2454:
2451:
2449:
2446:
2444:
2441:
2440:
2438:
2431:
2430:
2426:
2422:
2421:Shenyqwilliam
2417:
2413:
2408:
2406:
2401:
2397:
2393:
2385:
2379:
2375:
2371:
2370:Ebony Jackson
2367:
2363:
2359:
2358:
2357:
2356:
2355:
2354:
2350:
2346:
2333:
2321:
2318:
2317:
2316:
2314:
2306:
2302:
2298:
2294:
2289:
2288:
2284:
2280:
2279:
2278:
2277:
2273:
2269:
2264:
2258:
2246:
2242:
2238:
2233:
2227:
2223:
2219:
2214:
2213:
2212:
2208:
2204:
2200:
2199:
2198:
2194:
2190:
2186:
2182:
2181:
2180:
2176:
2172:
2169:
2166:
2164:
2161:
2158:
2154:
2150:
2146:
2142:
2137:
2136:
2135:
2134:
2133:
2132:
2127:
2123:
2119:
2116:
2113:
2110:
2107:
2106:
2105:
2104:
2101:
2097:
2093:
2087:
2083:
2080:
2076:
2073:
2070:
2066:
2050:
2047:
2044:
2041:
2038:
2031:
2030:
2028:
2010:
2006:
2002:
1999:
1994:
1989:
1985:
1979:
1976:
1973:
1968:
1964:
1956:
1955:
1953:
1937:
1934:
1931:
1928:
1925:
1922:
1919:
1916:
1909:
1908:
1906:
1887:
1884:
1878:
1875:
1872:
1869:
1866:
1863:
1860:
1857:
1854:
1851:
1848:
1845:
1838:
1824:
1821:
1818:
1815:
1812:
1809:
1806:
1803:
1800:
1797:
1794:
1791:
1788:
1781:
1780:
1778:
1761:
1756:
1752:
1748:
1745:
1742:
1739:
1736:
1732:
1726:
1721:
1717:
1710:
1707:
1704:
1701:
1698:
1691:
1677:
1672:
1668:
1664:
1661:
1658:
1655:
1649:
1644:
1640:
1633:
1630:
1627:
1624:
1621:
1614:
1613:
1597:
1594:
1572:
1567:
1559:
1556:
1553:
1550:
1546:
1543:
1542:
1540:
1537:
1534:
1533:
1514:
1511:
1506:
1503:
1500:
1497:
1491:
1487:
1482:
1474:
1470:
1467:
1463:
1460:
1459:
1457:
1454:
1451:
1447:
1444:
1440:
1436:
1434:
1430:
1425:
1424:
1422:
1419:
1416:
1415:
1414:
1407:
1403:
1399:
1395:
1394:
1393:
1389:
1385:
1380:
1379:
1378:
1377:
1373:
1369:
1365:
1364:
1360:
1357:
1344:
1339:
1335:
1331:
1328:
1325:
1322:
1319:
1316:
1310:
1305:
1301:
1294:
1291:
1288:
1285:
1282:
1279:
1274:
1270:
1266:
1263:
1260:
1257:
1251:
1246:
1242:
1235:
1232:
1229:
1226:
1223:
1215:
1214:
1210:
1207:
1191:
1179:
1165:
1156:
1153:
1140:
1137:
1130:
1126:
1120:
1117:
1114:
1107:
1103:
1097:
1094:
1091:
1088:
1085:
1082:
1079:
1076:
1073:
1070:
1067:
1064:
1061:
1058:
1055:
1052:
1049:
1046:
1043:
1040:
1037:
1034:
1031:
1026:
1021:
1018:
1015:
1012:
1009:
1003:
999:
992:
989:
986:
983:
980:
977:
974:
971:
968:
965:
962:
959:
956:
953:
947:
943:
936:
933:
930:
922:
921:
917:
914:
901:
898:
893:
888:
885:
882:
879:
876:
873:
870:
867:
862:
857:
854:
851:
848:
845:
839:
835:
828:
825:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
777:
771:
768:
762:
759:
756:
753:
750:
747:
744:
741:
738:
732:
728:
721:
718:
715:
712:
706:
703:
697:
694:
691:
681:
680:
676:
661:
652:
651:
647:
642:
641:
638:
635:
634:
628:
621:
617:
613:
608:
604:
600:
596:
584:
580:
576:
572:
568:
567:Ebony Jackson
563:
561:
557:
553:
552:Ebony Jackson
548:
545:
539:
534:
533:
532:
528:
524:
520:
516:
511:
509:
505:
501:
497:
493:
489:
485:
477:
472:
471:
470:
469:
466:
462:
458:
452:
447:
446:
443:
439:
435:
431:
427:
420:
415:
414:
413:
412:
408:
404:
388:
378:
372:
371:
367:
362:
361:
358:
355:
354:
348:
340:
335:
330:
329:
315:
314:
311:
310:
306:
302:
298:
297:
293:
288:
283:
282:
279:
264:
260:
254:
251:
250:
247:
230:
226:
222:
221:
213:
207:
202:
200:
197:
193:
192:
188:
182:
179:
176:
172:
167:
163:
157:
149:
145:
140:
139:
132:
127:
119:
117:
116:
112:
109:
105:
104:
100:
98:
97:
93:
90:
86:
85:
81:
78:
75:
74:
69:
65:
61:
60:
55:
51:
47:
46:
45:
39:
36:
33:
29:
28:
19:
2415:
2409:
2404:
2389:
2325:
2310:
2265:
2262:
2085:
2081:
2078:
2074:
2029:and finally
1557:
1544:
1538:
1531:
1530:
1529:, but it is
1472:
1461:
1455:
1449:
1442:
1432:
1428:
1426:
1420:
1417:Five points.
1412:
1366:
1361:
1358:
1216:
1211:
1208:
1180:
1157:
1154:
923:
918:
915:
682:
677:
653:
645:
593:— Preceding
544:your "proof"
429:
425:
373:
365:
333:
299:
291:
278:
259:Mid-priority
258:
218:
184:Mid‑priority
162:WikiProjects
130:
113:
94:
89:June 5, 2007
59:reassessment
57:
42:
41:
37:
2405:approximate
2392:onion proof
1471:The number
1398:PrimeHunter
637:WP:NOTFORUM
357:WP:NOTFORUM
234:Mathematics
225:mathematics
181:Mathematics
54:renominated
2437:Categories
2416:unwrapping
2400:derivation
2398:, but the
2394:refers to
2069:Archimedes
120:Not listed
2203:Gmac4247
2171:Gmac4247
2118:Gmac4247
2086:learning
2077:Please,
2075:Point 5.
1558:Point 4.
1539:Point 3.
1456:Point 2.
1421:Point 1.
1368:Gmac4247
612:Gmac4247
607:contribs
599:Gmac4247
595:unsigned
575:Gmac4247
538:Gmac4247
523:Gmac4247
476:Gmac4247
457:Gmac4247
419:Gmac4247
403:Gmac4247
292:Archives
101:Approved
2366:WP:CALC
2283:WP:CALC
2189:MrOllie
2079:please,
334:30 days
261:on the
152:C-class
79:Process
2362:CiaPan
2345:CiaPan
2293:Mgnbar
2237:CiaPan
2218:CiaPan
2145:Mgnbar
2092:CiaPan
2082:PLEASE
1954:hence
1587:, not
1450:exists
1384:Mgnbar
515:CiaPan
500:CiaPan
451:CiaPan
434:CiaPan
377:CiaPan
158:scale.
82:Result
40:was a
2332:WP:OR
1213:300px
920:300px
679:300px
2425:talk
2374:talk
2349:talk
2297:talk
2272:talk
2241:talk
2222:talk
2207:talk
2193:talk
2175:talk
2149:talk
2122:talk
2096:talk
2048:<
2042:<
2000:<
1974:<
1932:<
1923:<
1907:and
1504:<
1498:<
1402:talk
1388:talk
1372:talk
616:talk
603:talk
579:talk
556:talk
527:talk
504:talk
498:. --
490:and
461:talk
438:talk
432:. --
407:talk
76:Date
2360:Hi
1532:not
542:In
253:Mid
2439::
2427:)
2376:)
2368:.
2351:)
2343:--
2334:.
2299:)
2274:)
2243:)
2235:--
2224:)
2216:--
2209:)
2195:)
2187:.
2177:)
2151:)
2124:)
2098:)
2090:--
1980:⋅
1749:⋅
1711:⋅
1634:⋅
1610:.
1501:π
1492:71
1488:10
1473:71
1443:pi
1404:)
1390:)
1374:)
1332:∗
1295:∗
1236:∗
1166:π
1138:∗
1127:12
1115:∗
1098:∗
1077:∗
1053:∗
1032:∗
1022:∗
1010:∗
993:∗
954:∗
899:∗
889:∗
868:∗
858:∗
846:∗
829:∗
805:∗
784:∗
763:∗
739:∗
662:π
618:)
605:•
581:)
558:)
529:)
521:ok
506:)
486:,
463:)
440:)
426:IS
409:)
389:π
307:,
303:,
2423:(
2372:(
2347:(
2322:.
2295:(
2285:.
2270:(
2239:(
2220:(
2205:(
2191:(
2173:(
2147:(
2120:(
2094:(
2051:4
2045:c
2039:2
2011:2
2007:a
2003:2
1995:2
1990:2
1986:a
1977:c
1969:2
1965:a
1938:4
1935:A
1929:3
1926:A
1920:2
1917:A
1888:4
1885:c
1879:=
1876:4
1873:A
1870::
1867:3
1864:A
1861:=
1858:2
1855:A
1852::
1849:1
1846:A
1825:2
1822:=
1819:2
1816:A
1813::
1810:4
1807:A
1804:=
1801:1
1798:A
1795::
1792:3
1789:A
1762:;
1757:2
1753:a
1746:2
1743:=
1740:4
1737:A
1733:;
1727:2
1722:2
1718:a
1708:c
1705:=
1702:3
1699:A
1678:;
1673:2
1669:a
1665:=
1662:2
1659:A
1656:;
1650:4
1645:2
1641:a
1631:c
1628:=
1625:1
1622:A
1598:a
1595:2
1573:2
1568:a
1515:7
1512:1
1507:3
1483:3
1400:(
1386:(
1370:(
1345:;
1340:2
1336:a
1329:2
1326:=
1323:4
1320:A
1317:;
1311:2
1306:2
1302:a
1292:c
1289:=
1286:3
1283:A
1280:;
1275:2
1271:a
1267:=
1264:2
1261:A
1258:;
1252:4
1247:2
1243:a
1233:c
1230:=
1227:1
1224:A
1192:3
1141:a
1131:3
1121:=
1118:a
1108:3
1104:2
1095:6
1092:=
1089:4
1086:P
1083:;
1080:a
1074:c
1071:2
1068:=
1065:3
1062:P
1059:;
1056:a
1050:6
1047:=
1044:2
1041:P
1038:;
1035:a
1027:3
1019:c
1016:=
1013:a
1004:2
1000:3
990:c
987:2
984:=
981:1
978:P
975:;
972:a
969:=
966:3
963:r
960:;
957:a
948:2
944:3
937:=
934:1
931:r
902:a
894:2
886:4
883:=
880:4
877:P
874:;
871:a
863:2
855:c
852:=
849:a
840:2
836:2
826:c
823:2
820:=
817:3
814:P
811:;
808:a
802:4
799:=
796:2
793:P
790:;
787:a
781:c
778:=
772:2
769:a
760:c
757:2
754:=
751:1
748:P
745:;
742:a
733:2
729:2
722:=
719:3
716:r
713:;
707:2
704:a
698:=
695:1
692:r
614:(
601:(
577:(
569::
565:@
554:(
540::
536:@
525:(
517::
513:@
502:(
478::
474:@
459:(
453::
449:@
436:(
430:π
421::
417:@
405:(
379::
375:@
309:3
305:2
301:1
265:.
164::
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
