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1651:(b) What you have written here is not the way people use quaternions or other number systems in practice. Again, feel free to invent whatever number system you want in your own writings (self-published papers, blog posts, etc.). However, it’s not relevant to this Knowledge article. Let’s try to keep discussion focused on improving the article; Knowledge talk pages are not a general-purpose forum. –
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that as a problem then I don't know what to tell you. I have no problem with people using shorthand notation, I do it all the time, but in an encyclopedic article that is attempting to rigorously define something, you have to at least discuss the formal long form notation at least one, and ideally also provide wiki links to all of the assumed knowledge that is necessary to understand it.
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to be discoveries, since they are fundamental to so much. Matrices I consider to be an invention, since, despite their flexibility and utility value, I've always regarded them as being rather arbitrary (full disclosure: I never did like matrices :). Quaternions also seem to fall into the invention
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It’s hard to tell what you are trying to say. But as a general rule, Knowledge follows whatever the commonly accepted convention is in reliable sources (or when there are multiple common convention, picks one and mentions the alternatives). Do you have a reliable source for your "h" here? If you are
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What you call clutter I call lack of completeness and attention to detail, you've just literally admitted the point that I was originally attempting to make, that the wikipedia article is using sloppy shorthand notation in its attempt to rigorously define what a quaternion even is. If you don't see
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Knowledge is using the standard notation used by literally every source about this topic for the past 150 years. You can run a weird crusade against conventions you dislike somewhere else, but the job of
Knowledge is to describe encyclopedic topics as established in reliable sources, which is what
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Why? a, x, and y have no relevance to the topic at hand, we are talking about our four-demential quaternion number system, the entirety of the equations including the Arabic numerals themself are symbolic representations of abstract ideas. We're dealing with algebra here, and anyone who has passed
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The formula for the square root of a quaternion essentially uses the trigonometric identity for the sine of a half angle $ \sin(\theta/2) = \sqrt{(1-\cos(\theta))/2}$ . The formula looses precision for small angles and should never be used for numerical calculation. This is similar to finding the
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Pretty much anyone who does mathematics can think of several notation conventions they dislike for one reason or another, but if they want to change the conventions they can make those arguments in blog posts, journal papers, textbooks, etc.; speculative conversations about possible non-standard
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Firstly, the standard basis of the vector space of the quaternions contains also the real number 1. Secondly, one may understand what are quaternions without knowing vector spaces, bases of vector spaces, and standard bases. So, the change you suggest would make the article unnecessarily more
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for the use of h as a square root of minus one which commutes with i, j, and k. The algebra of biquaternions is only four dimensions when considered over the field of complex numbers x + yh. Biquaternions provide a representation of
Minkowski space and Lorentz transformations described by
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category (more full disclosure: I love quaternions). Complex numbers are harder to so categorize; while the term "imaginary part" may argue for "invention", they are so closely tied to fundamentals (e.g., two-dimensional
Euclidean space) that "discovery" also seems accurate.
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Details on a specific author does not belong to this article. For not being promotional, an independent source is needed. Such a source must discuss the importance, if any, of the results. Without that, the paragraph is there only for promoting an author.
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It means that the complex numbers can be considered as a subset of the quaternions, with the same behavior as quaternions that they have as complex numbers, but quaternions also include additional elements which combine compatibly with the existing ones.
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2708:" or "axial vectors" because they transform differently than ordinary vectors, the "polar vectors". This is possible in 3 dimensional Euclidean space (but no other dimension) because every plane has a unique perpendicular axis. When you take the
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A certain amount of it is accessible to non-experts, and a certain amount of it isn't. But it's a technical subject, and that's about what we should expect. Unless you can be more specific, the tag isn't really helpful, so I've removed it.
578:, but this because they were taught short hand arithmetic notation starting in primary school. Even when dealing with only real numbers, 0i is always still there as part of the equation, it's also just simply omitted in short hand notation.
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in mathematics was originated by
Hamilton to refer to the "imaginary" part of a quaternion. But later Gibbs/Heaviside adopted it in their formulation of electrodynamics based on dot and cross products (popularized in the book
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was not elaborated when
Hamilton introduced quaternions, and this may make terminology slightly confusing. Indeed, 1 is a vector (element) in the vector space of all quaternions, but is not a "vector quaternion", the
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Because this is a technical article, technical terms should be well defined. Unfortunately, the technical term "extends" appears in the article without a definition, which motivated me to hyperlink "extends" to
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3128:, it means a function defined on a manifold (including manifolds like ordinary Euclidean spaces); and if the result (image) of the function is a vector (at each point of the manifold) then it is called a
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Why refer to i, j, and k as the “basic quaternions” and not the “standard basis vectors”? I have not seen the term basic quaternion before and did not find any relevant information when looking it up.
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Your expressions here are incoherent because you have not defined a, x, y, or h. But don’t bother to define them; it’s a waste of your (and everyone’s) time. If you have a question (Example question:
2704:("imaginary") part. Both Hamilton and Gibbs/Heaviside somewhat conflated the concepts of vectors (line-oriented magnitudes) and bivectors (plane-oriented magnitudes), sometimes calling the latter "
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In this context, "extends" does not need to be interpreted as a precise technical term; the ordinary
English meaning of the word is plenty clear. I would not bother wiki-linking it to anything. –
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I think the sentence: 'Quaternions are generally represented in the form where the coefficients a, b, c, d are real numbers, and 1, i, j, k are the basis vectors or basis elements.'
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The section on "P.R. Girard's 1984 essay..." is full of references to the author. I'm too busy, but someone needs to clean that up or delete the entire ugly self-promotion.
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Should read: 'Quaternions are generally represented in the form where the coefficients a, b, c, d are real numbers, and i, j, k are the basis vectors or basis elements.'
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3217:: We are familiar with complex numbers, but now you want to introduce some things even more complicated than these complex ones. What do you propose to call such things?
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The article is currently too technical for non-experts to understand; I am adding a tag to suggest the article be improved to be understandable to non-experts.
2581:). Also, the concept of a vector space has been introduced years after the quaternions, and I guess that bases of vector spaces have been so named after the
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it means a set with a commutative addition and commutative multiplication operation and various additional properties; this is the present discussion. In
2652:. The mathematician's concept of a "vector" is different enough that applying the word to the imaginary part of a quaternion causes some confusion today. –
2558:“ Quaternions are generally represented in the form a + bi + cj + dk where a, b, c, and d are real numbers; and i, j, and k are the basic quaternions.”
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just throwing out ideas, you may want to write a blog post or self-published paper, as you are unlikely to find support for their inclusion here. –
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The image showing the cycles of multiplication appears to be incorrect. In particular, the arrows in the three outer cycles should be inverted.
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2446:"You are welcome to do it that way if you want. Most mathematicians like to skip redundant symbols where possible to reduce clutter."
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I was not attempting to multiple them, it was just simple addition on a system of polynomial equations, here is a better example..
513:. It's always there, but it's most often omitted due to a combination of short hand mathematical notation and/or ignorance about
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correctly observed that
Quaternion are not a field. Quaternion are not commutative, which is a required property of a field.
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Wait, why delete this section. From what i see and find, the references are indeed correct. How can this be self-promotion?
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partly to be consistent with the rest of the article, partly because I found a reference for it, and partly because
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2494:– that’s fine, you don't need to tell us anything. This whole conversation is off topic and should end ASAP. –
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1068:{\textstyle 1=h^{2}i^{2}j^{2}k^{2}=({\sqrt {-1}})^{2}({\sqrt {-1}})^{2}({\sqrt {-1}})^{2}({\sqrt {-1}})^{2}}
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The same is true for the outer red and green cycles. However, inverting the direction fixes the error.
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To me, it seems that some things in mathematics are discoveries, and some are inventions. I consider
1648:(a) This Youtube video is well made and worth showing to students but it does not support your claims.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Maybe make a blog or social media post out of this instead of chitchatting about it here. Cf.
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of two vectors to get a "pseudovector", it would be conceptually clearer to instead take the
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For example, starting at positive j, cycling along the blue path counter clockwise (xk):
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There is an additional point of confusion, which is that as the even sub-algebra of the
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The diagram is correct. As you can see in several places in the article (for example,
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of two vectors to get a bivector, treated as a conceptually different type of object. –
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or try some mathematics discussion forum like reddit or mathematics stack exchange. –
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This article is "Quaternions for Pure
Mathematicians". For practical aspects, see
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college algebra knows that you can have coefficients and variables in an equation.
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We're missing h, it's call the
Hamilton set for a reason, Hamilton was a human...
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does not say that a field extension might not be a field. Should that be fixed?
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angle between two vectors using arccos formula, which is generally unacceptable.
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There is an implied symbolic coefficient, in this instance the coefficient of
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1589:{\textstyle k^{2}={\frac {1}{h^{2}i^{2}j^{2}}}={\frac {1}{(-1)(-1)(-1)}}=-1}
1462:{\textstyle j^{2}={\frac {1}{h^{2}i^{2}k^{2}}}={\frac {1}{(-1)(-1)(-1)}}=-1}
1335:{\textstyle i^{2}={\frac {1}{h^{2}j^{2}k^{2}}}={\frac {1}{(-1)(-1)(-1)}}=-1}
1208:{\textstyle h^{2}={\frac {1}{i^{2}j^{2}k^{2}}}={\frac {1}{(-1)(-1)(-1)}}=-1}
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I don't see this in the History section, so perhaps it should be included.—
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What does the term "extends" mean in the first sentence of this article?
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Vector products and also not commutative, however "vector fields" exist.
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It's basic primary school mathematics, you shouldn't need a source for
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That is, the '1, ' before the 'i' should be deleted. Is that correct?
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of dimension 4 over the reals. However, the modern concept of a
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in 1914, but the original algebra comes from Hamilton's
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2450:Knowledge:Reference desk/Mathematics
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3284:Multiplication of basis elements
2492:"I don't know what to tell you."
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106:and see a list of open tasks.
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3190:dihedral group of order 8
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2230:{\displaystyle 0}
2210:{\displaystyle k}
2190:{\displaystyle j}
2170:{\displaystyle i}
1663:In his notation,
1575:
1527:
1448:
1400:
1321:
1273:
1194:
1146:
1053:
1030:
1007:
984:
725:{\displaystyle h}
705:{\displaystyle 0}
571:{\displaystyle 0}
484:{\displaystyle h}
421:
416:
403:
398:
385:
380:
367:
362:
278:
277:
243:
242:
194:
193:
148:
147:
144:
143:
140:
139:
3380:
3182:quaternion group
3138:
2949:
2923:
2921:
2920:
2915:
2804:
2802:
2801:
2796:
2784:
2782:
2781:
2776:
2696:Clifford algebra
2444:Example answer:
2441:
2437:
2433:
2423:
2400:
2398:
2397:
2392:
2369:
2367:
2366:
2361:
2359:
2358:
2349:
2348:
2313:
2311:
2310:
2305:
2303:
2302:
2293:
2292:
2256:
2254:
2253:
2248:
2236:
2234:
2233:
2228:
2216:
2214:
2213:
2208:
2196:
2194:
2193:
2188:
2176:
2174:
2173:
2168:
2154:
2152:
2151:
2146:
2144:
2143:
2134:
2133:
2106:
2105:
2096:
2095:
2068:
2067:
2058:
2057:
2030:
2029:
2020:
2019:
1984:
1982:
1981:
1976:
1974:
1973:
1964:
1963:
1936:
1935:
1926:
1925:
1898:
1897:
1888:
1887:
1860:
1859:
1850:
1849:
1799:
1797:
1796:
1791:
1595:
1593:
1592:
1587:
1576:
1574:
1533:
1528:
1526:
1525:
1524:
1515:
1514:
1505:
1504:
1491:
1486:
1485:
1468:
1466:
1465:
1460:
1449:
1447:
1406:
1401:
1399:
1398:
1397:
1388:
1387:
1378:
1377:
1364:
1359:
1358:
1341:
1339:
1338:
1333:
1322:
1320:
1279:
1274:
1272:
1271:
1270:
1261:
1260:
1251:
1250:
1237:
1232:
1231:
1214:
1212:
1211:
1206:
1195:
1193:
1152:
1147:
1145:
1144:
1143:
1134:
1133:
1124:
1123:
1110:
1105:
1104:
1074:
1072:
1071:
1066:
1064:
1063:
1054:
1046:
1041:
1040:
1031:
1023:
1018:
1017:
1008:
1000:
995:
994:
985:
977:
969:
968:
959:
958:
949:
948:
939:
938:
904:
902:
901:
896:
753:
751:
750:
745:
743:
731:
729:
728:
723:
711:
709:
708:
703:
683:
681:
680:
675:
577:
575:
574:
569:
557:
555:
554:
549:
512:
510:
509:
504:
502:
490:
488:
487:
482:
439:
437:
436:
431:
426:
420:
415:
408:
402:
397:
390:
384:
379:
372:
366:
361:
281:Overly technical
273:
257:
217:
216:
206:
198:
188:October 16, 2010
184:October 16, 2009
180:October 16, 2008
176:October 16, 2007
172:October 16, 2006
157:
150:
120:
119:
116:
113:
110:
89:
84:
83:
73:
66:
65:
55:
48:
31:
25:
24:
16:
3388:
3387:
3383:
3382:
3381:
3379:
3378:
3377:
3333:
3332:
3245:
3227:, of course. —
3187:
3179:
3174:group extension
3134:
3060:Field extension
3044:Field extension
3011:
2947:
2942:
2897:
2896:
2859:
2787:
2786:
2764:
2763:
2760:
2740:
2645:Vector Analysis
2577:technical (see
2556:
2524:
2439:
2435:
2434:with real part
2425:
2418:
2374:
2373:
2350:
2340:
2317:
2316:
2294:
2284:
2261:
2260:
2239:
2238:
2219:
2218:
2199:
2198:
2179:
2178:
2159:
2158:
2135:
2125:
2097:
2087:
2059:
2049:
2021:
2011:
1988:
1987:
1965:
1955:
1927:
1917:
1889:
1879:
1851:
1841:
1818:
1817:
1665:
1664:
1537:
1516:
1506:
1496:
1495:
1477:
1472:
1471:
1410:
1389:
1379:
1369:
1368:
1350:
1345:
1344:
1283:
1262:
1252:
1242:
1241:
1223:
1218:
1217:
1156:
1135:
1125:
1115:
1114:
1096:
1091:
1090:
1055:
1032:
1009:
986:
960:
950:
940:
930:
919:
918:
764:
763:
734:
733:
714:
713:
694:
693:
588:
587:
560:
559:
528:
527:
515:lateral numbers
493:
492:
473:
472:
353:
352:
347:
283:
269:
258:
252:
211:
117:
114:
111:
108:
107:
85:
78:
32:on Knowledge's
29:
12:
11:
5:
3386:
3384:
3376:
3375:
3370:
3365:
3360:
3355:
3350:
3345:
3335:
3334:
3331:
3330:
3265:
3264:
3261:
3258:
3255:
3244:
3241:
3240:
3239:
3218:
3185:
3177:
3170:
3169:
3168:
3167:
3166:
3165:
3153:
3114:
3092:
3078:ring extension
3056:
3053:
3050:User:Quantling
3047:
3010:
3007:
3006:
3005:
3004:
3003:
3002:
3001:
2941:
2938:
2937:
2936:
2913:
2910:
2907:
2904:
2858:
2855:
2854:
2853:
2835:
2794:
2774:
2771:
2759:
2756:
2739:
2736:
2735:
2734:
2733:
2732:
2731:
2730:
2729:
2728:
2727:
2726:
2667:
2666:
2665:
2664:
2663:
2662:
2613:basis elements
2598:
2597:
2555:
2552:
2523:
2520:
2519:
2518:
2517:
2516:
2515:
2514:
2513:
2512:
2511:
2510:
2509:
2508:
2507:
2506:
2505:
2504:
2489:
2485:
2466:
2390:
2387:
2384:
2381:
2370:
2357:
2353:
2347:
2343:
2339:
2336:
2333:
2330:
2327:
2324:
2314:
2301:
2297:
2291:
2287:
2283:
2280:
2277:
2274:
2271:
2268:
2258:
2246:
2226:
2206:
2186:
2166:
2155:
2142:
2138:
2132:
2128:
2124:
2121:
2118:
2115:
2112:
2109:
2104:
2100:
2094:
2090:
2086:
2083:
2080:
2077:
2074:
2071:
2066:
2062:
2056:
2052:
2048:
2045:
2042:
2039:
2036:
2033:
2028:
2024:
2018:
2014:
2010:
2007:
2004:
2001:
1998:
1995:
1985:
1972:
1968:
1962:
1958:
1954:
1951:
1948:
1945:
1942:
1939:
1934:
1930:
1924:
1920:
1916:
1913:
1910:
1907:
1904:
1901:
1896:
1892:
1886:
1882:
1878:
1875:
1872:
1869:
1866:
1863:
1858:
1854:
1848:
1844:
1840:
1837:
1834:
1831:
1828:
1825:
1815:
1789:
1786:
1783:
1780:
1777:
1774:
1771:
1768:
1765:
1762:
1759:
1756:
1753:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1729:
1726:
1723:
1720:
1717:
1714:
1711:
1708:
1705:
1702:
1699:
1696:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1649:
1646:
1623:
1622:
1621:
1620:
1603:
1601:
1600:
1599:
1598:
1597:
1596:
1585:
1582:
1579:
1573:
1570:
1567:
1564:
1561:
1558:
1555:
1552:
1549:
1546:
1543:
1540:
1536:
1531:
1523:
1519:
1513:
1509:
1503:
1499:
1494:
1489:
1484:
1480:
1469:
1458:
1455:
1452:
1446:
1443:
1440:
1437:
1434:
1431:
1428:
1425:
1422:
1419:
1416:
1413:
1409:
1404:
1396:
1392:
1386:
1382:
1376:
1372:
1367:
1362:
1357:
1353:
1342:
1331:
1328:
1325:
1319:
1316:
1313:
1310:
1307:
1304:
1301:
1298:
1295:
1292:
1289:
1286:
1282:
1277:
1269:
1265:
1259:
1255:
1249:
1245:
1240:
1235:
1230:
1226:
1215:
1204:
1201:
1198:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1155:
1150:
1142:
1138:
1132:
1128:
1122:
1118:
1113:
1108:
1103:
1099:
1082:
1080:
1079:
1078:
1077:
1076:
1075:
1062:
1058:
1052:
1049:
1044:
1039:
1035:
1029:
1026:
1021:
1016:
1012:
1006:
1003:
998:
993:
989:
983:
980:
975:
972:
967:
963:
957:
953:
947:
943:
937:
933:
929:
926:
910:
908:
907:
906:
905:
894:
891:
888:
885:
882:
879:
876:
873:
870:
867:
864:
861:
858:
855:
852:
849:
846:
843:
840:
837:
834:
831:
828:
825:
822:
819:
816:
813:
810:
807:
804:
801:
798:
795:
792:
789:
786:
783:
780:
777:
774:
771:
758:
757:
756:
755:
742:
721:
701:
687:
686:
685:
684:
673:
670:
667:
664:
661:
658:
655:
652:
649:
646:
643:
640:
637:
634:
631:
628:
625:
622:
619:
616:
613:
610:
607:
604:
601:
598:
595:
582:
581:
580:
579:
567:
547:
544:
541:
538:
535:
521:
520:
519:
518:
501:
480:
466:
465:
429:
425:
419:
414:
411:
407:
401:
396:
393:
389:
383:
378:
375:
371:
365:
360:
346:
343:
342:
341:
318:
317:
282:
279:
276:
275:
263:
260:
259:
254:
250:
248:
245:
244:
241:
240:
234:
233:
228:
223:
213:
212:
207:
201:
192:
191:
158:
146:
145:
142:
141:
138:
137:
130:
124:
123:
121:
104:the discussion
91:
90:
74:
62:
61:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
3385:
3374:
3371:
3369:
3366:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3344:
3341:
3340:
3338:
3329:
3325:
3321:
3317:
3313:
3309:
3305:
3301:
3297:
3293:
3289:
3285:
3281:
3280:
3279:
3278:
3274:
3270:
3262:
3259:
3256:
3253:
3252:
3251:
3248:
3242:
3238:
3234:
3230:
3226:
3222:
3219:
3216:
3213:
3212:
3211:
3208:
3207:
3203:
3199:
3195:
3191:
3183:
3175:
3164:
3161:
3158:
3154:
3152:
3148:
3144:
3140:
3137:
3131:
3127:
3123:
3119:
3115:
3113:
3109:
3105:
3101:
3097:
3093:
3091:
3087:
3083:
3079:
3075:
3074:
3073:
3069:
3065:
3061:
3057:
3054:
3051:
3048:
3045:
3040:
3039:
3038:
3035:
3032:
3027:
3026:
3025:
3024:
3020:
3016:
3008:
3000:
2996:
2992:
2987:
2986:
2985:
2981:
2977:
2973:
2972:
2971:
2967:
2963:
2959:
2958:
2957:
2956:
2953:
2952:
2940:What the eff?
2939:
2935:
2931:
2927:
2911:
2908:
2905:
2902:
2894:
2889:
2885:
2881:
2880:
2879:
2878:
2874:
2870:
2865:
2862:
2856:
2852:
2848:
2844:
2840:
2836:
2834:
2831:
2828:
2824:
2820:
2819:
2818:
2817:
2813:
2809:
2792:
2772:
2769:
2757:
2755:
2754:
2750:
2746:
2737:
2725:
2722:
2719:
2715:
2714:wedge product
2711:
2710:cross product
2707:
2706:pseudovectors
2703:
2702:
2697:
2693:
2689:
2688:
2687:
2683:
2679:
2675:
2674:
2673:
2672:
2671:
2670:
2669:
2668:
2661:
2658:
2655:
2651:
2647:
2646:
2640:
2636:
2632:
2631:
2630:
2626:
2622:
2618:
2614:
2610:
2609:basis vectors
2606:
2602:
2601:
2600:
2599:
2596:
2592:
2588:
2585:quaternions.
2584:
2580:
2575:
2574:
2573:
2572:
2568:
2564:
2563:76.151.136.63
2559:
2553:
2551:
2550:
2546:
2542:
2538:
2534:
2529:
2521:
2503:
2500:
2497:
2493:
2490:
2486:
2482:
2481:
2480:
2476:
2472:
2467:
2463:
2462:
2461:
2458:
2455:
2451:
2447:
2443:
2432:
2428:
2421:
2414:
2413:
2412:
2408:
2404:
2388:
2385:
2382:
2379:
2371:
2355:
2351:
2345:
2337:
2334:
2331:
2325:
2322:
2315:
2299:
2295:
2289:
2281:
2278:
2275:
2269:
2266:
2259:
2244:
2224:
2204:
2184:
2164:
2156:
2140:
2136:
2130:
2122:
2119:
2116:
2110:
2107:
2102:
2098:
2092:
2084:
2081:
2078:
2072:
2069:
2064:
2060:
2054:
2046:
2043:
2040:
2034:
2031:
2026:
2022:
2016:
2008:
2005:
2002:
1996:
1993:
1986:
1970:
1966:
1960:
1952:
1949:
1946:
1940:
1937:
1932:
1928:
1922:
1914:
1911:
1908:
1902:
1899:
1894:
1890:
1884:
1876:
1873:
1870:
1864:
1861:
1856:
1852:
1846:
1838:
1835:
1832:
1826:
1823:
1816:
1813:
1812:
1811:
1807:
1803:
1787:
1784:
1781:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1745:
1742:
1739:
1736:
1733:
1730:
1727:
1724:
1721:
1718:
1715:
1709:
1703:
1700:
1697:
1694:
1691:
1688:
1685:
1682:
1679:
1676:
1673:
1662:
1661:
1660:
1657:
1654:
1650:
1647:
1645:
1641:
1637:
1633:
1629:
1628:
1627:
1626:
1625:
1624:
1619:
1615:
1611:
1608:
1607:
1606:
1605:
1604:
1583:
1580:
1577:
1568:
1565:
1556:
1553:
1544:
1541:
1534:
1529:
1521:
1517:
1511:
1507:
1501:
1497:
1492:
1487:
1482:
1478:
1470:
1456:
1453:
1450:
1441:
1438:
1429:
1426:
1417:
1414:
1407:
1402:
1394:
1390:
1384:
1380:
1374:
1370:
1365:
1360:
1355:
1351:
1343:
1329:
1326:
1323:
1314:
1311:
1302:
1299:
1290:
1287:
1280:
1275:
1267:
1263:
1257:
1253:
1247:
1243:
1238:
1233:
1228:
1224:
1216:
1202:
1199:
1196:
1187:
1184:
1175:
1172:
1163:
1160:
1153:
1148:
1140:
1136:
1130:
1126:
1120:
1116:
1111:
1106:
1101:
1097:
1089:
1088:
1087:
1086:
1085:
1084:
1083:
1060:
1050:
1047:
1037:
1027:
1024:
1014:
1004:
1001:
991:
981:
978:
970:
965:
961:
955:
951:
945:
941:
935:
931:
927:
924:
917:
916:
915:
914:
913:
912:
911:
892:
889:
886:
883:
880:
877:
874:
871:
868:
865:
862:
859:
856:
853:
847:
844:
841:
838:
835:
832:
829:
826:
823:
820:
817:
814:
808:
802:
799:
796:
793:
790:
787:
784:
781:
778:
775:
772:
762:
761:
760:
759:
719:
699:
691:
690:
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40:WikiProjects
2869:MathewMunro
2823:WP:NOTFORUM
170:section on
167:On this day
109:Mathematics
100:mathematics
59:Mathematics
3337:Categories
2603:I changed
3320:Anita5192
3157:jacobolus
3031:jacobolus
2827:jacobolus
2745:Arcshinus
2718:jacobolus
2678:Anita5192
2654:jacobolus
2621:Anita5192
2496:jacobolus
2454:jacobolus
1653:jacobolus
1636:Anita5192
457:jacobolus
287:Betanote4
238:Archive 4
231:Archive 3
226:Archive 2
221:Archive 1
162:Main Page
3223:: Well,
3147:contribs
3139:uantling
3126:analysis
2991:D.Lazard
2962:D.Lazard
2926:D.Lazard
2701:bivector
2587:D.Lazard
2539:(1853).
266:365 days
209:Archives
3310:, and –
3229:Rgdboer
3221:Teacher
3215:Student
3198:Rgdboer
3180:to the
3122:algebra
3104:Rgdboer
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2808:BMJ-pdx
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