702:
describe what a glide reflection or screw motion is, has no discussion of differential geometry, only mentions 'analytic geometry' per se in a throwaway aside, barely mentions other coordinate systems (and what little it does is inaccessibly jargony/abstract), makes no mention of the geometry of oriented planes, etc. etc. The fundamental notions that make a "Euclidean space" are lines (and higher-dimensional flat subspaces), parallelism, angles and perpendicularity, and distance and spheres. Just as planar
Euclidean geometry substantially focuses on lines and line segments, angles, triangles and circles (and then also conics, algebraic curves, ...), higher-dimensional Euclidean geometry substantially focuses on those same planar objects and higher-dimensional analogs like tetrahedrons, spheres, and quadrics.
248:
238:
217:
184:
790:, why does it matter, what implications does it have (Berger spends 2 volumes on this subject, only a few pages of which we are describing here), what is its mathematical context, how has the idea changed over time, etc. Or when it comes to formal definitions per se: why was this one chosen, which other definitions are equivalent, how does it relate to definitions of other structures, and so on. For instance, this article currently makes no mention of
144:
175:
829:, then proceeding to discuss axiom systems, a (currently very incomplete and somewhat idiosyncratic) historical summary, an idiosyncratic smattering of sentences and pictures about applications, and concrete details mainly provided as examples rather than as the primary topic. It would also be great to dramatically improve the article
379:}; that is, it identifies clearly and unambiguously the subject of the article in a way that is understandable to everybody. The same applies to the short description, which is aimed to help to recognize the searched article in the result of a search query. This aim is clearly and perfectly fulfilled by the present short description.
785:
generally coming here because they want to find out the formal/technical details and logical ordering of the basic definition(s) Marcel Berger chose to use in his (very fine) textbook, which was convenient for his particular purposes of setting up a framework for the rest of the book, in a logically
1427:
Having both a singular and a plural form would be very confusing to most readers. The ambiguity between “the
Euclidean space” (which is three dimensional) and “a Euclidean space” (which can have any dimension), is not an artefact of Knowledge, but relies on the common use. So, it cannot be resolved
1087:
It’s fine to make a separate article (which can even be significantly expanded). However, all of the material currently on this page is easily in scope (indeed, the material on this page should be further expanded here), and removing it and replacing with a useless 'excerpt' is a major regression.
991:
There should be an article at 'Euclidean space', it should focus on
Euclidean space per se as its primary topic (but also including discussion of the relationship to non-Euclidean, pseudo-Euclidean, affine, projective, etc. spaces), and it should encompass both the basic geometry and more abstract
697:
The same is to some extent true of this article in general. As many concepts/sections as possible should be pitched to be legible to e.g. high school students or laypeople. It should include more specific details about concrete geometrical figures (or at least obvious links to other articles where
809:
The standard way to mathematically define a
Euclidean space, as carried out in the remainder of this article, is as a set of points on which a real vector space acts, the space of translations which is equipped with an inner product. The action of translations makes the space an affine space, and
701:
It’s wild to me that this article does not discuss the concepts of spheres or conics/quadrics (or any other curves or surfaces) or simplexes (or any other polyhedra), only mentions the word "triangle" in the context of the triangle inequality and does not mention the word "trigonometry", does not
630:
Today, a well-meaning editor added a one-sentence paragraph to the lede, stating that
Euclidean space is a metric space. That's true, but it's just one of many such statements that could be added. I propose that the paragraph be either deleted or expanded --- perhaps to something like, "Euclidean
877:
Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's
Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension, including the
677:
is far too general and abstract and filled with jargon. This section should focus on isometries of
Euclidean space specifically, describe them concretely and in lay-accessible language with concrete examples and link to more advanced (abstract) articles for anyone who wants a more expert-level
514:
This article is about the current mathematical concept of
Euclidean space. There is essentially one example per natural number. The evidence suggests that the example corresponding to the natural number 2 is at least as old as the example corresponding to the natural number 3.
786:
consistent order, intended for a 2-semester undergraduate course. Readers of Berger's book per se can just directly refer to the relevant definitions in context. Instead, many readers who come here are looking for a more accessible and/or broader view: what is the concept
1395:. Moreover, I do not agree that "the" Euclidean space is the three-dimensional one. That is contrary to my sense of the math literature, where the word "space" does not imply three dimensions. The sentence, that Fgnievinski is citing from this article, should be changed.
335:
The lead reluctantly gives out a definition only in the last paragraph. Definitions should appear in the opening sentence. The short description is equally vage: "Fundamental space of geometry". Can we anticipate some sort of definition, e.g., "Euclidean space is a
1494:
Most of the time there's no problem figuring out from context which among
Euclidean 3-space vs. any Euclidean space is intended. When there is some ambiguity authors can just explicitly say "Euclidean 3-space" or "any Euclidean space" or whatever.
1302:
does not currently successfully define what that means, and makes a poor redirect target. (Aside: This article could probably also do a better job in the lead section of clearly describing what makes a space "Euclidean" per se.)
820:
I agree that some such material as I mentioned in my previous comment could also conceivably fit in an article titled 'Euclidean geometry'. But elaboration about such details mostly does not fit particularly well at the article
729:
and a couple of other editors broke the equilibrium and essentially re-wrote it (mostly for the better, in my opinion). My point is that the current text is, in a sense, new/immature and ripe for continued polishing/expansion.
962:
The renaming was necessary to make more explicit the scope of the present article. It is not specifically about the ordinary three-dimensional
Euclidean space, it's about the general case of Euclidean spaces of any dimension.
1370:. Most people -- including scientists, engineers, etc. (mathematicians excepted) -- would equate "Euclidean space" with 3D, not n-dimensional spaces. (I'd like to thank for the arguments, pro or con, and note this is not a
398:
formula", the definite article "the" is wrong, as the linked article uses "a space"; also, "Euclidean distance formula" is not defined in Knowledge, and as far as I know, it is not definied either in any reliable source.
413:
The lede currently says that three-dimensional Euclidean space was the first example. The nearest citation does not support this claim. I suspect (without citation) that two-dimensional Euclidean space was the first
584:
That section doesn't define a unique "Euclidean distance formula", but instead gives several examples of formulae, all of which calculate Euclidean distance in different situations or given different information.
816:
This is mostly incoherent to someone without significant math background; we are more or less assuming someone has studied 2+ years of undergraduate level pure math courses before trying to approach this
1409:
That's a crucial point: should the article title reflect the usage in modern mathematical literature or the broader literature in physics, science, engineering, etc.? How about a less verbose version: "
500:(plural in space geometry of books 11–13) as specific spaces. (By the way, this is a difficult problem for a non-native English speaker to know when an article is needed before "space" and when not.)
438:
in which "space" was the three-dimensional space of both the physical world and the mathematical one (which were clearly distinguished only centuries later). The (Euclidean) plane was not called a
304:
1549:
833:, which is currently a wreck. But even if we assumed that those articles were rewritten / dramatically expanded, the scope of this article should be broad enough to include a summary. –
805:
Even if we accepted the current structure this article is very hard for non-expert readers. For example the concepts of "inner product" and "affine space" are first mentioned as:
431:
The citation is about the existence of Euclidean spaces of any dimension, not about the origin of the concept (I guess without having accedded to it). "Originally" refers to
135:
1539:
725:
You raise good points. If I recall history correctly, this article sat at a particular, heavily contested equilibrium for many years. Then, over the past year or two,
686:
or about the changing conception of Euclidean space as the focus shifted from studying physical forces toward rigid motions for their own sake (concretely studied by
613:? That article should (at least as a summary) cover most of the same ground as this one, but then go into further detail about geometry that is specifically planar. –
609:
This article seems pretty good in structure/content (albeit with insufficient references to external sources). Does anyone here want to take a crack at cleaning up
1554:
1443:
are different articles. Both leads could certainly be improved for better resolving the ambiguities, but playing with article titles is certainly not a solution.
390:" is certainly a Euclidean space, but the converse is wrong: A Euclidean space where coordinates are not defined is not a coordinate space. Similarly, in "the
1016:
188:
445:
I agree that "model" is not convenient in the first sentence, as being somehow anachronic. I'll replace it with "represent". Also, I'll add a reference to
1564:
1428:
by manipulating article titles. Apparently, you did not read the second sentence of the article, which is clearly intended for explaining this ambiguity.
294:
79:
1534:
1544:
488:, and Euclid never used the terms "dimension", "2D" and "3D", and also never used "space" for dimension two. So it is definitevely true true that
44:
1155:– This article has been the subject of moves, reverts and technical requests. Opening this RM to assess if there is indeed consensus to move it.
270:
1483:
It should be singular, following prevailing practice in the majority of Knowledge articles. It is trivial for authors of other pages to write
1559:
1051:
594:
85:
1171:
1119:
Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a
470:
makes it seem that books 1-10 deal with 2D geometry (with digressions into non-geometric topics) and books 11-13 deal with 3D geometry.
775:
1363:
1186:
261:
222:
658:
This probably does not need to be in the lead section, but it could be useful to add to a new section near the bottom of the page.
810:
this allows defining lines, planes, subspaces, dimension, and parallelism. The inner product allows defining distance and angles.
548:"Euclidean distance formula" is not defined in Knowledge, and as far as I know, it is not definied either in any reliable source.
670:. Ideally any discussion would aim to be lay-accessible, leaving interested readers to click through for more advanced coverage.
1529:
1431:
Also, except for mathematical oriented physical literature, “Euclidean space” is not used in physics. Physicists use normally "
99:
30:
855:
This seems like a serious regression. The name 'Euclidean space' is significantly more common and just fine for this topic. @
131:
127:
104:
20:
1516:
Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
859:
can you please try to start up conversations and reach some kind of consensus before making sweeping disruptive changes? –
666:) could profitably fill out at least one top-level section near the bottom. There is a little bit of relevant material in
74:
197:
1324:
65:
564:
the Euclidean distance between two points in Euclidean space is the length of a line segment between the two points
143:
122:
1110:
1028:
866:
825:
as it is currently structured. That article is organized around meta-discussion, starting with a description of
154:
636:
1175:
878:
three-dimensional Euclidean space, the Euclidean plane (dimension two) and the Euclidean line (dimension one).
791:
1391:. The proposed title is unnecessarily verbose. It requires, but cannot offer, an explanation of the variable
1436:
1432:
1299:
997:
931:
911:
109:
1367:
1358:
says: "Euclidean space is the fundamental space of geometry, intended to represent physical space". I.e.,
492:, Euclidean space (without article) denoted the three dimensional space, and that Euclid never considered
1418:
1379:
1340:
1320:
1261:
1194:
1120:
1077:
968:
662:
is linked from the "see also" section, but that and other structures generalizing Euclidean space (e.g.
590:
575:
383:
357:
337:
203:
1207:. I've started this RM to see if we can formally document consensus. I'm personally against this move.
417:
If I am right, then the claim that Euclidean space aims to model physical space needs to be clarified.
247:
794:, which could provide an alternate of Euclidean space. It also is entirely focused on the geometry of
382:
Your sugggestions are not only much too technical for the lead, but are also mathematically wrong: A "
1069:
442:
before 19th (or possibly 18th) century. So, the plane is far from being the first example of a space.
174:
1499:
1473:
1458:
1307:
1092:
1004:
950:
863:
837:
713:
617:
55:
1238:
1208:
1156:
1123:
after discussing it on the closer's talk page. No further edits should be made to this discussion.
269:
on Knowledge. If you would like to participate, please visit the project page, where you can join
1466:
1462:
1448:
1362:
Euclidean space is understood as the three-dimensional one. Otherwise, where should the redirect
1316:
1282:
1136:
1024:
915:
904:
822:
761:
749:
683:
551:
505:
467:
457:
446:
432:
404:
395:
391:
349:
345:
253:
159:
70:
237:
216:
1242:
1212:
1160:
949:(dimension one). The qualifier "Euclidean" is used to distinguish Euclidean spaces from other
51:
756:
of Euclidean geometry, not about that that can be done with it, which is Euclidean geometry.
1414:
1410:
1400:
1375:
1355:
1336:
1257:
1222:
1190:
1073:
982:
964:
856:
735:
691:
687:
648:
586:
571:
567:
520:
475:
422:
387:
353:
341:
156:
344:"? If it's too technical, how about something more informal, like: "Euclidean space is the
1488:
1440:
1295:
1146:
993:
939:
892:
771:
706:
679:
674:
667:
610:
24:
371:
This is not a definition in the mathematical sense, but it follows exactly the guideline
369:
Euclidean space is the fundamental space of geometry, aimed to model the physical space.
1496:
1470:
1371:
1332:
1304:
1230:
1089:
1001:
945:
900:
860:
834:
830:
745:
710:
614:
559:
1523:
1444:
1278:
1274:
1234:
1132:
1020:
757:
726:
659:
558:
in anything they say. All I'm proposing is to invert the definition given in article
555:
543:
501:
453:
400:
330:
1015:
I agree with the opponents to this move, and I have requested to revert the move at
640:
631:
space is an important archetype for many kinds of spaces in mathematics, including
1315:
Incoming links have mixed usage and would deserve disambiguation, for example: in
1396:
1226:
978:
919:
731:
644:
516:
471:
418:
266:
781:
Joking aside, I think this focus poorly serves many/most readers. Readers are
744:
This should need further discussion. However, in my opinion, most topics that
243:
678:
discussion discussion. Readers would be better served by e.g. material about
1366:
be targeted? Knowledge serves a wide audience and titles should reflect the
748:
would add to this article would be better placed (if they are not there) in
158:
896:
663:
632:
372:
1502:
1476:
1452:
1422:
1404:
1383:
1344:
1310:
1286:
1265:
1246:
1216:
1198:
1179:
1164:
1140:
1095:
1081:
1007:
986:
972:
840:
765:
739:
716:
652:
620:
579:
524:
509:
479:
461:
426:
408:
361:
954:
698:
those are discussed) and less reliance on lofty abstraction and jargon.
977:
I agree with Jacobolus, that this name change is an anti-improvement.
709:
for some of this, except that article has most of the same problems. –
496:(without? article, when used in the sense of the 10 first books) and
566:. To break circularity, the norm would be defined first in terms of
1435:”. This is because of these multiple uses of the word “space” that
1275:§ Why was this moved from 'Euclidean space' to 'Euclidean n-space’
992:
topics, including most of what is currently on this page. Having
1328:
851:
Why was this moved from 'Euclidean space' to 'Euclidean n-space'
802:, which is equally much a fundamental part of "Euclidean space".
1465:
spacetime ("Minkowski space") is explicitly non-Euclidean. In
883:
I've just linked as written literally and inserted the number
168:
160:
15:
798:
in Euclidean space, ignoring Laguerre's dual geometry of
1151:
937:, including the three-dimensional Euclidean space, the
377:
The first paragraph should define or identify the topic
1491:
if that name makes more grammatical sense in context.
1070:
Talk:Geometric_space#Splitting_from_Euclidean_n-space
850:
265:, a collaborative effort to improve the coverage of
872:Because the lead said (and still mostly says) so:
752:, as this article is about the definition of the
33:for general discussion of the article's subject.
1550:Knowledge level-5 vital articles in Mathematics
776:one modern formal definition of Euclidean space
1050:sfn error: no target: CITEREFSolomentsev2001 (
1017:Knowledge:Requested moves/Technical requests‎‎
8:
1045:
550:Given the existence of article and section
1109:The following is a closed discussion of a
211:
1189:has also been nominated for discussion.
1064:Splitting of section "Geometrical space"
1540:Knowledge vital articles in Mathematics
1038:
484:I know that, but this article is about
213:
172:
1323:: "in the three-dimensional ]..."; in
808:
376:
368:
1555:B-Class vital articles in Mathematics
1319:: "] is a good approximation..."; in
7:
1256:Don't see how it's an improvement. -
1128:The result of the move request was:
694:), rather than nitpicky formalities.
552:Euclidean_distance#Distance_formulas
259:This article is within the scope of
23:for discussing improvements to the
1461:space is implicitly Euclidean. In
668:Euclidean space § Metric structure
14:
1565:Top-priority mathematics articles
1364:three-dimensional Euclidean space
1327:: "in an n-dimensional ]..."; in
1187:Three-dimensional Euclidean space
279:Knowledge:WikiProject Mathematics
1535:Knowledge level-5 vital articles
1512:The discussion above is closed.
705:We could in theory lean more on
673:While we are at it, the section
282:Template:WikiProject Mathematics
246:
236:
215:
182:
173:
142:
45:Click here to start a new topic.
1469:space gets all wibble-wobbly. –
1294:. There are many wiki-links to
299:This article has been rated as
1545:B-Class level-5 vital articles
1331:: "four-dimensional ]..."; in
1019:, before reading this thread.
1000:is much worse in my opinion. –
953:that were later considered in
202:It is of interest to multiple
1:
841:20:51, 13 February 2023 (UTC)
766:09:22, 13 February 2023 (UTC)
740:02:39, 13 February 2023 (UTC)
717:01:45, 13 February 2023 (UTC)
653:23:29, 12 February 2023 (UTC)
273:and see a list of open tasks.
42:Put new text under old text.
1560:B-Class mathematics articles
1273:. Clear disimprovement. See
1102:Requested move 11 March 2023
895:is the fundamental space of
675:Euclidean space § Isometries
621:02:59, 5 November 2022 (UTC)
1325:Cartesian coordinate system
690:in 1840 decades before the
50:New to Knowledge? Welcome!
1581:
1503:22:56, 12 March 2023 (UTC)
1477:22:58, 12 March 2023 (UTC)
1453:10:49, 12 March 2023 (UTC)
1423:04:59, 12 March 2023 (UTC)
1405:04:24, 12 March 2023 (UTC)
1384:03:42, 12 March 2023 (UTC)
1345:03:55, 12 March 2023 (UTC)
1311:16:44, 11 March 2023 (UTC)
1287:15:08, 11 March 2023 (UTC)
1266:14:55, 11 March 2023 (UTC)
1247:13:43, 11 March 2023 (UTC)
1217:13:40, 11 March 2023 (UTC)
1199:04:51, 12 March 2023 (UTC)
1185:Procedural note: redirect
1180:20:53, 12 March 2023 (UTC)
1165:13:39, 11 March 2023 (UTC)
1141:16:43, 18 March 2023 (UTC)
1096:08:40, 11 March 2023 (UTC)
1082:06:51, 11 March 2023 (UTC)
1029:11:04, 11 March 2023 (UTC)
1008:08:36, 11 March 2023 (UTC)
987:07:07, 11 March 2023 (UTC)
973:06:45, 11 March 2023 (UTC)
903:. Originally, that is, in
867:06:32, 11 March 2023 (UTC)
637:topological vector spaces
298:
231:
210:
80:Be welcoming to newcomers
1514:Please do not modify it.
1221:Notifying participants @
1116:Please do not modify it.
943:(dimension two) and the
930:of any positive integer
899:, intended to represent
305:project's priority scale
1437:Three dimensional space
1433:three dimensional space
1300:three-dimensional space
998:Three-dimensional space
957:and modern mathematics.
912:three-dimensional space
626:Generalizations in lede
595:21:30, 4 May 2022 (UTC)
580:17:26, 4 May 2022 (UTC)
525:17:17, 4 May 2022 (UTC)
510:15:58, 4 May 2022 (UTC)
480:15:07, 4 May 2022 (UTC)
462:14:19, 4 May 2022 (UTC)
427:13:49, 4 May 2022 (UTC)
409:11:21, 4 May 2022 (UTC)
362:03:38, 4 May 2022 (UTC)
262:WikiProject Mathematics
1530:B-Class vital articles
959:
880:
367:The first sentence is
324:Definition in the lead
75:avoid personal attacks
1321:Differential geometry
996:(double-)redirect to
890:
875:
440:two-dimensional space
384:real coordinate space
338:real coordinate space
189:level-5 vital article
136:Auto-archiving period
100:Neutral point of view
792:Cayley–Klein metrics
285:mathematics articles
105:No original research
1459:Newtonian mechanics
1413:", in plural form?
1467:general relativity
1463:special relativity
1317:Euclidean geometry
1068:Please comment at
916:Euclidean geometry
823:Euclidean geometry
750:Euclidean geometry
684:inverse kinematics
396:Euclidean distance
392:mathematical space
386:equipped with the
350:Euclidean distance
346:mathematical space
340:equipped with the
254:Mathematics portal
198:content assessment
86:dispute resolution
47:
1354:. As the lead of
1152:Euclidean n-space
770:But the title is
556:assume good faith
468:Euclid's Elements
319:
318:
315:
314:
311:
310:
167:
166:
66:Assume good faith
43:
1572:
1489:Euclidean spaces
1486:
1411:Euclidean spaces
1356:Euclidean spaces
1298:and the article
1154:
1118:
1056:
1055:
1046:Solomentsev 2001
1043:
918:, but in modern
692:Erlangen program
688:Olinde Rodrigues
388:Euclidean metric
342:Euclidean metric
334:
287:
286:
283:
280:
277:
256:
251:
250:
240:
233:
232:
227:
219:
212:
195:
186:
185:
178:
177:
169:
161:
147:
146:
137:
95:Article policies
16:
1580:
1579:
1575:
1574:
1573:
1571:
1570:
1569:
1520:
1519:
1518:
1517:
1484:
1441:Euclidean space
1335:: "in ] is..."
1296:Euclidean space
1150:
1147:Euclidean space
1114:
1104:
1066:
1061:
1060:
1059:
1049:
1044:
1040:
994:Euclidean space
940:Euclidean plane
893:Euclidean space
853:
800:oriented planes
772:Euclidean space
707:Euclidean plane
680:crystallography
628:
611:Euclidean plane
607:
605:Euclidean plane
568:Pythagoras' law
554:, it's hard to
328:
326:
284:
281:
278:
275:
274:
252:
245:
225:
196:on Knowledge's
193:
183:
163:
162:
157:
134:
116:
115:
114:
91:
61:
25:Euclidean space
12:
11:
5:
1578:
1576:
1568:
1567:
1562:
1557:
1552:
1547:
1542:
1537:
1532:
1522:
1521:
1511:
1510:
1509:
1508:
1507:
1506:
1505:
1492:
1481:
1480:
1479:
1429:
1386:
1361:
1349:
1348:
1347:
1333:Absolute value
1289:
1268:
1251:
1250:
1249:
1183:
1182:
1172:88.111.123.182
1144:
1126:
1125:
1111:requested move
1105:
1103:
1100:
1099:
1098:
1065:
1062:
1058:
1057:
1037:
1036:
1032:
1013:
1012:
1011:
1010:
989:
960:
946:Euclidean line
901:physical space
888:
881:
873:
852:
849:
848:
847:
846:
845:
844:
843:
831:solid geometry
818:
814:
813:
812:
803:
779:
742:
720:
719:
703:
699:
695:
671:
627:
624:
606:
603:
602:
601:
600:
599:
598:
597:
560:Euclidean norm
538:
537:
536:
535:
534:
533:
532:
531:
530:
529:
528:
527:
443:
415:
380:
325:
322:
317:
316:
313:
312:
309:
308:
297:
291:
290:
288:
271:the discussion
258:
257:
241:
229:
228:
220:
208:
207:
201:
179:
165:
164:
155:
153:
152:
149:
148:
118:
117:
113:
112:
107:
102:
93:
92:
90:
89:
82:
77:
68:
62:
60:
59:
48:
39:
38:
35:
34:
28:
13:
10:
9:
6:
4:
3:
2:
1577:
1566:
1563:
1561:
1558:
1556:
1553:
1551:
1548:
1546:
1543:
1541:
1538:
1536:
1533:
1531:
1528:
1527:
1525:
1515:
1504:
1501:
1498:
1493:
1490:
1482:
1478:
1475:
1472:
1468:
1464:
1460:
1456:
1455:
1454:
1450:
1446:
1442:
1438:
1434:
1430:
1426:
1425:
1424:
1420:
1416:
1412:
1408:
1407:
1406:
1402:
1398:
1394:
1390:
1387:
1385:
1381:
1377:
1373:
1369:
1368:primary topic
1365:
1359:
1357:
1353:
1350:
1346:
1342:
1338:
1334:
1330:
1326:
1322:
1318:
1314:
1313:
1312:
1309:
1306:
1301:
1297:
1293:
1290:
1288:
1284:
1280:
1276:
1272:
1269:
1267:
1263:
1259:
1255:
1252:
1248:
1244:
1240:
1236:
1232:
1228:
1224:
1220:
1219:
1218:
1214:
1210:
1206:
1203:
1202:
1201:
1200:
1196:
1192:
1188:
1181:
1177:
1173:
1169:
1168:
1167:
1166:
1162:
1158:
1153:
1148:
1143:
1142:
1138:
1134:
1131:
1124:
1122:
1117:
1112:
1107:
1106:
1101:
1097:
1094:
1091:
1086:
1085:
1084:
1083:
1079:
1075:
1071:
1063:
1053:
1047:
1042:
1039:
1035:
1031:
1030:
1026:
1022:
1018:
1009:
1006:
1003:
999:
995:
990:
988:
984:
980:
976:
975:
974:
970:
966:
961:
958:
956:
952:
948:
947:
942:
941:
936:
933:
929:
927:
921:
917:
913:
910:, it was the
909:
908:
902:
898:
894:
889:
886:
882:
879:
874:
871:
870:
869:
868:
865:
862:
858:
842:
839:
836:
832:
828:
824:
819:
815:
811:
807:
806:
804:
801:
797:
793:
789:
784:
780:
777:
773:
769:
768:
767:
763:
759:
755:
751:
747:
743:
741:
737:
733:
728:
727:User:D.Lazard
724:
723:
722:
721:
718:
715:
712:
708:
704:
700:
696:
693:
689:
685:
681:
676:
672:
669:
665:
661:
660:Hilbert space
657:
656:
655:
654:
650:
646:
642:
641:metric spaces
638:
634:
625:
623:
622:
619:
616:
612:
604:
596:
592:
588:
583:
582:
581:
577:
573:
569:
565:
561:
557:
553:
549:
545:
542:
541:
540:
539:
526:
522:
518:
513:
512:
511:
507:
503:
499:
495:
491:
487:
483:
482:
481:
477:
473:
469:
465:
464:
463:
459:
455:
451:
450:
444:
441:
437:
436:
430:
429:
428:
424:
420:
416:
412:
411:
410:
406:
402:
397:
393:
389:
385:
381:
378:
374:
370:
366:
365:
364:
363:
359:
355:
351:
347:
343:
339:
332:
323:
321:
306:
302:
296:
293:
292:
289:
272:
268:
264:
263:
255:
249:
244:
242:
239:
235:
234:
230:
224:
221:
218:
214:
209:
205:
199:
191:
190:
180:
176:
171:
170:
151:
150:
145:
141:
133:
129:
126:
124:
120:
119:
111:
110:Verifiability
108:
106:
103:
101:
98:
97:
96:
87:
83:
81:
78:
76:
72:
69:
67:
64:
63:
57:
53:
52:Learn to edit
49:
46:
41:
40:
37:
36:
32:
26:
22:
18:
17:
1513:
1487:to generate
1392:
1388:
1351:
1291:
1270:
1253:
1204:
1184:
1145:
1129:
1127:
1115:
1108:
1067:
1041:
1033:
1014:
944:
938:
934:
925:
923:
906:
891:
884:
876:
854:
827:The Elements
826:
799:
795:
787:
782:
753:
629:
608:
563:
547:
497:
493:
489:
485:
466:The article
448:
439:
434:
394:obeying the
348:obeying the
327:
320:
301:Top-priority
300:
260:
226:Top‑priority
204:WikiProjects
187:
139:
121:
94:
19:This is the
1415:fgnievinski
1376:fgnievinski
1337:fgnievinski
1258:Kj cheetham
1223:Fgnievinski
1191:fgnievinski
1170:I disagree
1121:move review
1074:fgnievinski
965:fgnievinski
920:mathematics
857:Fgnievinski
572:fgnievinski
354:fgnievinski
276:Mathematics
267:mathematics
223:Mathematics
31:not a forum
1524:Categories
1130:not moved.
1034:References
924:Euclidean
922:there are
587:XOR'easter
490:originally
352:formula"?
1497:jacobolus
1471:jacobolus
1305:jacobolus
1239:Dr. Vogel
1231:Jacobolus
1209:Dr. Vogel
1157:Dr. Vogel
1090:jacobolus
1002:jacobolus
932:dimension
905:Euclid's
861:jacobolus
835:jacobolus
746:jacobolus
711:jacobolus
664:Lp spaces
633:manifolds
615:jacobolus
447:Euclid's
433:Euclid's
192:is rated
88:if needed
71:Be polite
21:talk page
1445:D.Lazard
1279:D.Lazard
1235:D.Lazard
1133:Favonian
1021:D.Lazard
907:Elements
897:geometry
817:article.
758:D.Lazard
643:, ...".
544:D.Lazard
502:D.Lazard
454:D.Lazard
449:Elements
435:Elements
414:example.
401:D.Lazard
373:MOS:OPEN
331:D.Lazard
140:365Â days
123:Archives
56:get help
29:This is
27:article.
1372:WP:VOTE
1352:Support
955:physics
928:-spaces
303:on the
194:B-class
1397:Mgnbar
1389:Oppose
1292:Oppose
1271:Oppose
1254:Oppose
1227:Mgnbar
1205:Oppose
979:Mgnbar
951:spaces
796:points
774:, not
732:Mgnbar
645:Mgnbar
517:Mgnbar
498:planes
472:Mgnbar
419:Mgnbar
200:scale.
788:about
778:. ;-)
754:space
546:said
494:plane
486:space
181:This
84:Seek
1449:talk
1439:and
1419:talk
1401:talk
1380:talk
1341:talk
1329:Cube
1283:talk
1262:talk
1243:talk
1213:talk
1195:talk
1176:talk
1161:talk
1137:talk
1078:talk
1052:help
1025:talk
983:talk
969:talk
762:talk
736:talk
649:talk
591:talk
576:talk
521:talk
506:talk
476:talk
458:talk
423:talk
405:talk
358:talk
73:and
1500:(t)
1474:(t)
1457:In
1374:.)
1360:the
1308:(t)
1233:, @
1229:, @
1225:, @
1093:(t)
1005:(t)
914:of
864:(t)
838:(t)
783:not
714:(t)
682:or
618:(t)
295:Top
1526::
1485:]s
1451:)
1421:)
1403:)
1382:)
1343:)
1285:)
1277:.
1264:)
1245:)
1237:.
1215:)
1197:)
1178:)
1163:)
1149:→
1139:)
1113:.
1080:)
1072:.
1027:)
985:)
971:)
764:)
738:)
651:)
639:,
635:,
593:)
578:)
570:.
562::
523:)
508:)
478:)
460:)
452:.
425:)
407:)
360:)
138::
130:,
54:;
1495:–
1447:(
1417:(
1399:(
1393:n
1378:(
1339:(
1303:–
1281:(
1260:(
1241:(
1211:(
1193:(
1174:(
1159:(
1135:(
1088:–
1076:(
1054:)
1048:.
1023:(
981:(
967:(
935:n
926:n
887::
885:n
760:(
734:(
647:(
589:(
574:(
519:(
504:(
474:(
456:(
421:(
403:(
375:(
356:(
333::
329:@
307:.
206:.
132:2
128:1
125::
58:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
