521:(Deleting previous comment.) How silly of me. Of course, the metatheorem that Euclidean geometry = analytic geometry is proven somewhere in the course of Tarski's proof that Euclidean geometry is decidable. The key steps are to show that Tarski's axioms are interpretable in the theory of real closed fields and that there exists a decision-procedure for the latter via quantifier elimination. To clarify, Grobner bases provide more efficient algorithms for the second step. An immediate consequence is that elementary geometry is routine.
320:
310:
289:
256:
401:
216:
247:
699:
598:
I really can not see an advantage to having words on the tin that don't match what is in the tin. An article entitled "Analytic
Geometry" should be about the modern subject of analytic geometry. A separate article entitled "Co-ordinate Geometry" should be about, well how about, co-ordinate
486:
It seems non-trivial. Euclidean geometry is consistent, yet the same cannot be said of arithmetic. Tarski's work comes to mind. So how do you quickly show that analytic geometry doesn't let you talk about the integers or rationals? Analytic geometry is routine and algorithmically decidable via
653:
Yes, it is missing negative signs. This illustration has been defective since Jan. 2015 and the creator of the diagram was aware of this as it is mentioned on the file page for this illustration. It probably should be removed.
575:
This article has Too little info on the modern and advanced meaning. Maybe this article should be renamed
Analytic geometry(classical meaning) and a new article should be created Analytic geometry(modern and advanced meaning)
166:
619:
There is a lot of implicit mention of algebraic geometric concepts such as algebraic curves. To my knowledge analytic geometry is simply the study of coordinate systems. Perhaps this should be fixed.
376:
639:
763:
711:
472:
I've changed it to what I assume it meant. A mildly interesting point for our wonkish bretheren: can this metatheorem that everyone knows be given an accessible reference?
160:
207:
753:
638:
Am I missing something extremely obvious, or is the very first illustration in this article (the one captioned "Cartesian coordinates") missing some negative signs?
460:
The relationship between algebra and geometry is nontrivial. There exist proofs of this relationship based on the theory of geometry and notions of geometric length.
768:
260:
778:
366:
92:
748:
57:
758:
599:
geometry. Surely it would be obtuse to have it any other way, especially as this is an encyclopedia with an object of clarifying material.
342:
773:
98:
620:
583:
549:
707:
691:
333:
294:
643:
414:
203:
181:
743:
503:
112:
43:
148:
117:
33:
87:
269:
723:
444:
78:
215:
198:
142:
423:
226:
138:
624:
587:
553:
122:
719:
188:
703:
473:
275:
319:
714:
until a consensus is reached, and readers of this page are welcome to contribute to the discussion.
604:
579:
545:
491:
246:
499:
174:
68:
341:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
677:
659:
463:
429:
325:
231:
83:
309:
288:
154:
64:
37:
425:
400:
228:
600:
522:
495:
737:
673:
655:
338:
315:
427:
230:
729:
681:
663:
647:
628:
608:
591:
557:
525:
507:
476:
466:
712:
Knowledge:Redirects for discussion/Log/2022 February 14#Analytisk geometri
698:
672:
It has now been replaced (not by me) with a correct illustration. --
702:
An editor has identified a potential problem with the redirect
430:
394:
240:
232:
28:
15:
173:
337:, a collaborative effort to improve the coverage of
571:Too little info on the modern and advanced meaning
46:for general discussion of the article's subject.
764:Knowledge level-4 vital articles in Mathematics
542:The line is true but has nothing to do here.
438:This page has archives. Sections older than
187:
8:
489:
283:
455:Relationship between algebra and geometry
754:Knowledge vital articles in Mathematics
615:Analytic geometry vs Algebraic geometry
285:
244:
448:when more than 5 sections are present.
769:B-Class vital articles in Mathematics
7:
331:This article is within the scope of
640:2604:2000:EFC0:2:6101:CCF:CD4B:8D4E
274:It is of interest to the following
36:for discussing improvements to the
14:
779:Top-priority mathematics articles
442:may be automatically archived by
351:Knowledge:WikiProject Mathematics
749:Knowledge level-4 vital articles
710:. This discussion will occur at
697:
399:
354:Template:WikiProject Mathematics
318:
308:
287:
254:
245:
214:
58:Click here to start a new topic.
690:"Analytisk geometri" listed at
371:This article has been rated as
759:B-Class level-4 vital articles
1:
730:06:05, 14 February 2022 (UTC)
592:00:56, 30 November 2011 (UTC)
558:00:57, 30 November 2011 (UTC)
345:and see a list of open tasks.
55:Put new text under old text.
774:B-Class mathematics articles
609:14:01, 1 December 2013 (UTC)
477:21:24, 26 October 2006 (UTC)
467:19:23, 26 October 2006 (UTC)
526:03:22, 6 January 2007 (UTC)
508:02:12, 6 January 2007 (UTC)
63:New to Knowledge? Welcome!
795:
629:12:10, 11 March 2014 (UTC)
682:17:27, 4 April 2018 (UTC)
664:03:31, 4 April 2018 (UTC)
648:23:50, 3 April 2018 (UTC)
370:
303:
282:
93:Be welcoming to newcomers
22:Skip to table of contents
692:Redirects for discussion
377:project's priority scale
21:
706:and has thus listed it
487:Grobner bases, I think.
334:WikiProject Mathematics
744:B-Class vital articles
720:User:1234qwer1234qwer4
462:What does this mean?
445:Lowercase sigmabot III
88:avoid personal attacks
261:level-4 vital article
208:Auto-archiving period
113:Neutral point of view
357:mathematics articles
118:No original research
704:Analytisk geometri
326:Mathematics portal
270:content assessment
99:dispute resolution
60:
582:comment added by
548:comment added by
510:
494:comment added by
452:
451:
391:
390:
387:
386:
383:
382:
239:
238:
79:Assume good faith
56:
38:Analytic geometry
27:
26:
786:
728:
727:
701:
674:Bill Cherowitzo
656:Bill Cherowitzo
594:
560:
474:Charles Matthews
447:
431:
403:
395:
359:
358:
355:
352:
349:
328:
323:
322:
312:
305:
304:
299:
291:
284:
267:
258:
257:
250:
249:
241:
233:
219:
218:
209:
192:
191:
177:
108:Article policies
29:
16:
794:
793:
789:
788:
787:
785:
784:
783:
734:
733:
718:
715:
695:
636:
617:
577:
573:
543:
457:
443:
432:
426:
408:
356:
353:
350:
347:
346:
324:
317:
297:
268:on Knowledge's
265:
255:
235:
234:
229:
206:
134:
129:
128:
127:
104:
74:
12:
11:
5:
792:
790:
782:
781:
776:
771:
766:
761:
756:
751:
746:
736:
735:
717:
708:for discussion
694:
688:
687:
686:
685:
684:
667:
666:
635:
634:Negative Signs
632:
616:
613:
612:
611:
572:
569:
568:
567:
566:
565:
564:
563:
562:
561:
533:
532:
531:
530:
529:
528:
514:
513:
512:
511:
480:
479:
456:
453:
450:
449:
437:
434:
433:
428:
424:
422:
419:
418:
410:
409:
404:
398:
389:
388:
385:
384:
381:
380:
369:
363:
362:
360:
343:the discussion
330:
329:
313:
301:
300:
292:
280:
279:
273:
251:
237:
236:
227:
225:
224:
221:
220:
194:
193:
131:
130:
126:
125:
120:
115:
106:
105:
103:
102:
95:
90:
81:
75:
73:
72:
61:
52:
51:
48:
47:
41:
25:
24:
19:
13:
10:
9:
6:
4:
3:
2:
791:
780:
777:
775:
772:
770:
767:
765:
762:
760:
757:
755:
752:
750:
747:
745:
742:
741:
739:
732:
731:
725:
721:
713:
709:
705:
700:
693:
689:
683:
679:
675:
671:
670:
669:
668:
665:
661:
657:
652:
651:
650:
649:
645:
641:
633:
631:
630:
626:
622:
621:67.252.103.23
614:
610:
606:
602:
597:
596:
595:
593:
589:
585:
584:220.255.2.141
581:
570:
559:
555:
551:
550:220.255.2.166
547:
541:
540:
539:
538:
537:
536:
535:
534:
527:
524:
520:
519:
518:
517:
516:
515:
509:
505:
501:
497:
493:
488:
484:
483:
482:
481:
478:
475:
471:
470:
469:
468:
465:
464:Richard Pinch
461:
454:
446:
441:
436:
435:
421:
420:
417:
416:
412:
411:
407:
402:
397:
396:
393:
378:
374:
368:
365:
364:
361:
344:
340:
336:
335:
327:
321:
316:
314:
311:
307:
306:
302:
296:
293:
290:
286:
281:
277:
271:
263:
262:
252:
248:
243:
242:
223:
222:
217:
213:
205:
202:
200:
196:
195:
190:
186:
183:
180:
176:
172:
168:
165:
162:
159:
156:
153:
150:
147:
144:
140:
137:
136:Find sources:
133:
132:
124:
123:Verifiability
121:
119:
116:
114:
111:
110:
109:
100:
96:
94:
91:
89:
85:
82:
80:
77:
76:
70:
66:
65:Learn to edit
62:
59:
54:
53:
50:
49:
45:
39:
35:
31:
30:
23:
20:
18:
17:
696:
637:
618:
578:— Preceding
574:
544:— Preceding
490:— Preceding
485:
459:
458:
439:
413:
405:
392:
373:Top-priority
372:
332:
298:Top‑priority
276:WikiProjects
259:
211:
197:
184:
178:
170:
163:
157:
151:
145:
135:
107:
32:This is the
348:Mathematics
339:mathematics
295:Mathematics
161:free images
44:not a forum
738:Categories
601:FreeFlow99
523:Amcfreely
496:Amcfreely
264:is rated
101:if needed
84:Be polite
34:talk page
580:unsigned
546:unsigned
504:contribs
492:unsigned
440:365 days
406:Archives
212:365 days
199:Archives
69:get help
42:This is
40:article.
375:on the
266:B-class
167:WP refs
155:scholar
272:scale.
139:Google
253:This
182:JSTOR
143:books
97:Seek
724:talk
716:~~~~
678:talk
660:talk
644:talk
625:talk
605:talk
588:talk
554:talk
500:talk
175:FENS
149:news
86:and
367:Top
189:TWL
740::
680:)
662:)
654:--
646:)
627:)
607:)
590:)
556:)
506:)
502:•
210::
169:)
67:;
726:)
722:(
676:(
658:(
642:(
623:(
603:(
586:(
552:(
498:(
415:1
379:.
278::
204:1
201::
185:·
179:·
171:·
164:·
158:·
152:·
146:·
141:(
71:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
