84:
74:
53:
22:
601:
I'm not sure what's the best option to proceed here. One option might be to make (leave?) this a statement about real numbers of distance one and change the terminology accordingly. Another option might be to make make this statement about sequential integers or naturals (I suppose you intended that)
595:
I agree that current terminology is not helpful if it is understood as a statement about real numbers (and I couldn't find any book or paper using such terminology in a superficial search). The reason why I reverted this was that if restricted to natural numbers it somewhat redundant to the theorem
694:
Well allowing (positive) real numbers instead of natural numbers turns the whole thing into (trivial) geometric theorem (as stated above and the notion of bases makes sense as base side) rather than being just an geometric illustration of number theoretic theorem. Whether such a "geometric theorem"
607:
As far as "adjacent squares" in terms of real numbers are concerned, there is a way to make some sense of geometrically. That if the side length of 2 squares differ by one, then the difference in area in identical to the sum of their base sides (ignoring units). You can visualize that nicely by
662:
article. I'm not sure what the additional benefit is in allowing for real numbers here. The concept of "adjacent" squares loses its meaning and actually any real number can be expressed as a difference of squares in infinitely many
608:
placing the squares on top of each and we could actually include such drawing into the article. Maybe that's even what the original author had in mind, but that's pure speculation on my side now.--
649:
the sum of the square roots. I agree that the statement that an odd number can be expressed as a difference of (consecutive perfect) squares is redundant, so that sentence could simply be deleted.
140:
262:
The geometric illustration does not point out that the two rectangles represent (a-b)b. A better account of the picture would vastly help some people understand the whole article.
575:, but why would all this be worth mentioning? Describing two real numbers as adjacent is meaningless since they are uncountable and calling the square root "base" is misleading.
476:
569:
695:
is worthwhile to mention here is imho a matter of taste/editorial discretion, it certainly doesn't need to be in the article, but I see no harm in mentioning it either.--
520:
602:
and explain the terminology in that context (or modify it). In that case however we should merge that with theorem directly after to avoided having the same proof twice.
421:
296:
There is also a formula derivable from a difference of two squares to receive the difference's value. when a is a perfect square, x^2 - a = (x - a)^2 - a(a + 2x -1)
742:
Wiktionary doesn’t state anything about numbers other than real, Wiktionary isn’t any particular authority on algebra and, at the end, Wiktionary is no more than a
275:
A more explicit connection between the text and illustrations could help readers of wikipedia.(After all, mathematical prodigies don't need it in the first place)
194:
672:
My view is that it would be more interesting to discuss how the difference of consecutive perfect squares leads to a recursive formula for calculating the
775:
130:
770:
106:
282:
303:
383:
The statement about the difference of two consecutive perfect squares makes sense here, but why would statements about real numbers
97:
58:
368:
It actually makes sense to mention it both articles, here it is an example for another application of the difference of squares.--
33:
259:
Many students would find it helpful to be told more of the relationship between the equations and the illustration.
327:
220:
Could someone create a disambiguation page that also links DOTS here. I've seen DOTS as an abbreviation for this.
221:
720:
286:
224:
21:
307:
751:
349:
I think the contents of the section
Difference of adjacent squares would make more sense in the article
323:
322:
This addition moved here for consideration. The identity is valid but didn't really fit well as placed.
207:
39:
83:
426:
299:
278:
676:
th perfect square from the previous one and mention the concept of squarity testing as described in
242:
228:
525:
105:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
728:
89:
226:. However, there's another page that has DOTS as a redirect. I was just unsure how to do this.
73:
52:
685:
580:
481:
358:
747:
700:
613:
373:
203:
394:
173:
755:
736:
704:
689:
617:
584:
377:
362:
331:
311:
290:
248:
234:
210:
764:
724:
677:
659:
630:
350:
681:
576:
354:
696:
609:
369:
102:
240:
Oh, I'm not sure if the sum of two squares should also be added to this page.
79:
629:
of this section was referring to was that the difference of two consecutive
658:
The geometrical interpretation that you propose is already included in the
199:
341:(x^2-y^2)= 2dx-d^2 (Where "d" is the difference between the numbers)
743:
15:
680:. In any case, there should also be a link to that article.
198:) format, because the latter fails to render properly. See
391:
with a certain distance between them be relevant? Yes, if
627:
528:
484:
429:
397:
176:
101:, a collaborative effort to improve the coverage of
719:Is this only for real numbers as inferred from the
571:
and of course any real number can be expressed as 4
563:
514:
470:
415:
188:
596:about odd numbers following directly afterwards.
8:
47:
19:
546:
533:
527:
483:
447:
434:
428:
396:
337:An alternative method, Momaney's Theorem:
175:
590:Sorry for my somewhat premature reverts.
269:ab-b^2 + (a^2 - 2ab + b^2) + ab - b^2 =
266:(a-b)b + (a-b)(a-b) + (a-b)b =
49:
170:" (''b'' − ''a'') format, instead of "
7:
626:I think what the "original" wording
95:This article is within the scope of
38:It is of interest to the following
14:
776:Low-priority mathematics articles
162:The math markup is currently in "
115:Knowledge:WikiProject Mathematics
471:{\displaystyle a^{2}-b^{2}=2b+1}
118:Template:WikiProject Mathematics
82:
72:
51:
20:
771:Stub-Class mathematics articles
135:This article has been rated as
564:{\displaystyle a^{2}-b^{2}=4x}
332:12:55, 23 September 2011 (UTC)
312:01:14, 22 September 2010 (UTC)
1:
705:22:06, 15 November 2013 (UTC)
690:11:47, 15 November 2013 (UTC)
618:00:35, 15 November 2013 (UTC)
585:19:04, 14 November 2013 (UTC)
378:12:52, 14 November 2013 (UTC)
363:11:14, 14 November 2013 (UTC)
211:23:04, 24 December 2006 (UTC)
109:and see a list of open tasks.
249:01:40, 6 December 2007 (UTC)
235:23:21, 5 December 2007 (UTC)
255:Clarifying the illustration
792:
291:06:55, 12 April 2008 (UTC)
515:{\displaystyle a+1=b-1=x}
134:
67:
46:
756:15:21, 2 July 2019 (UTC)
737:14:14, 2 July 2019 (UTC)
141:project's priority scale
98:WikiProject Mathematics
565:
516:
472:
417:
190:
28:This article is rated
566:
517:
473:
418:
416:{\displaystyle a=b+1}
191:
641:-1)th, is equal to 2
526:
482:
427:
395:
174:
121:mathematics articles
318:Moved from the page
189:{\displaystyle b-a}
561:
512:
468:
413:
247:
233:
186:
90:Mathematics portal
34:content assessment
302:comment added by
293:
281:comment added by
244:S♦s♦e♦b♦a♦l♦l♦o♦s
241:
230:S♦s♦e♦b♦a♦l♦l♦o♦s
227:
197:b-a</math: -->
155:
154:
151:
150:
147:
146:
783:
570:
568:
567:
562:
551:
550:
538:
537:
521:
519:
518:
513:
477:
475:
474:
469:
452:
451:
439:
438:
422:
420:
419:
414:
324:Charles Matthews
314:
276:
245:
231:
196:" (<math: -->
195:
193:
192:
187:
123:
122:
119:
116:
113:
92:
87:
86:
76:
69:
68:
63:
55:
48:
31:
25:
24:
16:
791:
790:
786:
785:
784:
782:
781:
780:
761:
760:
717:
542:
529:
524:
523:
480:
479:
443:
430:
425:
424:
393:
392:
347:
320:
297:
257:
243:
229:
218:
172:
171:
160:
120:
117:
114:
111:
110:
88:
81:
61:
32:on Knowledge's
29:
12:
11:
5:
789:
787:
779:
778:
773:
763:
762:
759:
758:
716:
713:
712:
711:
710:
709:
708:
707:
667:
666:
665:
664:
653:
652:
651:
650:
631:square numbers
621:
620:
604:
603:
598:
597:
592:
591:
560:
557:
554:
549:
545:
541:
536:
532:
511:
508:
505:
502:
499:
496:
493:
490:
487:
467:
464:
461:
458:
455:
450:
446:
442:
437:
433:
412:
409:
406:
403:
400:
381:
380:
346:
343:
339:
338:
319:
316:
283:198.53.140.155
265:
256:
253:
252:
251:
217:
216:DOTS disambig?
214:
185:
182:
179:
159:
156:
153:
152:
149:
148:
145:
144:
133:
127:
126:
124:
107:the discussion
94:
93:
77:
65:
64:
56:
44:
43:
37:
26:
13:
10:
9:
6:
4:
3:
2:
788:
777:
774:
772:
769:
768:
766:
757:
753:
749:
745:
741:
740:
739:
738:
734:
732:
726:
722:
714:
706:
702:
698:
693:
692:
691:
687:
683:
679:
678:square number
675:
671:
670:
669:
668:
661:
660:square number
657:
656:
655:
654:
648:
644:
640:
636:
632:
628:
625:
624:
623:
622:
619:
615:
611:
606:
605:
600:
599:
594:
593:
589:
588:
587:
586:
582:
578:
574:
558:
555:
552:
547:
543:
539:
534:
530:
509:
506:
503:
500:
497:
494:
491:
488:
485:
465:
462:
459:
456:
453:
448:
444:
440:
435:
431:
410:
407:
404:
401:
398:
390:
386:
379:
375:
371:
367:
366:
365:
364:
360:
356:
352:
351:square number
345:Section split
344:
342:
336:
335:
334:
333:
329:
325:
317:
315:
313:
309:
305:
301:
294:
292:
288:
284:
280:
273:
270:
267:
263:
260:
254:
250:
246:
239:
238:
237:
236:
232:
225:
222:
215:
213:
212:
209:
205:
201:
183:
180:
177:
169:
165:
157:
142:
138:
132:
129:
128:
125:
108:
104:
100:
99:
91:
85:
80:
78:
75:
71:
70:
66:
60:
57:
54:
50:
45:
41:
35:
27:
23:
18:
17:
730:
718:
673:
646:
642:
638:
634:
572:
388:
384:
382:
348:
340:
321:
304:24.44.52.119
295:
274:
272:(a^2 - b^2)
271:
268:
264:
261:
258:
219:
167:
163:
161:
137:Low-priority
136:
96:
62:Low‑priority
40:WikiProjects
748:Incnis Mrsi
746:. Risible.
298:—Preceding
277:—Preceding
112:Mathematics
103:mathematics
59:Mathematics
765:Categories
721:wiktionary
633:, say the
30:Stub-class
725:Sobreira
637:th and (
300:unsigned
279:unsigned
200:bug 8373
682:Isheden
577:Isheden
478:and if
355:Isheden
204:grendel
139:on the
731:parlez
697:Kmhkmh
610:Kmhkmh
370:Kmhkmh
158:Markup
36:scale.
727:◣◥ ፧
663:ways.
522:then
423:then
752:talk
744:wiki
723:. ※
701:talk
686:talk
647:i.e.
645:-1,
614:talk
581:talk
387:and
374:talk
359:talk
328:talk
308:talk
287:talk
223:and
208:khan
735:⁇﹖
131:Low
767::
754:)
703:)
688:)
616:)
583:)
540:−
501:−
441:−
376:)
361:)
353:.
330:)
310:)
289:)
202:.
181:−
166:−
750:(
733:)
729:(
715:R
699:(
684:(
674:n
643:n
639:n
635:n
612:(
579:(
573:x
559:x
556:4
553:=
548:2
544:b
535:2
531:a
510:x
507:=
504:1
498:b
495:=
492:1
489:+
486:a
466:1
463:+
460:b
457:2
454:=
449:2
445:b
436:2
432:a
411:1
408:+
405:b
402:=
399:a
389:b
385:a
372:(
357:(
326:(
306:(
285:(
206:|
184:a
178:b
168:a
164:b
143:.
42::
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
