43:
188:
279:
194:
199:
95:
647:
617:
664:{{Information |Description=Geometric proof without words that quadratic mean (root mean square) > arithmetic mean > geometric mean > harmonic mean, drawn by CMG Lee based on Figure 4 on http://maa.org/book/export/html/466289 . |Source={{own}} |Date= |Author=
240:– You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
786:
746:
791:
824:
Geometric proof without words that quadratic mean (root mean square) > arithmetic mean > geometric mean > harmonic mean, drawn by CMG Lee based on Figure 4 on
143:
Geometric proof without words that quadratic mean (root mean square) > arithmetic mean > geometric mean > harmonic mean, drawn by CMG Lee based on Figure 4 on
728:
69:
65:
61:
57:
53:
47:
296:
106:
78:
723:
294:; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled
286:
646:
641:
562:
526:
509:
473:
804:
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
247:
546:
457:
431:
416:
401:
291:
493:
374:
357:
672:
209:
408:
807:
If the file has been modified from its original state, some details may not fully reflect the modified file.
776:
684:
The following pages on the
English Knowledge (XXG) use this file (pages on other projects are not listed):
616:
611:
42:
246:– If you remix, transform, or build upon the material, you must distribute your contributions under the
688:
206:
114:
713:
273:
284:
Permission is granted to copy, distribute and/or modify this document under the terms of the
718:
698:
423:
693:
703:
669:
708:
181:
I, the copyright holder of this work, hereby publish it under the following licenses:
101:
665:
657:
627:
165:
825:
144:
766:
584:
Click on a date/time to view the file as it appeared at that time.
756:
89:
510:
Creative
Commons Attribution-ShareAlike 4.0 International
341:
Add a one-line explanation of what this file represents
83:(SVG file, nominally 512 × 384 pixels, file size: 3 KB)
527:
290:, Version 1.2 or any later version published by the
133:
113:
Commons is a freely licensed media file repository.
729:Template:QM AM GM HM inequality visual proof.svg
257:https://creativecommons.org/licenses/by-sa/4.0
94:
263:Creative Commons Attribution-Share Alike 4.0
187:
8:
223:– to copy, distribute and transmit the work
46:Size of this PNG preview of this SVG file:
809:
586:
337:
322:You may select the license of your choice.
739:The following other wikis use this file:
424:https://commons.wikimedia.org/user:Cmglee
210:Attribution-Share Alike 4.0 International
839:
831:
819:
811:
686:
560:
544:
524:
507:
491:
471:
455:
388:
372:
355:
352:
333:
326:
139:QM AM GM HM inequality visual proof.svg
826:http://maa.org/book/export/html/466289
724:User:Kazkaskazkasako/Books/Mathematics
145:http://maa.org/book/export/html/466289
7:
302:http://www.gnu.org/copyleft/fdl.html
816:QM AM GM HM inequality visual proof
575:
198:
193:
802:
668:|Permission= |other_versions= }}
346:
340:
321:
184:
180:
126:
76:
345:
331:
278:
277:
234:Under the following conditions:
205:This file is licensed under the
197:
192:
186:
93:
31:
21:
328:
14:
327:
308:GNU Free Documentation License
297:GNU Free Documentation License
287:GNU Free Documentation License
26:
1:
563:original creation by uploader
36:
673:Category:Inequality (ethics)
353:Items portrayed in this file
861:
783:Usage on th.wikipedia.org
773:Usage on ja.wikipedia.org
763:Usage on fr.wikipedia.org
753:Usage on es.wikipedia.org
743:Usage on bg.wikipedia.org
248:same or compatible license
576:
155:
16:
330:
292:Free Software Foundation
214:
100:This is a file from the
767:Moyenne pythagoricienne
747:Средностепенна стойност
663:
633:
161:
151:
136:
104:. Information from its
642:17:44, 13 October 2020
612:19:53, 13 October 2020
107:description page there
634:Bold and align text.
70:2,560 × 1,920 pixels
229:– to adapt the work
52:Other resolutions:
432:author name string
402:Wikimedia username
66:1,280 × 960 pixels
62:1,024 × 768 pixels
848:
847:
735:Global file usage
714:Pythagorean means
677:
494:copyright license
339:
319:
318:
171:
170:
122:
121:
102:Wikimedia Commons
32:Global file usage
852:
810:
757:Media aritmética
719:Root mean square
699:Generalized mean
689:AM–GM inequality
654:
624:
458:copyright status
439:
436:
426:
421:
411:
406:
315:
312:
309:
306:
303:
281:
280:
274:
270:
267:
264:
261:
258:
250:as the original.
207:Creative Commons
201:
200:
196:
195:
190:
189:
157:
140:
134:
118:
97:
96:
90:
84:
73:
58:640 × 480 pixels
54:320 × 240 pixels
48:512 × 384 pixels
860:
859:
855:
854:
853:
851:
850:
849:
798:
787:มัชฌิมพีทาโกรัส
733:
694:Arithmetic mean
685:
678:
660:
652:
630:
622:
578:
577:
574:
573:
572:
571:
570:
569:
568:
567:
565:
553:
552:
551:
549:
538:
537:
536:
535:
534:
533:
532:
531:
529:
518:
517:
516:
515:
514:
512:
500:
499:
498:
496:
485:
484:
483:
482:
481:
480:
479:
478:
476:
464:
463:
462:
460:
449:
448:
447:
446:
445:
444:
443:
442:
441:
440:
437:
434:
428:
427:
422:
419:
413:
412:
407:
404:
395:
394:
393:
391:
381:
380:
379:
377:
366:
365:
364:
363:
362:
360:
344:
343:
342:
325:
324:
323:
313:
310:
307:
304:
301:
272:
271:
268:
265:
262:
259:
256:
255:
213:
202:
183:
182:
177:
172:
138:
131:
124:
123:
112:
111:
110:is shown below.
86:
82:
75:
74:
51:
12:
11:
5:
858:
856:
846:
845:
842:
838:
837:
834:
830:
829:
822:
818:
817:
814:
801:
797:
796:
795:
794:
792:มัชฌิมเรขาคณิต
789:
781:
780:
779:
771:
770:
769:
761:
760:
759:
751:
750:
749:
737:
736:
732:
731:
726:
721:
716:
711:
706:
704:Geometric mean
701:
696:
691:
683:
682:
681:
676:
675:
670:Category:Means
662:
658:
655:
649:
644:
639:
636:
635:
632:
628:
625:
619:
614:
609:
605:
604:
601:
598:
595:
592:
589:
582:
581:
566:
561:
559:
558:
557:
556:
555:
554:
550:
547:source of file
545:
543:
542:
541:
540:
539:
530:
525:
523:
522:
521:
520:
519:
513:
508:
506:
505:
504:
503:
502:
501:
497:
492:
490:
489:
488:
487:
486:
477:
472:
470:
469:
468:
467:
466:
465:
461:
456:
454:
453:
452:
451:
450:
430:
429:
415:
414:
400:
399:
398:
397:
396:
392:
389:
387:
386:
385:
384:
383:
382:
378:
373:
371:
370:
369:
368:
367:
361:
356:
354:
351:
350:
349:
348:
347:
336:
335:
332:
329:
320:
317:
316:
282:
254:
253:
252:
251:
241:
232:
231:
230:
224:
217:You are free:
204:
203:
185:
179:
178:
176:
173:
169:
168:
163:
159:
158:
153:
149:
148:
141:
132:
130:
127:
125:
120:
119:
98:
88:
87:
45:
41:
40:
39:
34:
29:
24:
19:
13:
10:
9:
6:
4:
3:
2:
857:
843:
840:
835:
832:
827:
823:
820:
815:
812:
808:
805:
799:
793:
790:
788:
785:
784:
782:
778:
775:
774:
772:
768:
765:
764:
762:
758:
755:
754:
752:
748:
745:
744:
742:
741:
740:
734:
730:
727:
725:
722:
720:
717:
715:
712:
710:
709:Harmonic mean
707:
705:
702:
700:
697:
695:
692:
690:
687:
679:
674:
671:
667:
661:
656:
650:
648:
645:
643:
640:
638:
637:
631:
626:
620:
618:
615:
613:
610:
607:
606:
602:
599:
596:
593:
590:
588:
587:
585:
579:
564:
548:
528:
511:
495:
475:
459:
433:
425:
418:
410:
403:
376:
359:
299:
298:
293:
289:
288:
283:
276:
275:
260:CC BY-SA 4.0
249:
245:
242:
239:
236:
235:
233:
228:
225:
222:
219:
218:
216:
215:
211:
208:
191:
174:
167:
164:
160:
154:
150:
146:
142:
135:
128:
116:
109:
108:
103:
99:
92:
91:
85:
80:
79:Original file
71:
67:
63:
59:
55:
49:
44:
38:
35:
33:
30:
28:
25:
23:
20:
18:
15:
806:
803:
738:
583:
580:File history
295:
285:
243:
237:
226:
220:
115:You can help
105:
77:
22:File history
821:Image title
813:Short title
474:copyrighted
244:share alike
238:attribution
137:Description
680:File usage
651:512 × 384
621:512 × 384
597:Dimensions
390:some value
27:File usage
594:Thumbnail
591:Date/Time
175:Licensing
800:Metadata
334:Captions
227:to remix
221:to share
212:license.
156:Own work
37:Metadata
777:ピタゴラス平均
608:current
603:Comment
375:creator
358:depicts
338:English
129:Summary
81:
841:Height
666:Cmglee
659:Cmglee
653:(3 KB)
629:Cmglee
623:(3 KB)
438:Cmglee
409:Cmglee
166:Cmglee
162:Author
152:Source
833:Width
844:100%
836:100%
600:User
314:true
311:true
305:GFDL
269:true
266:true
17:File
417:URL
435::
420::
405::
68:|
64:|
60:|
56:|
50:.
828:.
300:.
147:.
117:.
72:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
