Satz von Sard

de

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Satz von Sard

Quality:

Sard's theorem - theorem that the set of the critical values of a smooth function has measure zero. Article “Satz von Sard” in German Wikipedia has 7.8 points for quality (as of July 1, 2025). The article contains 1 references and 2 sections.

This article has the best quality in Russian Wikipedia. However, the most popular language version of this article is English.

In June 2025 the article “Satz von Sard” was edited by 1 authors in German Wikipedia and written by 1 authors in all languages.

Since the creation of article “Satz von Sard”, its content was written by 32 registered users of German Wikipedia and edited by 169 registered Wikipedia users in all languages.

The article is cited 11 times in German Wikipedia and cited 399 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (German): #6363 in March 2005
  • Global: #35915 in March 2005

The highest popularity rank from 2008:

  • Local (German): #299289 in November 2013
  • Global: #540123 in December 2014

There are 12 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2025 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1Russian (ru)
Теорема Сарда
28.1285
2Turkish (tr)
Sard teoremi
23.2307
3Dutch (nl)
Stelling van Sard
21.6271
4French (fr)
Théorème de Sard
19.4968
5English (en)
Sard's theorem
18.5758
6Korean (ko)
사드의 정리
17.0469
7Galician (gl)
Teorema de Sard
14.5003
8German (de)
Satz von Sard
7.8333
9Spanish (es)
Teorema de Sard
3.8751
10Ukrainian (uk)
Теорема Сарда
3.4339
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Satz von Sard" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Sard's theorem
267 127
2French (fr)
Théorème de Sard
37 182
3German (de)
Satz von Sard
30 398
4Russian (ru)
Теорема Сарда
24 685
5Japanese (ja)
サードの定理
18 634
6Spanish (es)
Teorema de Sard
11 058
7Korean (ko)
사드의 정리
7 132
8Ukrainian (uk)
Теорема Сарда
3 687
9Italian (it)
Teorema di Sard
2 545
10Dutch (nl)
Stelling van Sard
452
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2025

The most popular language versions of the article "Satz von Sard" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Sard's theorem
1 632
2Russian (ru)
Теорема Сарда
159
3Japanese (ja)
サードの定理
144
4German (de)
Satz von Sard
142
5French (fr)
Théorème de Sard
119
6Italian (it)
Teorema di Sard
62
7Spanish (es)
Teorema de Sard
50
8Turkish (tr)
Sard teoremi
20
9Galician (gl)
Teorema de Sard
11
10Korean (ko)
사드의 정리
11
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Satz von Sard" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Sard's theorem
47
2French (fr)
Théorème de Sard
34
3German (de)
Satz von Sard
32
4Russian (ru)
Теорема Сарда
18
5Italian (it)
Teorema di Sard
8
6Japanese (ja)
サードの定理
8
7Ukrainian (uk)
Теорема Сарда
7
8Spanish (es)
Teorema de Sard
5
9Korean (ko)
사드의 정리
4
10Galician (gl)
Teorema de Sard
2
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2025

Language versions of the article "Satz von Sard" with the highest AI in June 2025
#LanguageAI awardRelative AI
1German (de)
Satz von Sard
1
2English (en)
Sard's theorem
0
3Spanish (es)
Teorema de Sard
0
4French (fr)
Théorème de Sard
0
5Galician (gl)
Teorema de Sard
0
6Italian (it)
Teorema di Sard
0
7Japanese (ja)
サードの定理
0
8Korean (ko)
사드의 정리
0
9Dutch (nl)
Stelling van Sard
0
10Russian (ru)
Теорема Сарда
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Satz von Sard" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Sard's theorem
329
2French (fr)
Théorème de Sard
14
3German (de)
Satz von Sard
11
4Russian (ru)
Теорема Сарда
11
5Japanese (ja)
サードの定理
8
6Turkish (tr)
Sard teoremi
7
7Korean (ko)
사드의 정리
6
8Dutch (nl)
Stelling van Sard
4
9Ukrainian (uk)
Теорема Сарда
4
10Spanish (es)
Teorema de Sard
3
More...

Scores

Estimated value for Wikipedia:
German:
Global:
Popularity in June 2025:
German:
Global:
Popularity in all years:
German:
Global:
Authors in June 2025:
German:
Global:
Registered authors in all years:
German:
Global:
Citations:
German:
Global:

Quality measures

Interwikis

#LanguageValue
deGerman
Satz von Sard
enEnglish
Sard's theorem
esSpanish
Teorema de Sard
frFrench
Théorème de Sard
glGalician
Teorema de Sard
itItalian
Teorema di Sard
jaJapanese
サードの定理
koKorean
사드의 정리
nlDutch
Stelling van Sard
ruRussian
Теорема Сарда
trTurkish
Sard teoremi
ukUkrainian
Теорема Сарда

Popularity rank trends

Best Rank German:
#299289
11.2013
Global:
#540123
12.2014

AI rank trends

Best Rank German:
#6363
03.2005
Global:
#35915
03.2005

Local AI rank history

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Sard's theorem from Wikipedia articles about Coarea formula, Integration by substitution, Morse theory, Evgenii Landis and Homotopy group of a sphere. Whereas reading the article about Sard's theorem people most often go to Wikipedia articles on Critical point, Arthur Sard, Generic property, Anthony Morse and Lebesgue measure.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 28 January 2026

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In German Wikipedia the most popular articles on that day were: Whitney Houston, Fall Gil Ofarim, Gil Ofarim, Handball-Europameisterschaft der Männer 2026, Der neue Freund, Tova Friedman, Sven Schulze (Politiker, 1979), Liste der größten Auslegerbrücken, Bobbi Kristina Brown, Patricia Aulitzky.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 44 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2025. When calculating current popularity and AI of articles data from June 2025 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2025... More information