Gauss–Lucas theorem

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Gauss–Lucas theorem

Quality:

Gauss–Lucas theorem - geometric relation between the roots of a polynomial and those of its derivative. Article "Gauss–Lucas theorem" in English Wikipedia has 15.5 points for quality (as of July 1, 2025). The article contains 2 references and 7 sections.

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

Since the creation of article "Gauss–Lucas theorem", its content was written by 46 registered users of English Wikipedia and edited by 195 registered Wikipedia users in all languages.

The article is cited 19 times in English Wikipedia and cited 150 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (English): #67129 in February 2007
  • Global: #88351 in March 2012

The highest popularity rank from 2008:

  • Local (English): #462281 in May 2021
  • Global: #628845 in May 2021

There are 15 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
1German (de)
Satz von Gauß-Lucas
32.4689
2Turkish (tr)
Gauss-Lucas teoremi
19.4242
3English (en)
Gauss–Lucas theorem
15.5242
4French (fr)
Théorème de Gauss-Lucas
15.5228
5Dutch (nl)
Stelling van Gauss-Lucas
14.8746
6Chinese (zh)
高斯-卢卡斯定理
13.0135
7Italian (it)
Teorema di Gauss-Lucas
11.566
8Spanish (es)
Teorema de Gauss-Lucas
10.4169
9Korean (ko)
가우스-뤼카 정리
9.1402
10Hebrew (he)
משפט גאוס-לוקאס
7.2334
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 "Gauss–Lucas theorem" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Gauss–Lucas theorem
177 954
2French (fr)
Théorème de Gauss-Lucas
54 938
3Spanish (es)
Teorema de Gauss-Lucas
24 130
4Russian (ru)
Теорема Гаусса — Люка
21 883
5Korean (ko)
가우스-뤼카 정리
11 613
6German (de)
Satz von Gauß-Lucas
6 726
7Hungarian (hu)
Gauss–Lucas-tétel
6 446
8Hebrew (he)
משפט גאוס-לוקאס
5 854
9Polish (pl)
Twierdzenie Gaussa-Lucasa
5 286
10Chinese (zh)
高斯-卢卡斯定理
3 598
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 "Gauss–Lucas theorem" in June 2025
#LanguagePopularity awardRelative popularity
1English (en)
Gauss–Lucas theorem
743
2French (fr)
Théorème de Gauss-Lucas
185
3Spanish (es)
Teorema de Gauss-Lucas
53
4Russian (ru)
Теорема Гаусса — Люка
51
5Chinese (zh)
高斯-卢卡斯定理
38
6German (de)
Satz von Gauß-Lucas
35
7Korean (ko)
가우스-뤼카 정리
33
8Italian (it)
Teorema di Gauss-Lucas
24
9Polish (pl)
Twierdzenie Gaussa-Lucasa
21
10Hebrew (he)
משפט גאוס-לוקאס
15
More...

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

The highest AI

Language versions of the article "Gauss–Lucas theorem" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Gauss–Lucas theorem
46
2French (fr)
Théorème de Gauss-Lucas
35
3German (de)
Satz von Gauß-Lucas
19
4Russian (ru)
Теорема Гаусса — Люка
19
5Hebrew (he)
משפט גאוס-לוקאס
13
6Italian (it)
Teorema di Gauss-Lucas
11
7Hungarian (hu)
Gauss–Lucas-tétel
10
8Polish (pl)
Twierdzenie Gaussa-Lucasa
9
9Spanish (es)
Teorema de Gauss-Lucas
7
10Dutch (nl)
Stelling van Gauss-Lucas
7
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 "Gauss–Lucas theorem" with the highest AI in June 2025
#LanguageAI awardRelative AI
1Arabic (ar)
مبرهنة غاوس–لوكاس
0
2German (de)
Satz von Gauß-Lucas
0
3English (en)
Gauss–Lucas theorem
0
4Spanish (es)
Teorema de Gauss-Lucas
0
5French (fr)
Théorème de Gauss-Lucas
0
6Hebrew (he)
משפט גאוס-לוקאס
0
7Hungarian (hu)
Gauss–Lucas-tétel
0
8Italian (it)
Teorema di Gauss-Lucas
0
9Korean (ko)
가우스-뤼카 정리
0
10Dutch (nl)
Stelling van Gauss-Lucas
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 "Gauss–Lucas theorem" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1French (fr)
Théorème de Gauss-Lucas
73
2English (en)
Gauss–Lucas theorem
19
3Chinese (zh)
高斯-卢卡斯定理
16
4Russian (ru)
Теорема Гаусса — Люка
6
5German (de)
Satz von Gauß-Lucas
5
6Spanish (es)
Teorema de Gauss-Lucas
5
7Korean (ko)
가우스-뤼카 정리
5
8Arabic (ar)
مبرهنة غاوس–لوكاس
4
9Hungarian (hu)
Gauss–Lucas-tétel
4
10Italian (it)
Teorema di Gauss-Lucas
4
More...

Scores

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

Quality measures

Interwikis

#LanguageValue
arArabic
مبرهنة غاوس–لوكاس
deGerman
Satz von Gauß-Lucas
enEnglish
Gauss–Lucas theorem
esSpanish
Teorema de Gauss-Lucas
frFrench
Théorème de Gauss-Lucas
heHebrew
משפט גאוס-לוקאס
huHungarian
Gauss–Lucas-tétel
itItalian
Teorema di Gauss-Lucas
koKorean
가우스-뤼카 정리
nlDutch
Stelling van Gauss-Lucas
plPolish
Twierdzenie Gaussa-Lucasa
ruRussian
Теорема Гаусса — Люка
trTurkish
Gauss-Lucas teoremi
ukUkrainian
Теорема Гаусса — Люка
zhChinese
高斯-卢卡斯定理

Popularity rank trends

Best Rank English:
#462281
05.2021
Global:
#628845
05.2021

AI rank trends

Best Rank English:
#67129
02.2007
Global:
#88351
03.2012

Languages comparison

Important global interconnections (July 2024 – June 2025)

Wikipedia readers most often find their way to information on Gauss–Lucas theorem from Wikipedia articles about Vietas formulas, Rolles theorem, Descartes rule of signs, Lucas theorem and Rational root theorem. Whereas reading the article about Gauss–Lucas theorem people most often go to Wikipedia articles on Mardens theorem, Convex hull, Rolles theorem, Sendovs conjecture and Logarithmic derivative.

Cumulative results of quality and popularity of the Wikipedia article

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

News from 12 August 2025

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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