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triangle inequality theorem

inequality of the form |x + y| ≤ |x| + |y|
Class type of: inequality, subadditivity Q208216

Facts

7 properties
Instance of
theorem
Subclass of
inequality, subadditivity
Defining formula
z \leq x + y
In defining formula
x, y, z
Maintained by WikiProject
WikiProject Mathematics[6]
Statement describes
triangle[4]
Studied by
Euclidean geometry[5]
🏷️ Also known as
en triangle inequality theorem ar لامساواة المثلث ar متباينة المثلث ar لامساواه المثلث cs trojúhelníková nerovnost da Trekantsuligheden da Trekantuligheden de Dreiecksungleichung el Τριγωνική ανισότητα es desigualdad triangular es desigualdad del triángulo fa نابرابری مثلثی fa نامساوی مثلث fi kolmioepäyhtälö fr inégalité triangulaire he אי שוויון המשולש he אי-שוויון המשולש he אי שיוויון המשולש he אי-שיוויון המשולש he אשמ"ש
🔖 Identifiers · 16
OpenAlex ID
C182964748
Brilliant Wiki ID
triangle-inequality
Dictionary of Algorithms and Data Structures ID
trianglnqlty
Digital Library of Mathematical Functions ID
1.2.E52
Encyclopædia Britannica Online ID
topic/triangle-inequality
Freebase ID
/m/0f3hj
Great Norwegian Encyclopedia ID
trekantulikheten
Lex ID
trekantsuligheden
MathWorld ID
TriangleInequality
Microsoft Academic ID (discontinued)
182964748
NL CR AUT ID
ph602139
NLab ID
triangle inequality
Show all 16 identifiers +4
ProofWiki ID
Triangle_Inequality
ScienceDirect topic ID
computer-science/triangle-inequality, engineering/triangle-inequality, mathematics/triangle-inequality
Treccani's Enciclopedia della Matematica ID
disuguaglianza-triangolare
Vikidia article ID
fr:Inégalité_triangulaire

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🔗 Connections
← Has characteristic 2
triangle, absolute value
Instance of 1
theorem
Maintained by WikiProject 1
WikiProject Mathematics
Statement describes 1
triangle
Studied by 1
Euclidean geometry
Subclass of 1
inequality
Subtypes 1
Cauchy–Schwarz inequality
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Summary

triangle inequality theorem is a theorem[1]. It is a type of inequality[2] and subadditivity[3].

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [2] ↑ . wikidata.org.
  2. [3] ↑ . wikidata.org.
  3. [4] ↑ . wikidata.org.
  4. [5] ↑ . wikidata.org.
  5. [6] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

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Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). triangle inequality theorem. Retrieved November 2, 2026, from https://4ort.xyz/entity/triangle-inequality-theorem
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BibTeX @misc{4ortxyz_triangle-inequality-theorem_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{triangle inequality theorem}}, year = {2026}, url = {https://4ort.xyz/entity/triangle-inequality-theorem}, note = {Accessed: 2026-11-02}}
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Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 2d ago · Artoria2e5 · 2026-11-02 view diff on Wikidata ↗
    Statement describes → triangle
    Wikipedia languages → ['als', 'ar', 'be', 'bg', 'ca', 'ckb', 'commons', 'cs', 'cv', 'da', 'de', 'el',
    Instance of → theorem
    Studied by → Euclidean geometry
    + 6 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ Subclass of: subadditivity"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.