What does triangle inequality mean?
Definitions for triangle inequality
tri·an·gle inequal·i·ty
This dictionary definitions page includes all the possible meanings, example usage and translations of the word triangle inequality.
Wiktionary
triangle inequalitynoun
The inequality that states that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitudes of the vectors, or any equivalent inequality in other spaces.
Wikidata
Triangle inequality
In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. In Euclidean geometry and some other geometries the triangle inequality is a theorem about distances. In Euclidean geometry, for right triangles it is a consequence of the Pythagorean theorem, and for general triangles a consequence of the law of cosines, although it may be proven without these theorems. The inequality can be viewed intuitively in either R² or R³. The figure at the right shows three examples beginning with clear inequality and approaching equality. In the Euclidean case, equality occurs only if the triangle has a 180° angle and two 0° angles, making the three vertices collinear, as shown in the bottom example. Thus, in Euclidean geometry, the shortest distance between two points is a straight line. In spherical geometry, the shortest distance between two points is an arc of a great circle, but the triangle inequality holds provided the restriction is made that the distance between two points on a sphere is the length of a minor spherical line segment with those endpoints.p
Numerology
Chaldean Numerology
The numerical value of triangle inequality in Chaldean Numerology is: 7
Pythagorean Numerology
The numerical value of triangle inequality in Pythagorean Numerology is: 3
Translations for triangle inequality
From our Multilingual Translation Dictionary
Get even more translations for triangle inequality »
Translation
Find a translation for the triangle inequality definition in other languages:
Select another language:
- - Select -
- 简体中文 (Chinese - Simplified)
- 繁體中文 (Chinese - Traditional)
- Español (Spanish)
- Esperanto (Esperanto)
- 日本語 (Japanese)
- Português (Portuguese)
- Deutsch (German)
- العربية (Arabic)
- Français (French)
- Русский (Russian)
- ಕನ್ನಡ (Kannada)
- 한국어 (Korean)
- עברית (Hebrew)
- Gaeilge (Irish)
- Українська (Ukrainian)
- اردو (Urdu)
- Magyar (Hungarian)
- मानक हिन्दी (Hindi)
- Indonesia (Indonesian)
- Italiano (Italian)
- தமிழ் (Tamil)
- Türkçe (Turkish)
- తెలుగు (Telugu)
- ภาษาไทย (Thai)
- Tiếng Việt (Vietnamese)
- Čeština (Czech)
- Polski (Polish)
- Bahasa Indonesia (Indonesian)
- Românește (Romanian)
- Nederlands (Dutch)
- Ελληνικά (Greek)
- Latinum (Latin)
- Svenska (Swedish)
- Dansk (Danish)
- Suomi (Finnish)
- فارسی (Persian)
- ייִדיש (Yiddish)
- հայերեն (Armenian)
- Norsk (Norwegian)
- English (English)
Word of the Day
Would you like us to send you a FREE new word definition delivered to your inbox daily?
Citation
Use the citation below to add this definition to your bibliography:
Style:MLAChicagoAPA
"triangle inequality." Definitions.net. STANDS4 LLC, 2025. Web. 15 Jan. 2025. <https://www.definitions.net/definition/triangle+inequality>.
Discuss these triangle inequality definitions with the community:
Report Comment
We're doing our best to make sure our content is useful, accurate and safe.
If by any chance you spot an inappropriate comment while navigating through our website please use this form to let us know, and we'll take care of it shortly.
Attachment
You need to be logged in to favorite.
Log In