Convexity: meaning, definitions and examples
๐
convexity
[ kษnหvษksษชti ]
mathematics field
Convexity refers to the property of a set or a function where a line segment connecting any two points within the set remains entirely within the set. In mathematical terms, a function is said to be convex if its second derivative is greater than or equal to zero. This concept is widely used in optimization and economic theory.
Synonyms
Examples of usage
- The convexity of the function makes it easier to find the minimum.
- In economics, the convexity of the utility function indicates preferences.
- The convexity of this shape allows for better structural integrity.
Translations
Translations of the word "convexity" in other languages:
๐ต๐น convexidade
๐ฎ๐ณ เคเคคเฅเคฅเคฒเคคเคพ
๐ฉ๐ช Konvexitรคt
๐ฎ๐ฉ konveksitas
๐บ๐ฆ ะฒะธะฟัะบะปัััั
๐ต๐ฑ wypukลoลฤ
๐ฏ๐ต ๅธๆง (ใจใคใใ)
๐ซ๐ท convexitรฉ
๐ช๐ธ convexidad
๐น๐ท konvekslik
๐ฐ๐ท ๋ณผ๋ก์ฑ
๐ธ๐ฆ ุชุญุฏุจ
๐จ๐ฟ konvexnost
๐ธ๐ฐ konvexnosลฅ
๐จ๐ณ ๅธๆง (tลซxรฌng)
๐ธ๐ฎ konveksnost
๐ฎ๐ธ hvolf
๐ฐ๐ฟ ะดำฉาฃะตัะปัะบ
๐ฌ๐ช แแแแแแแแแแแแแ
๐ฆ๐ฟ konvekslik
๐ฒ๐ฝ convexidad
Etymology
The term 'convexity' is derived from the Latin word 'convexus,' which means 'vaulted' or 'arched.' In geometry, the concept has roots that go back to ancient Greek mathematics, where the properties of curves were studied. The modern usage of 'convexity' in mathematical analysis became prominent in the 19th century as the study of calculus and topology expanded. Over time, the notion of convex sets and functions has gained significance in various fields such as economics, statistics, and optimization, illustrating the relationship between geometric shapes and analytical properties.