Convexity: meaning, definitions and examples

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convexity

 

[ kษ™nหˆvษ›ksษชti ]

Noun
Context #1 | Noun

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

bulge, curvature, roundness

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:

๐Ÿ‡ต๐Ÿ‡น convexidade

๐Ÿ‡ฎ๐Ÿ‡ณ เค‰เคคเฅเคฅเคฒเคคเคพ

๐Ÿ‡ฉ๐Ÿ‡ช Konvexitรคt

๐Ÿ‡ฎ๐Ÿ‡ฉ konveksitas

๐Ÿ‡บ๐Ÿ‡ฆ ะฒะธะฟัƒะบะปั–ัั‚ัŒ

๐Ÿ‡ต๐Ÿ‡ฑ wypukล‚oล›ฤ‡

๐Ÿ‡ฏ๐Ÿ‡ต ๅ‡ธๆ€ง (ใจใคใ›ใ„)

๐Ÿ‡ซ๐Ÿ‡ท convexitรฉ

๐Ÿ‡ช๐Ÿ‡ธ convexidad

๐Ÿ‡น๐Ÿ‡ท konvekslik

๐Ÿ‡ฐ๐Ÿ‡ท ๋ณผ๋ก์„ฑ

๐Ÿ‡ธ๐Ÿ‡ฆ ุชุญุฏุจ

๐Ÿ‡จ๐Ÿ‡ฟ konvexnost

๐Ÿ‡ธ๐Ÿ‡ฐ konvexnosลฅ

๐Ÿ‡จ๐Ÿ‡ณ ๅ‡ธๆ€ง (tลซxรฌng)

๐Ÿ‡ธ๐Ÿ‡ฎ konveksnost

๐Ÿ‡ฎ๐Ÿ‡ธ hvolf

๐Ÿ‡ฐ๐Ÿ‡ฟ ะดำฉาฃะตัะปั–ะบ

๐Ÿ‡ฌ๐Ÿ‡ช แƒ’แƒแƒ›แƒแƒ™แƒ•แƒ”แƒ—แƒ˜แƒšแƒแƒ‘แƒ

๐Ÿ‡ฆ๐Ÿ‡ฟ konvekslik

๐Ÿ‡ฒ๐Ÿ‡ฝ convexidad

Word origin

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.

Word Frequency Rank

With rank #19,768, this word belongs to specialized vocabulary. While not common in everyday speech, it enriches your ability to express complex ideas.