Convexity Meaning: Definition, Examples, and Translations
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convexity
[kษnหvษksษชti ]
Definition
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
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Origin of 'convexity'
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.