Convexity is a term used in geometry to describe the curvature of a shape. The spelling of this word is based on the IPA phonetic transcription [kənˈvɛksəti], which indicates that the first syllable is pronounced with a short "u" sound, as in "cup," followed by a stressed "e" sound, as in "ever." The second syllable is pronounced with a schwa sound, followed by a stressed "s" and a soft "t" at the end. Despite its unusual spelling, convexity remains an essential concept in mathematics and physics.
Convexity is a concept that refers to the curve or shape of a surface or object. In mathematics, it specifically describes the property of being curved outward or having a surface that is bulging outwards. A convex shape can be thought of as one that does not have any indentations or concave sections. Instead, it has a smooth, outwardly curving surface.
Convexity plays a vital role in various fields such as geometry, optics, economics, and physics. In geometry, it is used to classify shapes and determine their properties. In optics, convex lenses are utilized to converge light rays and create focused images. Economically, the concept of convexity is employed to analyze the relationship between changes in interest rates and bond prices. In physics, convex mirrors are implemented to reflect light and create wider fields of view.
To determine whether a shape or object is convex, one can employ a simple test. If a straight line segment connecting any two points on the surface lies within or on the object, then the object is convex. On the other hand, if the line segment intersects the surface or is outside of it, the object is not convex.
Overall, convexity is a fundamental concept that pertains to the outward curvature of an object or surface. Its applicability reaches a broad range of fields and its understanding is crucial for grasping various mathematical, scientific, and economic principles.
A roundness of surface.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
The word "convexity" originated from the Latin word "convexus", which means "arched" or "rounded". It is derived from the prefix "con-" meaning "together" and "vexus" meaning "bending". The term was initially used in mathematics to describe a curve or surface that bulges outward, creating a rounded shape. Over time, the term expanded to be used in various fields to denote the quality or property of being convex.