Arc lengthArc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. A rectifiable curve has a finite number of segments in its rectification (so the curve has a finite length). If a curve can be parameterized as an injective and continuously differentiable function (i.e., the derivative is a continuous function) , then the curve is rectifiable (i.
Public-domain softwarePublic-domain software is software that has been placed in the public domain, in other words, software for which there is absolutely no ownership such as copyright, trademark, or patent. Software in the public domain can be modified, distributed, or sold even without any attribution by anyone; this is unlike the common case of software under exclusive copyright, where licenses grant limited usage rights.
Isolated pointIn mathematics, a point x is called an isolated point of a subset S (in a topological space X) if x is an element of S and there exists a neighborhood of x that does not contain any other points of S. This is equivalent to saying that the singleton {x} is an open set in the topological space S (considered as a subspace of X). Another equivalent formulation is: an element x of S is an isolated point of S if and only if it is not a limit point of S.
Jordan curve theoremIn topology, the Jordan curve theorem asserts that every Jordan curve (a plane simple closed curve) divides the plane into an "interior" region bounded by the curve and an "exterior" region containing all of the nearby and far away exterior points. Every continuous path connecting a point of one region to a point of the other intersects with the curve somewhere. While the theorem seems intuitively obvious, it takes some ingenuity to prove it by elementary means.
Precision marketingPrecision marketing is a marketing technique that suggests successful marketing is to retain, cross-sell, and upsell existing customers. Precision marketing emphasizes relevance as part of the technique. To achieve Precision Marketing, marketers solicit personal preferences directly from recipients. They also collect and analyze behavioral and transactional data. The development of precision marketing coincides with the development of market segmentation, advancements in technology and the customer's reaction to the proliferation of mass marketing.
