tangency solution
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Singular solution — A singular solution ys ( x ) of an ordinary differential equation is a solution that is tangent to every solution from the family of general solutions. By tangent we mean that there is a point x where ys ( x ) = yc ( x ) and y s ( x ) = y c ( x ) … Wikipedia
Corner solution — A corner solution is a special solution to an agent s maximization problem in which the quantity of one of the arguments in the maximized function is zero. The more usual solution will lie in the non zero interior at the point of tangency between … Wikipedia
Problem of Apollonius — In Euclidean plane geometry, Apollonius problem is to construct circles that are tangent to three given circles in a plane (Figure 1); two circles are tangent if they touch at a single point. Apollonius of Perga (ca. 262 BC ndash; ca. 190 BC)… … Wikipedia
Special cases of Apollonius' problem — In Euclidean geometry, Apollonius problem is to construct all the circles that are tangent to three given circles. Limiting cases of Apollonius problem are those in which at least one of the given circles is a point or line, i.e., is a circle of… … Wikipedia
utility and value — ▪ economics Introduction in economics, the determination of the prices of goods and services. The modern industrial economy is characterized by a high degree of interdependence of its parts. The supplier of components or raw materials … Universalium
Tangential quadrilateral — An example of a tangential quadrilateral In Euclidean geometry, a tangential quadrilateral or circumscribed quadrilateral is a convex quadrilateral whose sides all lie tangent to a single circle inscribed within the quadrilateral. This circle is… … Wikipedia
Malfatti circles — In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of … Wikipedia
Tangent lines to circles — In Euclidean plane geometry, tangent lines to circles form the subject of several theorems, and play an important role in many geometrical constructions and proofs. Since the tangent line to a circle at a point P is perpendicular to the radius to … Wikipedia
Analytic geometry — Cartesian coordinates. Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties. This article focuses on the classical and elementary meaning … Wikipedia
Apollonius of Perga — Apollonius of Perga. Apollonius of Perga [Pergaeus] (Ancient Greek: Ἀπολλώνιος) (ca. 262 BC – ca. 190 BC) was a Greek geometer and astronomer noted for his writings on conic sections. His innovative methodology and terminology, especially in the… … Wikipedia
Transversality — in mathematics is a notion that describes how spaces can intersect; transversality can be seen as the opposite of tangency, and plays a role in general position. It formalizes the idea of a generic intersection in differential topology. It is… … Wikipedia
