In statistics, quartiles are a type of quantiles which divide the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three quartiles, resulting in four data divisions, are as follows:
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset.
Mauritius is an island off Africa's southeast coast located in the Indian Ocean, east of Madagascar. It is geologically located within the Somali Plate.
The Northwest Angle, known simply as the Angle by locals, and coextensive with Angle Township, is a pene-exclave of northern Lake of the Woods County, Minnesota. Excluding surveying errors, it is the only place in the contiguous United States north of the 49th parallel, which forms the border between the U.S. and Canada from the Northwest Angle westward to the Strait of Georgia. The land area of the Angle is separated from the rest of Minnesota by Lake of the Woods, but shares a land border with Canada. It is one of six non-island locations in the 48 contiguous states that are practical exclaves of the United States. Oak Island, Angle Inlet and Penasse are in the Northwest Angle.
Convex or convexity may refer to:
In mathematics, an extreme point of a convex set in a real or complex vector space is a point in that does not lie in any open line segment joining two points of In linear programming problems, an extreme point is also called vertex or corner point of
This article lists extreme locations on Earth that hold geographical records or are otherwise known for their geophysical or meteorological superlatives. All of these locations are Earth-wide extremes; extremes of individual continents or countries are not listed.
This is a list of the extreme points of Europe: the geographical points that are higher or farther north, south, east or west than any other location in Europe. Some of these positions are open to debate, as the definition of Europe is diverse.
This is a list of the extreme points of Asia, the points that are farther north, south, east or west than any other location on the continent.
The extreme points of Norway include the coordinates that are farther north, south, east or west than any other location in Norway; and the highest and the lowest altitudes in the country. The northernmost point is Rossøya on Svalbard, the southernmost is Pysen in Lindesnes Municipality, the easternmost is Kræmerpynten on Svalbard, and the westernmost is Hoybergodden on Jan Mayen. The highest peak is Galdhøpiggen, standing at 2,469 m (8,100 ft) above mean sea level, while the lowest elevation is sea level at the coast.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts identify a convex polytope with its boundary.
Tarski's axioms are an axiom system for Euclidean geometry, specifically for that portion of Euclidean geometry that is formulable in first-order logic with identity. As such, it does not require an underlying set theory. The only primitive objects of the system are "points" and the only primitive predicates are "betweenness" and "congruence". The system contains infinitely many axioms.
In the mathematical theory of functional analysis, the Krein–Milman theorem is a proposition about compact convex sets in locally convex topological vector spaces (TVSs).
In mathematics, Choquet theory, named after Gustave Choquet, is an area of functional analysis and convex analysis concerned with measures which have support on the extreme points of a convex set C. Roughly speaking, every vector of C should appear as a weighted average of extreme points, a concept made more precise by generalizing the notion of weighted average from a convex combination to an integral taken over the set E of extreme points. Here C is a subset of a real vector space V, and the main thrust of the theory is to treat the cases where V is an infinite-dimensional topological vector space along lines similar to the finite-dimensional case. The main concerns of Gustave Choquet were in potential theory. Choquet theory has become a general paradigm, particularly for treating convex cones as determined by their extreme rays, and so for many different notions of positivity in mathematics.
Afro-Eurasia is a landmass comprising the continents of Africa, Europe, and Asia. The terms are compound words of the names of its constituent parts. Afro-Eurasia has also been called the "Old World", in contrast to the "New World" referring to the Americas.
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