For-a-convex-shape-in-the-plane-the-diameter-is

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For and convex

For example, a solid cube is convex, but anything that is hollow or has a dent in it, for example, a crescent shape, is not convex.

For the preceding property of unions of non-decreasing sequences of convex sets, the restriction to nested sets is important: The union of two convex sets need not be convex.

For a set of scattered points in the plane, the diameter of the points is the same as the diameter of their convex hull.

For example the central convex pentagon in the center of a pentagram has density 2.

For instance, when X is a bounded subset of the plane, the convex hull may be visualized as the shape formed by a rubber band stretched around X.

For each choice of coefficients, the resulting convex combination is a point in the convex hull, and the whole convex hull can be formed by choosing coefficients in all possible ways.

For points in two and three dimensions, output-sensitive algorithms are known that compute the convex hull in time O ( n log h ).

For dimensions d higher than 3, the time for computing the convex hull is, matching the worst-case output complexity of the problem.

* For a differentiable Lipschitz map ƒ: U → R m the inequality holds for the best Lipschitz constant of f, and it turns out to be an equality if the domain U is convex.

For n = 2 the theorem claims that a convex figure in the plane symmetric about the origin and with area greater than 4 encloses at least one lattice point in addition to the origin.

For instance, if we abstract sets of couples ( x, y ) of real numbers by enclosing convex polyhedra, there is no optimal abstraction to the disc defined by x 2 + y 2 ≤ 1.

For a converging lens ( for example a convex lens ), the focal length is positive, and is the distance at which a beam of collimated light will be focused to a single spot.

For any convex, real-valued function φ such that

For a convex polygon ( such as a triangle ), a surface normal can be calculated as the vector cross product of two ( non-parallel ) edges of the polygon.

For convex two-dimensional shapes, the centroid can be found by balancing the shape on a smaller shape, such as the top of a narrow cylinder.

For instance, a ( strictly ) convex function on an open set has no more than one minimum.

For a twice-differentiable function f, if the second derivative, f ′′( x ), is positive ( or, if the acceleration is positive ), then the graph is convex ; if f ′′( x ) is negative, then the graph is concave.

For a real convex function, numbers x 1 , x 2 , ..., x n in its domain, and positive weights a i , Jensen's inequality can be stated as:

For example, when the space of functions is a Banach space, the functional derivative becomes known as the Fréchet derivative, while one uses the Gâteaux derivative on more general locally convex spaces.

For and shape

For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area.

For a long time, scholars believed that the alphorn had been derived from the Roman-Etruscan lituus, because of their resemblance in shape, and because of the word liti, meaning Alphorn in the dialect of Obwalden.

For example, the Arabic letters transliterated as and have the same basic shape, but has one dot below,, and has two dots above,.

For example, a candle's flame takes the shape of a sphere.

For an axially loaded straight column with any end support conditions, the equation of static equilibrium, in the form of a differential equation, can be solved for the deflected shape and critical load of the column.

For example, the expanding profile of a laser beam, the beam shape of a radar antenna and the field of view of an ultrasonic transducer can all be analysed using diffraction equations.

For example, the name Delphi and its associated deity, Apollon Delphinios, are explained in the Homeric Hymn which tells of how Apollo carried Cretans over the sea in the shape of a dolphin () to make them his priests.

For this reason, the furlong was once also called an acre's length, though of course in modern usage an area of one acre can be any shape.

: For this vice deceives with the appearance and shape of a virtue,

For example, this map of Europe has been distorted to show population distribution, while the rough shape of the continent is still discernable.

For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism.

For Hydrology, Glaciology and Climatology as a boost investigated as studying geographic factors shape the landscape and affect the cycle.

For an nk-gon with k-fold rotational symmetry ( C k ), there are degrees of freedom for the shape.

For sibilants, there are additional complications involving tongue shape ; see the article on sibilants for a chart of possible articulations.

For example, in Chinese, a pun may be based on a similarity in shape of the written character, despite a complete lack of phonetic similarity in the words punned upon.

For instance, both wood and fiberglass hulls are allowed in the Albacore, Wayfarer, and Fireball classes, but the hull shape, weight, and sail area are tightly constrained.

For example, targets that formerly resembled humans or animals in their shape and size have are now a circular shape in order to avoid associating the sport with any form of violence.

For instance, a side of the Koch snowflake is both symmetrical and scale-invariant ; it can be continually magnified 3x without changing shape.

For all that, we do know what a square circle would be: a shape that is both square and circular.

For centuries, viola makers have experimented with the size and shape of the viola, often adjusting the proportions or shape to make a lighter instrument with shorter string lengths, but which still has a large enough sound box to create an unmistakable ' viola sound '.

For example, the shape of weather phenomena such as hurricanes are emergent structures.

For and plane

For if it did, the plane of L and l' would contain two generators of Af, which is impossible.

For the lines of any plane, **yp, meeting Q in a conic C, are transformed into the congruence of secants of the curve C' into which C is transformed in the point involution on Q.

For if such were the case, either the plane of the two lines would meet **zg in more than K points or, alternatively, the order of the image regulus of the pencil determined by the two lines would be too high.

For any pencil in a plane containing a Af-fold secant of **zg has an image regulus which meets the plane of the pencil in Af lines, namely the images of the lines of the pencil which pass through the intersection of **zg and the multiple secant, plus an additional component to account for the intersections of the images of the general lines of the pencil.

`` For three days now a German reconnaissance plane has been over the city taking pictures.

For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal.

For example, using Cartesian coordinates on the plane, the distance between two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is defined by the formula

For an object swinging around on the end of a rope in a horizontal plane, the centripetal force on the object is supplied by the tension of the rope.

For example, a point on the unit circle in the plane can be specified by two Cartesian coordinates, but one can make do with a single coordinate ( the polar coordinate angle ), so the circle is 1-dimensional even though it exists in the 2-dimensional plane.

For example, there are two fundamental operations on the plane.

For current cryptographic purposes, an elliptic curve is a plane curve which consists of the points satisfying the equation

For all pictures the magnetic quantum number m has been set to 0, and the cross-sectional plane is the xz-plane ( z is the vertical axis ).

For example an F 2 fold, with an S 2 axial plane foliation would be the result of a D 2 deformation.

For example, the sphere and torus are orientable, while the real projective plane is not ( because deleting a point or disk from the real projective plane produces the Möbius strip ).

For example, in the first Tomb Raider game manual, Lara Croft is said to have survived a plane crash in the Himalayas at the age of twenty one, and was later disowned by her parents, who are still living.

For example, if the given manifold is a 2-sphere, one can picture the tangent space at a point as the plane which touches the sphere at that point and is perpendicular to the sphere's radius through the point.

For N cities randomly distributed on a plane, the algorithm on average yields a path 25 % longer than the shortest possible path.

For example, during the development of the SR-71 Blackbird spy plane, Lockheed engineers at the " Skunk Works " under Clarence " Kelly " Johnson used unobtainium as a dysphemism for titanium.

For example, estimates of position on a plane may have less certainty in one direction than another.

For the plane wave ( left ), the wave-like probability distribution ψ the particle is likely to be found anywhere, due to the periodicity of the wave.

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