convex geometry definition
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Polygon In elementary geometry, a polygon /ˈpɒlɪɡɒn/ is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. These segments are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of the polygon is sometimes called its body. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon. A polygon is a 2-dimensional example of the more general polytope in any number of dimensions. The basic geometrical notion of a polygon has been adapted in various ways to suit particular purposes.
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- Opposite of concave . A geometric shape is convex if all its edges point outwards. That is no part of it curves or faces inwards. If a shape is convex, a line segment drawn between any two points on the shape will always lie inside the shape. The figure above is a convex pentagon. No part of it is caved in and any line segment, such as the red one shown, linking two points on it always lies inside the shape. See also Concave definition.
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Polygon 1 Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. 2  As a consequence, all its interior angles are less than 180°. 3  Equivalently, any line segment with endpoints on the boundary passes through only interior points between its endpoints.
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- Quick Answer. Convex mirrors work by reflecting parallel rays of light as if they all emanated from a single point somewhere behind the mirror. The distance between the actual surface of the mirror and this point depends on the level of curvature, with greater curvature resulting in lesser distance.
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Polyhedron A polyhedron has been defined as a set of points in real affine (or Euclidean) space of any dimension n that has flat sides. It may alternatively be defined as the union of a finite number of convex polyhedra, where a convex polyhedron is any point set that is the intersection of a finite number of half-spaces.
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What is a convex quadrilateral? A convex quadrilateral is a four-sided figure with interior angles of less than 180 degrees each and both of its diagonals contained within the shape. A diagonal is a line drawn from one angle to an opposite angle, and the two diagonals intersect at one point.
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Polyhedron A common and somewhat naive definition of a polyhedron is that it is a solid whose boundary can be covered by finitely many planes or that it is a solid formed as the union of finitely many convex polyhedra.
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convex 1. curving or bulging outwards. 2. (General Physics) physics having one or two surfaces curved or ground in the shape of a section of the exterior of a sphere, paraboloid, ellipsoid, etc: a convex lens. 3. (Mathematics) maths (of a polygon) containing no interior angle greater than 180°.
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- Geometry definition, the branch of mathematics that deals with the deduction of the properties, measurement, and relationships of points, lines, angles, and figures in space from their defining conditions by means of certain assumed properties of space. See more.
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convex curved or bowed outward like the outside of a bowl or sphere or circle Whewell Drops of water naturally form themselves into figures with a convex surface. (mathematics, not comparable, of a set) arranged such that for any two points in the set, a straight line between the two points is contained within the set.
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- A convex quadrilateral with one pair of parallel sides. Theorems: Two adjacent angles of a convex quadrilateral are supplementary iff it is a trapezoid. The diagonals cut each other in proportion of the lengths of the parallel sides.
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Scientific Revolution & Enlightenment Review Thinkers of the Enlightenment; Wanted to educate the socially elite, but not the masses; were not allowed to openly criticize church or state, so used satire and double-meaning in their writings to avoid being banned; Salons held by wealthy women also kept philosophes safe; They considered themselves part of an intellectual community, and wrote back ...
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GEOMETRY Noun. 1. analytic geometry-the use of algebra to study geometric properties; operates on symbols defined in a coordinate system. analytical geometry, coordinate geometry. math, mathematics, maths-a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement.
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- from The Century Dictionary and Cyclopedia. Curved, as a line or surface, in the manner of a circle or sphere when viewed from some point without it; curved away from the point of view; hence, bounded by such a line or surface: as, a convex mirror.
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geometry a. any branch of geometry using a particular notation or set of assumptions: analytical geometry. b. any branch of geometry referring to a particular set of objects: solid geometry. 3. a shape, configuration, or arrangement. 4. (Art Terms) arts the shape of a solid or a surface.
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Lenses A convex lens is also called a converging lens because it makes parallel light rays passing through it bend inward and meet (converge) at a spot just beyond the lens known as the focal point. Photo: A convex lens makes light rays converge (come together) at the focal point or focus. The distance from the center of the lens to the focal point is the focal length of the lens. Convex lenses are used in things like telescopes and binoculars to bring distant light rays to a focus in your eyes.
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Curved mirror A convex mirror diagram showing the focus, focal length, centre of curvature, principal axis, etc. A convex mirror, fish eye mirror or diverging mirror, is a curved mirror in which the reflective surface bulges toward the light source. Convex mirrors reflect light outwards, therefore they are not used to focus light.
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- Definition of Polygon. A polyhedron is a space figure each of whose faces is a polygon. In other words, a polyhedron is a solid shape whose faces are all polygons.
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- Definition: A polygon that has all interior angles less than 180°. (Result: All the vertices point 'outwards', away from the center.) Try this Adjust the polygon below by dragging any orange dot. If any vertex points 'inward' to towards the center of the polygon, it ceases to be a convex polygon.
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Polygon Edit this page Talk0. In geometry, a polygon is a plane figure bounded by a finite sequence of line segments, a two-dimensional polytope. The line segments that make up the polygon are called sides; their intersections are called vertices.
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- A convex polygon is defined as a polygon with all its interior angles less than 180°. This means that all the vertices of the polygon will point outwards, away from the interior of the shape. Think of it as a 'bulging' polygon. Note that a triangle (3-gon) is always convex. A convex polygon is the opposite of a concave polygon.
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- Exposure assessment data can be compared to established standards to help determine if the exposure is acceptable. An understanding of the relationship between the amount of a chemical present in the workplace and the biological response to that chemical is necessary to establish acceptable exposure levels.
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Pentagon A regular polygon has all angles equal and all sides equal, otherwise it is irregular. A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a cave in it)
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Geometry Calculations IPrimitive or IPrimitive[] Calculates an approximate concave hull that best fits the data. A concave hull is a shape that represents that a possible concave geometry that encloses all shapes in the specified data set. If a single unique Location is in the data set, a Pushpin is returned. If only two unique Locations are provided, or if all Locations form a line, a Polyline is returned.
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polygon The sum of the interior angles of any nonself-intersecting polygon with n sides is equal to (n — 2)180°. A polygon is said to be convex (see Figure l,a) if none of the lines determined by its sides cuts the polygon into two parts. A convex polygon can also be characterized by the property that a line segment connecting any two points of the plane lying within the polygon does not cross the polygon.
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Difference between Convex and Non-convex Non-convex is also referred to as concave. Convex and non-convex both define the types of curvature. Convex defines the curvature that extends outwards or bulges out. On the other hand, non-convex defines a curvature that extends or bends inward. Thus, the extension of the curve is used to differentiate between the two forms. Convex and non-convex are often used as adjectives to define the entities associated with the shape or curve defined by them.
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Vertex (geometry) In geometry, a vertex (plural: vertices or  vertexes) is a point where two or more curves, lines, or edges meet. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra are vertices.