Information about Convex Polygon
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A convex pentagon
- Every internal angle is at most 180 degrees.
- Every line segment between two vertices of the polygon does not go exterior to the polygon (i.e., it remains inside or on the boundary of the polygon).
Every triangle is strictly convex.
The sum of the interior angles of a regular convex polygon with n sides is equal to 180°(n - 2).
Concave polygon
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A simple concave hexagon
If a simple polygon is not convex, it is called concave. At least one internal angle of a concave polygon is larger than 180 degrees.
A concave polygon is often called a non-convex or re-entrant polygon (but in some cases the latter term has a different meaning).
External links
- Definition and properties of convex polygons With interactive animation
Geometry (Greek γεωμετρία; geo = earth, metria = measure) is a part of mathematics concerned with questions of size, shape, and relative position of figures and with properties of space. Geometry is one of the oldest sciences.
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simple polygon is a polygon whose sides do not intersect. They are also called Jordan polygons, because the Jordan curve theorem can be used to prove that such a polygon divides the plane into two regions, the region inside it and the region outside it.
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convex if for every pair of points within the object, every point on the straight line segment that joins them is also within the object. 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.
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In geometry, an interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. A simple polygon has exactly one internal angle per vertex.
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degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of plane angle, representing 1⁄360 of a full rotation.
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line segment is a part of a line that is bounded by two end points, which have a finite length, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square.
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- For other uses of the word, see Vertex.
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A triangle is one of the basic shapes of geometry: a polygon with three corners or and three sides or edges which are straight line segments.
In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
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In Euclidean geometry any three non-collinear points determine a triangle and a unique plane, i.e.
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In geometry, an interior angle (or internal angle) is an angle formed by two sides of a simple polygon that share an endpoint, namely, the angle on the inner side of the polygon. A simple polygon has exactly one internal angle per vertex.
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A re-entrant, or concave polygon is one in which at least one interior angle is more than 180 degrees (i.e. a reflex angle). A polygon is re-entrant or concave if there exist two points within the polygon which cannot be connected by a straight line which lies within the
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