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Vertex (geometry) A vertex of an angle is the endpoint where two lines or rays come together. In geometry, a vertex ( pl.: vertices or vertexes) is a point where two or more curves, lines, or edges meet or intersect. As a consequence of this definition, the point where two lines meet to form an angle and the corners of polygons and polyhedra ...
In geometry, Pick's theorem provides a formula for the area of a simple polygon with integer vertex coordinates, in terms of the number of integer points within it and on its boundary. The result was first described by Georg Alexander Pick in 1899. [2] It was popularized in English by Hugo Steinhaus in the 1950 edition of his book Mathematical ...
Shoelace formula. The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2] It is called the shoelace formula because of the constant cross-multiplying for the ...
Definition of congruence in analytic geometry. In a Euclidean system, congruence is fundamental; it is the counterpart of equality for numbers. In analytic geometry, congruence may be defined intuitively thus: two mappings of figures onto one Cartesian coordinate system are congruent if and only if, for any two points in the first mapping, the ...
In Euclidean geometry, Ceva's theorem is a theorem about triangles. Given a triangle ABC, let the lines AO, BO, CO be drawn from the vertices to a common point O (not on one of the sides of ABC ), to meet opposite sides at D, E, F respectively. (The segments AD, BE, CF are known as cevians .) Then, using signed lengths of segments ,
Polygon. Some polygons of different kinds: open (excluding its boundary), boundary only (excluding interior), closed (including both boundary and interior), and self-intersecting. In geometry, a polygon ( / ˈpɒlɪɡɒn /) is a plane figure made up of line segments connected to form a closed polygonal chain . The segments of a closed polygonal ...
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