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Starting from the graph of f, a horizontal translation means composing f with a function , for some constant number a, resulting in a graph consisting of points (, ()) . Each point ( x , y ) {\displaystyle (x,y)} of the original graph corresponds to the point ( x + a , y ) {\displaystyle (x+a,y)} in the new graph ...
A reflection against an axis followed by a reflection against a second axis parallel to the first one results in a total motion that is a translation. A reflection against an axis followed by a reflection against a second axis not parallel to the first one results in a total motion that is a rotation around the point of intersection of the axes.
The question can be phrased in graph theoretic terms as follows. Let G be the unit distance graph of the plane: an infinite graph with all points of the plane as vertices and with an edge between two vertices if and only if the distance between the two points is 1. The Hadwiger–Nelson problem is to find the chromatic number of G. As a ...
Note: solving for ′ returns the resultant angle in the first quadrant (< <). To find , one must refer to the original Cartesian coordinate, determine the quadrant in which lies (for example, (3,−3) [Cartesian] lies in QIV), then use the following to solve for :
The rigid transformations include rotations, translations, reflections, or any sequence of these. Reflections are sometimes excluded from the definition of a rigid transformation by requiring that the transformation also preserve the handedness of objects in the Euclidean space. (A reflection would not preserve handedness; for instance, it ...
The knight's tour problem is the mathematical problem of finding a knight's tour. Creating a program to find a knight's tour is a common problem given to computer science students. [ 3 ] Variations of the knight's tour problem involve chessboards of different sizes than the usual 8 × 8 , as well as irregular (non-rectangular) boards.
In the study of graph coloring problems in mathematics and computer science, a greedy coloring or sequential coloring [1] is a coloring of the vertices of a graph formed by a greedy algorithm that considers the vertices of the graph in sequence and assigns each vertex its first available color. Greedy colorings can be found in linear time, but ...
Machine translation, like DeepL or Google Translate, is a useful starting point for translations, but translators must revise errors as necessary and confirm that the translation is accurate, rather than simply copy-pasting machine-translated text into the English Wikipedia. Do not translate text that appears unreliable or low-quality.
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