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In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same distance in a given direction. A translation can also be interpreted as the addition of a constant vector to every point, or as shifting the origin of the coordinate system .
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
A half-translation surface is defined similarly to a translation surface but allowing the gluing maps to have a nontrivial linear part which is a half turn. Formally, a translation surface is defined geometrically by taking a collection of polygons in the Euclidean plane and identifying faces by maps of the form z ↦ ± z + w {\displaystyle z ...
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other. [ 1 ] More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry , i.e., a combination of rigid motions , namely a ...
Joseph Needham, a historian of China, speculated that some star charts of the Chinese Song dynasty may have been drafted on the Mercator projection; [1] however, this claim was presented without evidence, and astronomical historian Kazuhiko Miyajima concluded using cartometric analysis that these charts used an equirectangular projection instead.
Lists of shapes cover different types of geometric shape and related topics. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools. They include mathematics topics and other lists of shapes, such as shapes used by drawing or teaching tools.
In mathematics, a translation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x'y'-Cartesian coordinate system in which the x' axis is parallel to the x axis and k units away, and the y' axis is parallel to the y axis and h units away.
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