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Aside from the Orthographic, six standard principal views (Front; Right Side; Left Side; Top; Bottom; Rear), descriptive geometry strives to yield four basic solution views: the true length of a line (i.e., full size, not foreshortened), the point view (end view) of a line, the true shape of a plane (i.e., full size to scale, or not ...
An important uniform 5-polytope is the 5-demicube, h{4,3,3,3} has half the vertices of the 5-cube (16), bounded by alternating 5-cell and 16-cell hypercells. The expanded or stericated 5-simplex is the vertex figure of the A 5 lattice, . It and has a doubled symmetry from its symmetric Coxeter diagram.
Each iteration of the Sierpinski triangle contains triangles related to the next iteration by a scale factor of 1/2. In affine geometry, uniform scaling (or isotropic scaling [1]) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a scale factor that is the same in all directions (isotropically).
A point in the plane may be represented in homogeneous coordinates by a triple (x, y, z) where x/z and y/z are the Cartesian coordinates of the point. [10] This introduces an "extra" coordinate since only two are needed to specify a point on the plane, but this system is useful in that it represents any point on the projective plane without the ...
In a Cartesian plane, one can define canonical representatives of certain geometric figures, such as the unit circle (with radius equal to the length unit, and center at the origin), the unit square (whose diagonal has endpoints at (0, 0) and (1, 1)), the unit hyperbola, and so on. The two axes divide the plane into four right angles, called ...
In mathematics, a plane is a two-dimensional space or flat surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. When working exclusively in two-dimensional Euclidean space, the definite article is used, so the Euclidean plane refers to the ...
In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. [9] Such a drawing is called a plane graph or planar embedding of the graph.
Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world.