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A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc. More general is scaling with a separate scale factor for each axis direction.
One direction in metric geometry is finding purely metric ("synthetic") formulations of properties of Riemannian manifolds. For example, a Riemannian manifold is a CAT( k ) space (a synthetic condition which depends purely on the metric) if and only if its sectional curvature is bounded above by k . [ 20 ]
This scale was used by Revell for some ship models because it was one-half the size of the standard scale for wargaming models used by the U.S. Army. 1:535: 0.022: 0.570 mm: Ship models: Scale used by Revell for USS Missouri ship. Sometimes called "box scale" because chosen to fit a box size. 1:500: 0.610 mm: Architecture. Ship models. Die-cast ...
In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale. Thus on an architect's drawing one might read 'one centimeter to one meter', 1:100, 1/100, or 1 / 100 . A bar scale would also ...
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.
After forming and finishing in third place on the U.K.’s version of The X Factor in 2010, One Direction released four successful studio albums — Up All Night, Take Me Home, Midnight Memories ...
A plane segment or planar region (or simply "plane", in lay use) is a planar surface region; it is analogous to a line segment. A bivector is an oriented plane segment, analogous to directed line segments. [a] A face is a plane segment bounding a solid object. [1] A slab is a region bounded by two parallel planes.