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The template can accept parameters that describe the size of the object on the screen: |viewport_cm= or |viewport_px=. The template also accepts other geohack parameters to generate the scale argument: dim; type (e.g., "mountain" or "city") population (for type="city" only)
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A plane: the locus of x is a plane if A = P, a vector with a zero n o component. In a homogeneous projective space such a vector P represents a vector on the plane n o =1 that would be infinitely far from the origin (ie infinitely far outside the null cone), so g(x).P =0 corresponds to x on a sphere of infinite radius, a plane. In particular:
As an example, the distance squared between the points (0,0,0,0) and (1,1,1,0) is 3 in both the Euclidean and Minkowskian 4-spaces, while the distance squared between (0,0,0,0) and (1,1,1,1) is 4 in Euclidean space and 2 in Minkowski space; increasing b 4 decreases the metric distance. This leads to many of the well-known apparent "paradoxes ...
The terms are sometimes used in the absolute sense of the table, but other times in a relative sense. For example, a map reader whose work refers solely to large-scale maps (as tabulated above) might refer to a map at 1:500,000 as small-scale. In the English language, the word large-scale is often used to mean "extensive".
The restriction to 0, 1, 3 and 7 dimensions is related to Hurwitz's theorem, that normed division algebras are only possible in 1, 2, 4 and 8 dimensions. The cross product is formed from the product of the normed division algebra by restricting it to the 0, 1, 3, or 7 imaginary dimensions of the algebra, giving nonzero products in only three ...
The primary grid pattern is of quarter sections (1 ⁄ 2 mi × 1 ⁄ 2 mi (800 m × 800 m)). In U.S. land surveying under the Public Land Survey System (PLSS), a section is an area nominally one square mile (2.6 square kilometers), containing 640 acres (260 hectares), with 36 sections making up one survey township on a rectangular grid. [1]
In plane geometry there are three types of angles that may be preserved in a conformal map. [3] Each is hosted by its own real algebra, ordinary complex numbers, split-complex numbers, and dual numbers. The conformal maps are described by linear fractional transformations in each case. [4]