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Such a scaling changes the diameter of an object by a factor between the scale factors, the area by a factor between the smallest and the largest product of two scale factors, and the volume by the product of all three. The scaling is uniform if and only if the scaling factors are equal (v x = v y = v z). If all except one of the scale factors ...
In an orthogonal coordinate system the lengths of the basis vectors are known as scale factors. The scale factors for the elliptic coordinates ( μ , ν ) {\displaystyle (\mu ,\nu )} are equal to h μ = h ν = a sinh 2 μ + sin 2 ν = a cosh 2 μ − cos 2 ν . {\displaystyle h_{\mu }=h_{\nu }=a{\sqrt {\sinh ^{2}\mu +\sin ^{2 ...
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are the radial distance r along the line connecting the point to a fixed point called the origin; the polar angle θ between this radial line and a given polar axis; [a] and
The quotient is called the scale factor. Unless the projection is conformal at the point being considered, the scale factor varies by direction around the point. A map distorts angles wherever the angles measured on the model of the Earth are not conserved in the projection. This is expressed by an ellipse of distortion which is not a circle.
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The point scale factor is independent of direction. It is a function of y on the projection. (On the sphere it depends on latitude only.) The scale is true on the equator. • The point scale factor is independent of direction. It is a function of x on the projection. (On the sphere it depends on both latitude and longitude.)
If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school ...
The solid angle of a sphere measured from any point in its interior is 4 π sr. The solid angle subtended at the center of a cube by one of its faces is one-sixth of that, or 2 π /3 sr. The solid angle subtended at the corner of a cube (an octant) or spanned by a spherical octant is π /2 sr, one-eight of the solid angle of a sphere. [1]