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The plate scale of a telescope connects the angular separation of an object with the linear separation of its image at the focal plane. If focal length f {\displaystyle f} is measured in mm, the plate scale in radians per mm is given by angular separation θ and the linear separation of the image at the focal plane s , or by simply the focal ...
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 physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The scale factors for the elliptic coordinates (,) are equal to = = + = . Using the double argument identities for hyperbolic functions and trigonometric functions, the scale factors can be equivalently expressed as
Shape factors are dimensionless quantities used in image analysis and microscopy that numerically describe the shape of a particle, independent of its size. Shape factors are calculated from measured dimensions, such as diameter, chord lengths, area, perimeter, centroid, moments, etc. The dimensions of the particles are usually measured from ...
In an oblique pictorial drawing, the displayed angles among the axes as well as the foreshortening factors (scale) are arbitrary. The distortion created thereby is usually attenuated by aligning one plane of the imaged object to be parallel with the plane of projection thereby creating a true shape, full-size image of the chosen plane.
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This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x 2 + y 2 = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations. [18]