Search results
Results from the WOW.Com Content Network
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 ...
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
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.
The AOL.com video experience serves up the best video content from AOL and around the web, curating informative and entertaining snackable videos.
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
One implication of that is the "isotropy of scale factors", which means that the point scale factor is independent of direction, so that small shapes are preserved by the projection. This implies that the vertical scale factor, h, equals the horizontal scale factor, k. Since k = sec φ, so must h.
The azimuthal angle φ is given by the formula = The cylindrical radius ρ of the point P is given by ρ 2 = x 2 + y 2 {\displaystyle \rho ^{2}=x^{2}+y^{2}} and its distances to the foci in the plane defined by φ is given by d 1 2 = ( ρ + a ) 2 + z 2 d 2 2 = ( ρ − a ) 2 + z 2 {\displaystyle {\begin{aligned}d_{1}^{2}=(\rho +a)^{2}+z^{2 ...
The local (non-unit) basis vector is b 1 (notated h 1 above, with b reserved for unit vectors) and it is built on the q 1 axis which is a tangent to that coordinate line at the point P. The axis q 1 and thus the vector b 1 form an angle with the Cartesian x axis and the Cartesian basis vector e 1. It can be seen from triangle PAB that