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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 ...
The scalar projection is defined as [2] = ‖ ‖ = ^ where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b. The scalar projection is equal in absolute value to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b ...
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 azimuthal angle φ, which is the angle of rotation of the radial line around the polar axis. [b] (See graphic regarding the "physics convention".)
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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 ...
Scale at an angular distance of 5° (in longitude) away from the central meridian is less than 0.4% greater than scale at the central meridian, and is about 1.54% at an angular distance of 10°. In the secant version the scale is reduced on the equator and it is true on two lines parallel to the projected equator (and corresponding to two ...
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
Visual angle is the angle a viewed object subtends at the eye, usually stated in degrees of arc. It also is called the object's angular size . The diagram on the right shows an observer's eye looking at a frontal extent (the vertical arrow) that has a linear size S {\displaystyle S} , located in the distance D {\displaystyle D} from point O ...