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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 are equal to 1, we have directional scaling. In the case where v x = v y = v z = k, scaling increases the area of any surface by a factor of k 2 and the volume of any solid object by a factor of k 3.
Therefore, the shear factor m is the cotangent of the shear angle between the former verticals and the x-axis. (In the example on the right the square is tilted by 30°, so the shear angle is 60°.) (In the example on the right the square is tilted by 30°, so the shear angle is 60°.)
Comb binding (sometimes referred to as "cerlox" or "surelox" binding) is one of many ways to bind pages together into a book. This method uses round plastic spines with 19 rings (for US Letter size) or 21 rings (for A4 size) and a hole puncher that makes rectangular holes.
In ring theory, a branch of abstract algebra, a quotient ring, also known as factor ring, difference ring [1] or residue class ring, is a construction quite similar to the quotient group in group theory and to the quotient space in linear algebra. [2] [3] It is a specific example of a quotient, as viewed from the general setting of universal ...
The stretch factor of the pair is the ratio between these two distances, d(f(x),f(y))/d(x,y). The stretch factor of the whole mapping is the supremum of the stretch factors of all pairs of points. The stretch factor has also been called the distortion [disputed – discuss] or dilation of the mapping.
Binder jet 3D printing, known variously as "powder bed and inkjet" and "drop-on-powder" printing, is a rapid prototyping and additive manufacturing technology for making objects described by digital data such as a CAD file. Binder jetting is one of the seven categories of additive manufacturing processes according to ASTM and ISO. [1]
The lemniscate functions sl and cl can be defined as the solution to the initial value problem: [5] = (+ ) , = (+ ) , =, =, or equivalently as the inverses of an elliptic integral, the Schwarz–Christoffel map from the complex unit disk to a square with corners {,,,}: [6]
In mathematics, a transformation, transform, or self-map [1] is a function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f: X → X. [2] [3] [4] Examples include linear transformations of vector spaces and geometric transformations, which include projective transformations, affine transformations, and specific ...