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The concept of scale is applicable if a system is represented proportionally by another system. For example, for a scale model of an object, the ratio of corresponding lengths is a dimensionless scale, e.g. 1:25; this scale is larger than 1:50. In mathematics, two quantities are called proportional if they vary in such a way that one of the quantities is a constant multiple of the other, or equivalently if they have a constant ratio. ...
A scale model of the Tower of London. ...
In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units. ...
In the general case of a differentiable bijection, the concept of scale can, to some extent, still be used, but it may depend on location and direction. It can be described by the Jacobian matrix. The modulus of the matrix times a unit vector is the scale in that direction. The non-linear case applies for example if a curved surface like part of the Earth's surface is mapped to a plane, see map projection. A bijective function. ...
In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ...
The Mercator projection shows courses of constant bearing as straight lines. ...
In the case of an affine transformation the scale does not depend on location but it depends in general on direction. If the affine transformation can be decomposed into isometries and a transformation given by a diagonal matrix, we have directionally differential scaling and the diagonal elements (the eigenvalues) are the scale factors in two or three perpendicular directions. For example, on some profile maps horizontal and vertical scale are different; in particular elevation may be shown in a larger scale than horizontal distance. In geometry, an affine transformation or affine map (from the Latin, affinis, connected with) between two vector spaces (strictly speaking, two affine spaces) consists of a linear transformation followed by a translation: In the finite-dimensional case each affine transformation is given by a matrix A and a vector b...
In linear algebra, a diagonal matrix is a square matrix in which the entries outside the main diagonal are all zero. ...
In Euclidean geometry, uniform scaling is a linear transformation that enlarges or diminishes objects; the scale factor is the same in all directions; it is also called a homothety. ...
In this transformation of the Mona Lisa, the blue vector has been rotated, but the red one has not. ...
lol rofl taco hahaThere is also a nscale factor for the expansion of the Universe Scale factors are used in computer science when certain real world numbers need to be represented on a different scale in order to fit a required number format. ...
In the case of directional scaling (in one direction only) there is just one scale factor for one direction. lol rofl taco hahaThere is also a nscale factor for the expansion of the Universe Scale factors are used in computer science when certain real world numbers need to be represented on a different scale in order to fit a required number format. ...
The case of uniform scaling corresponds to a geometric similarity. There is just one scale throughout. Several equivalence relations in mathematics are called similarity. ...
In the case of an isometry the scale is 1:1. In mathematics, an isometry, isometric isomorphism or congruence mapping is a distance-preserving isomorphism between metric spaces. ...
In the more general case of one quantity represented by another one, the scale has also a physical dimension. E.g., if an arrow is drawn to represent a physical vector, the "scale" has a physical dimension equal to that of the vector, divided by length. For example, if a force of 1 newton is represented by an arrow of 2 cm, the scale is 1 m : 50 N. There is typically consistency in scale among quantities of the same dimension, but otherwise scales within the same diagram may vary; e.g "5 m" may also be represented by an arrow of 2 cm; in that case the scale for vectors which represent length is 1:250. Correspondingly, torques could be represented on the same map by areas in a scale of 1 m² : 12 500 Nm, which is equal to 1 m : 12 500 N. Torques in the plane of the map could be represented by arrows with an independent scale of e.g. 1 m : 300 Nm. Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. ...
A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ...
Torque applied via an adjustable end wrench Relationship between force, torque, and momentum vectors in a rotating system In physics, torque (or often called a moment) can informally be thought of as rotational force or angular force which causes a change in rotational motion. ...
The scale of a map or enlarged or reduced model indicates the ratio between the distances on the map or model and the corresponding distances in reality or the original. E.g. a map of scale 1:50,000 shows a distance of 50,000 cm (=500 m) as 1 cm on a map, and a model on a scale 1:25 of a building with a height of 30 m has a model height of 1.20 m. An alternative method of indicating the scale is by a scale bar. This can also be applied on a computer screen etc., where the ratio may vary, and also remains valid when enlarging or reducing a paper map. Variable scale to measure distances on maps An important property of a map is the scale. ...
Part of the one-tenth scale model of Bourton-on-the-Water at Bourton-on-the-Water, Gloucestershire, England A scale model of the Singapore City Centre. ...
A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ...
This article is about the unit of length. ...
¾i love UR mom==See also==
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