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Scale (ratio)
The scale ratio of a model represents the proportional ratio of a linear dimension of the model to the same feature of the original. Examples include a 3-dimensional scale model of a building or the scale drawings of the elevations or plans of a building. In such cases the scale is dimensionless and exact throughout the model or drawing. The scale can be expressed in four ways: in words (a lexical scale), as a ratio, as a fraction and as a graphical (bar) scale. Thus on an architect's drawing one might read 'one centimeter to one meter', 1:100, 1/100, or . A bar scale would also normally appear on the drawing. Colon may also be substituted with a specific, slightly raised ratio symbol , ie. . General representation Generally, a representation may involve more than one scale at the same time. For example, a drawing showing a new road in elevation might use different horizontal and vertical scales. An elevation of a bridge might be annotated with arrows with a length proportion ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Set (mathematics)
In mathematics, a set is a collection of different things; the things are '' elements'' or ''members'' of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, or other sets. A set may be finite or infinite. There is a unique set with no elements, called the empty set; a set with a single element is a singleton. Sets are ubiquitous in modern mathematics. Indeed, set theory, more specifically Zermelo–Fraenkel set theory, has been the standard way to provide rigorous foundations for all branches of mathematics since the first half of the 20th century. Context Before the end of the 19th century, sets were not studied specifically, and were not clearly distinguished from sequences. Most mathematicians considered infinity as potentialmeaning that it is the result of an endless processand were reluctant to consider infinite sets, that is sets whose number of members is not a natural number. Specific ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scales
Scale or scales may refer to: Mathematics * Scale (descriptive set theory), an object defined on a set of points * Scale (ratio), the ratio of a linear dimension of a model to the corresponding dimension of the original * Scale factor, a number which scales, or multiplies, some quantity * Long and short scales, how powers of ten are named and grouped in large numbers * Scale parameter, a description of the spread or dispersion of a probability distribution * Feature scaling, a method used to normalize the range of independent variables or features of data * Scale (analytical tool) Measurements * Scale (map), the ratio of the distance on a map to the corresponding actual distance * Scale (geography) * Weighing scale, an instrument used to measure mass * Scale (ratio), the ratio of the linear dimension of the model to the same dimension of the original * Spatial scale, a classification of sizes * Scale ruler, a tool for measuring lengths and transferring measurements at a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Scale
Spatial scale is a specific application of the term scale for describing or categorizing (e.g. into orders of magnitude) the size of a space (hence ''spatial''), or the extent of it at which a phenomenon or process occurs. For instance, in physics an object or phenomenon can be called microscopic if too small to be visible. In climatology, a micro-climate is a climate which might occur in a mountain, valley or near a lake shore. In statistics, a megatrend is a political, social, economical, environmental or technological trend which involves the whole planet or is supposed to last a very large amount of time. The concept is also used in geography, astronomy, and meteorology. These divisions are somewhat arbitrary; where, on this table, ''mega-'' is assigned global scope, it may only apply continentally or even regionally in other contexts. The interpretations of ''meso-'' and ''macro-'' must then be adjusted accordingly. See also * Astronomical units of length * Cosmic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Space
Scale-space theory is a framework for multi-scale signal representation developed by the computer vision, image processing and signal processing communities with complementary motivations from physics and biological vision. It is a formal theory for handling image structures at different scales, by representing an image as a one-parameter family of smoothed images, the scale-space representation, parametrized by the size of the smoothing kernel used for suppressing fine-scale structures. The parameter t in this family is referred to as the ''scale parameter'', with the interpretation that image structures of spatial size smaller than about \sqrt have largely been smoothed away in the scale-space level at scale t. The main type of scale space is the ''linear (Gaussian) scale space'', which has wide applicability as well as the attractive property of being possible to derive from a small set of '' scale-space axioms''. The corresponding scale-space framework encompasses a th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale Invariance
In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. *In mathematics, scale invariance usually refers to an invariance of individual functions or curves. A closely related concept is self-similarity, where a function or curve is invariant under a discrete subset of the dilations. It is also possible for the probability distributions of random processes to display this kind of scale invariance or self-similarity. *In classical field theory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically describe classical physical processes with no characteristic length scale. *In quantum field theory, scale inva ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scale (analytical Tool)
In the study of complex systems A complex system is a system composed of many components that may interact with one another. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication s ... and hierarchy theory, the concept of scale refers to the combination of (1) the level of analysis (for example, analyzing the whole or a specific component of the system); and (2) the level of observation (for example, observing a system as an external viewer or as an internal participant). The scale of analysis encompasses both the analytical choice of how to observe a given system or object of study, and the role of the observer in determining the identity of the system. This analytical tool is central to multi-scale analysis (see for example, MuSIASEM, land-use analysis). For example, on at the scale of analysis of a given population of zebras, the number of predators (e.g. lions) determines the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Scale Model Sizes
This is a list of scale model sizes, listing a variety of size ratios for scale model A scale model is a physical model that is geometrically similar to an object (known as the ''prototype''). Scale models are generally smaller than large prototypes such as vehicles, buildings, or people; but may be larger than small protot ...s. Model scales References {{DEFAULTSORT:List Of Scale Model Sizes Scale model sizes * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspect Ratio
The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape format, landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal Fraction (mathematics), fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: * Graphic / image ** Aspect ratio (image), Image aspect ratio ** Display aspect ratio ** Pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projection (mathematics)
In mathematics, a projection is an idempotent mapping of a set (or other mathematical structure) into a subset (or sub-structure). In this case, idempotent means that projecting twice is the same as projecting once. The restriction to a subspace of a projection is also called a ''projection'', even if the idempotence property is lost. An everyday example of a projection is the casting of shadows onto a plane (sheet of paper): the projection of a point is its shadow on the sheet of paper, and the projection (shadow) of a point on the sheet of paper is that point itself (idempotency). The shadow of a three-dimensional sphere is a disk. Originally, the notion of projection was introduced in Euclidean geometry to denote the projection of the three-dimensional Euclidean space onto a plane in it, like the shadow example. The two main projections of this kind are: * The projection from a point onto a plane or central projection: If is a point, called the center of projection, then t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Model
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided into physical models (e.g. a ship model or a fashion model) and abstract models (e.g. a set of mathematical equations describing the workings of the atmosphere for the purpose of weather forecasting). Abstract or conceptual models are central to philosophy of science. In scholarly research and applied science, a model should not be confused with a theory: while a model seeks only to represent reality with the purpose of better understanding or predicting the world, a theory is more ambitious in that it claims to be an explanation of reality. Types of model ''Model'' in specific contexts As a noun, ''model'' has specific meanings in certain fields, derived from its original meaning of "structural design or layout": * Model (art), a perso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scaling (geometry)
In affine geometry, uniform scaling (or isotropic scaling) is a linear transformation that enlarges (increases) or shrinks (diminishes) objects by a '' scale factor'' that is the same in all directions ( isotropically). The result of uniform scaling is similar (in the geometric sense) to the original. A scale factor of 1 is normally allowed, so that congruent shapes are also classed as similar. Uniform scaling happens, for example, when enlarging or reducing a photograph, or when creating a scale model of a building, car, airplane, etc. More general is scaling with a separate scale factor for each axis direction. Non-uniform scaling (anisotropic scaling) is obtained when at least one of the scaling factors is different from the others; a special case is directional scaling or stretching (in one direction). Non-uniform scaling changes the shape of the object; e.g. a square may change into a rectangle, or into a parallelogram if the sides of the square are not parallel to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
