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Compactness Measure
Compactness measure is a numerical quantity representing the degree to which a shape is compact. The circle and the sphere are the most compact planar and solid shapes, respectively. Properties Various compactness measures are used. However, these measures have the following in common: *They are applicable to all geometric shapes. *They are independent of scale and orientation. *They are dimensionless numbers. *They are not overly dependent on one or two extreme points in the shape. *They agree with intuitive notions of what makes a shape compact. Examples A common compactness measure is the isoperimetric quotient, the ratio of the area of the shape to the area of a circle (the most compact shape) having the same perimeter. In the plane, this is equivalent to the Polsby–Popper test. Alternatively, the shape's area could be compared to that of its bounding circle, its convex hull, or its minimum bounding box. Similarly, a comparison can be made between the perimeter of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Space
In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space by making precise the idea of a space having no "punctures" or "missing endpoints", i.e. that the space not exclude any ''limiting values'' of points. For example, the open interval (0,1) would not be compact because it excludes the limiting values of 0 and 1, whereas the closed interval ,1would be compact. Similarly, the space of rational numbers \mathbb is not compact, because it has infinitely many "punctures" corresponding to the irrational numbers, and the space of real numbers \mathbb is not compact either, because it excludes the two limiting values +\infty and -\infty. However, the ''extended'' real number line ''would'' be compact, since it contains both infinities. There are many ways to make this heuristic notion precise. These ways usually agree in a metric space, but may not be equivalent in other topologic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphericity
Sphericity is a measure of how closely the shape of an object resembles that of a perfect sphere. For example, the sphericity of the balls inside a ball bearing determines the quality of the bearing, such as the load it can bear or the speed at which it can turn without failing. Sphericity is a specific example of a compactness measure of a shape. Defined by Wadell in 1935, the sphericity, \Psi , of a particle is the ratio of the surface area of a sphere with the same volume as the given particle to the surface area of the particle: :\Psi = \frac where V_p is volume of the particle and A_p is the surface area of the particle. The sphericity of a sphere is unity by definition and, by the isoperimetric inequality, any particle which is not a sphere will have sphericity less than 1. Sphericity applies in three dimensions; its analogue in two dimensions, such as the cross sectional circles along a cylindrical object such as a shaft, is called roundness. Ellipsoidal objects ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Area To Volume Ratio
The surface-area-to-volume ratio, also called the surface-to-volume ratio and variously denoted sa/vol or SA:V, is the amount of surface area per unit volume of an object or collection of objects. SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface ''and'' the volume. Good examples for such processes are processes governed by the heat equation, i.e., diffusion and heat transfer by conduction. SA:V is used to explain the diffusion of small molecules, like oxygen and carbon dioxide between air, blood and cells, water loss by animals, bacterial morphogenesis, organism's thermoregulation, design of artificial bone tissue, artificial lungs and many more biological and biotechnological structures. For more examples see Glazier. The relation between SA:V and diffusion or heat conduction rate is explained from flux and surface perspective, focusing on the surface of a body a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reock Degree Of Compactness
The Reock degree of compactness, or Reock compactness score, is a ratio that quantifies the compactness of the geographic area of a voting district. The score is sometimes used as an indication of the extent to which a voting district may be considered gerrymandered In representative democracies, gerrymandering (, originally ) is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The m .... The Reock compactness score is computed by dividing the area of the voting district by the area of the smallest circle that would completely enclose it. Since the circle encloses the district, its area cannot be less than that of the district, and so the Reock compactness score will always be a number between zero and one (which may be expressed as a percentage). Criticism Because the Reock compactness score is defined in terms of a circle that must enclose all point ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Washington Post
''The Washington Post'' (also known as the ''Post'' and, informally, ''WaPo'') is an American daily newspaper published in Washington, D.C. It is the most widely circulated newspaper within the Washington metropolitan area and has a large national audience. Daily broadsheet editions are printed for D.C., Maryland, and Virginia. The ''Post'' was founded in 1877. In its early years, it went through several owners and struggled both financially and editorially. Financier Eugene Meyer purchased it out of bankruptcy in 1933 and revived its health and reputation, work continued by his successors Katharine and Phil Graham (Meyer's daughter and son-in-law), who bought out several rival publications. The ''Post'' 1971 printing of the Pentagon Papers helped spur opposition to the Vietnam War. Subsequently, in the best-known episode in the newspaper's history, reporters Bob Woodward and Carl Bernstein led the American press's investigation into what became known as the Watergate scandal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lot (real Estate)
In real estate, a lot or plot is a tract or parcel of land owned or meant to be owned by some owner(s). A plot is essentially considered a parcel of real property in some countries or immovable property (meaning practically the same thing) in other countries. Possible owner(s) of a plot can be one or more person(s) or another legal entity, such as a company/corporation, organization, government, or trust. A common form of ownership of a plot is called fee simple in some countries. A small area of land that is empty except for a paved surface or similar improvement, typically all used for the same purpose or in the same state is also often called a plot. Examples are a paved car park or a cultivated garden plot. This article covers plots (more commonly called lots in some countries) as defined parcels of land meant to be owned as units by an owner(s). Like most other types of property, lots or plots owned by private parties are subject to a periodic property tax payable by the o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zoning
Zoning is a method of urban planning in which a municipality or other tier of government divides land into areas called zones, each of which has a set of regulations for new development that differs from other zones. Zones may be defined for a single use (e.g. residential, industrial), they may combine several compatible activities by use, or in the case of form-based zoning, the differing regulations may govern the density, size and shape of allowed buildings whatever their use. The planning rules for each zone determine whether planning permission for a given development may be granted. Zoning may specify a variety of outright and conditional uses of land. It may indicate the size and dimensions of lots that land may be subdivided into, or the form and scale of buildings. These guidelines are set in order to guide urban growth and development. Zoning is the most common regulatory urban planning method used by local governments in developed countries. Exceptions include the Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerrymandering
In representative democracies, gerrymandering (, originally ) is the political manipulation of electoral district boundaries with the intent to create undue advantage for a party, group, or socioeconomic class within the constituency. The manipulation may involve "cracking" (diluting the voting power of the opposing party's supporters across many districts) or "packing" (concentrating the opposing party's voting power in one district to reduce their voting power in other districts). Gerrymandering can also be used to protect incumbents. Wayne Dawkins describes it as politicians picking their voters instead of voters picking their politicians. The term ''gerrymandering'' is named after American politician Elbridge Gerry, Vice President of the United States at the time of his death, who, as governor of Massachusetts in 1812, signed a bill that created a partisan district in the Boston area that was compared to the shape of a mythological salamander. The term has negative con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constituency
An electoral district, also known as an election district, legislative district, voting district, constituency, riding, ward, division, or (election) precinct is a subdivision of a larger State (polity), state (a country, administrative region, or other polity) created to provide its population with representation in the larger state's legislative body. That body, or the state's constitution or a body established for that purpose, determines each district's boundaries and whether each will be represented by a Single-member district, single member or multiple members. Generally, only voters (''constituents'') who Residency (domicile), reside within the district are permitted to vote in an election held there. District representatives may be elected by a first past the post, first-past-the-post system, a Proportional representation, proportional representative system, or another voting system, voting method. They may be selected by a direct election under universal suffrage, an ind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redistricting
Redistribution (re-districting in the United States and in the Philippines) is the process by which electoral districts are added, removed, or otherwise changed. Redistribution is a form of boundary delimitation that changes electoral district boundaries, usually in response to periodic census results. Redistribution is required by law or constitution at least every decade in most representative democracy systems that use first-past-the-post or similar electoral systems to prevent geographic malapportionment. The act of manipulation of electoral districts to favour a candidate or party is called gerrymandering. Australia In Australia, redistributions are carried out by independent and non-partisan commissioners in the Commonwealth, and in each state or territory. The various electoral acts require the population of each seat to be equal, within certain strictly limited variations. The longest period between two redistributions can be no greater than seven years. Many oth ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature ''at a point'' of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point. The curvature of a straight line is zero. In contrast to the tangent, which is a vector quantity, the curvature at a point is typically a scalar quantity, that is, it is expressed by a single real number. For surfaces (and, more generally for higher-dimensional manifolds), that are embedded in a Euclidean space, the concept of curvature is more complex, as it depends on the choice of a direction on the surface or man ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation. It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis. For bodies constrained to rotate in a plane, only their moment of inertia about an axis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
