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Compactness Measure Of A Shape
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. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it includes all ''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 topological spaces. One suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sphericity
Sphericity is a measure of how closely the shape of a physical object resembles that of a perfect sphere. For example, the sphericity of the ball (bearing), balls inside a ball bearing determines the quality (business), 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. Sphericity applies in three-dimensional space, three dimensions; its analogue in Plane (mathematics), two dimensions, such as the cross section (geometry), cross sectional circles along a cylinder, cylindrical object such as a shaft (mechanical engineering), shaft, is called roundness (object), ''roundness''. Definition Defined by Wadell in 1935, the sphericity, \Psi , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area: :\Psi = \frac where V_p is volume of the object and A_p is the surface area. The sphericity of a sphere is 1 (nu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Area To Volume Ratio
The surface-area-to-volume ratio or surface-to-volume ratio (denoted as SA:V, SA/V, or sa/vol) is the ratio between surface area and 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 the volume. Good examples for such processes are processes governed by the heat equation, that is, diffusion and heat transfer by thermal 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 as the place w ... [...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 In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it ... 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. 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 poi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Washington Post
''The Washington Post'', locally known as ''The'' ''Post'' and, informally, ''WaPo'' or ''WP'', is an American daily newspaper published in Washington, D.C., the national capital. It is the most widely circulated newspaper in the Washington metropolitan area and has a national audience. As of 2023, the ''Post'' had 130,000 print subscribers and 2.5 million digital subscribers, both of which were the List of newspapers in the United States, third-largest among U.S. newspapers after ''The New York Times'' and ''The Wall Street Journal''. The ''Post'' was founded in 1877. In its early years, it went through several owners and struggled both financially and editorially. In 1933, financier Eugene Meyer (financier), Eugene Meyer purchased it out of bankruptcy and revived its health and reputation; this work was continued by his successors Katharine Graham, Katharine and Phil Graham, Meyer's daughter and son-in-law, respectively, who bought out several rival publications. The ''Post ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lot (real Estate)
In real estate, a land lot or plot of land 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 owners of a plot can be one or more persons 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zoning
In urban planning, zoning is a method in which a municipality or other tier of government divides land into land-use "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 th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gerrymandering
Gerrymandering, ( , originally ) defined in the contexts of Representative democracy, representative electoral systems, is the political manipulation of Boundary delimitation, electoral district boundaries to advantage a Political party, 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, a professor at Morgan State University, describes it as politicians picking their voters instead of voters picking their politicians. The term ''gerrymandering'' is a portmanteau of a salamander and 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 distri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constituency
An electoral (congressional, legislative, etc.) district, sometimes called a constituency, riding, or ward, is a geographical portion of a political unit, such as a country, state or province, city, or administrative region, created to provide the voters therein with representation in a legislature or other polity. That legislative body, 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 or multiple members. Generally, only voters (''constituents'') who reside within the district are permitted to vote in an election held there. The district representative or representatives may be elected by single-winner first-past-the-post system, a multi-winner proportional representative system, or another voting method. The district members may be selected by a direct election under wide adult enfranchisement, an indirect election, or direct election using another form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redistricting
Redistricting in the United States is the process of drawing electoral district boundaries. For the United States House of Representatives, and state legislatures, redistricting occurs after each ten-year census. The U.S. Constitution in Article 1, Section 2, Clause 3 provides for proportional representation in the House of Representatives. The Reapportionment Act of 1929 required that the number of seats in the U.S. House of Representatives be kept at a constant 435, and a 1941 act made the reapportionment among the states by population automatic after every decennial census. Reapportionment occurs at the federal level followed by redistricting at the state level. According to , Article I, Section 4 left to the legislature of each state the authority to establish congressional districts; however, such decisions are subject to judicial review. In most states redistricting is subject to political maneuvering, but some state legislatures have created independent commissions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Curvature
In mathematics, curvature is any of several strongly related concepts in geometry that intuitively measure the amount by which a curve deviates from being a straight line or by which a surface deviates from being a plane. If a curve or surface is contained in a larger space, curvature can be defined ''extrinsically'' relative to the ambient space. Curvature of Riemannian manifolds of dimension at least two can be defined ''intrinsically'' without reference to a larger space. 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 q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Moment Of Inertia
The moment of inertia, otherwise known as the mass moment of inertia, angular/rotational mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is defined relatively to a rotational axis. It is the ratio between the torque applied and the resulting angular acceleration about that axis. It plays the same role in rotational motion as mass does in linear motion. A body's moment of inertia about a particular axis depends both on the mass and its distribution relative to the axis, increasing with mass and distance from the axis. It is an intensive and extensive properties, extensive (additive) property: for a point particle, 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 (physics), mome ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
