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Polsby–Popper Test
The Polsby–Popper test is a mathematical compactness measure of a shape developed to quantify the degree of gerrymandering of political districts. The method was developed by lawyers Daniel D. Polsby and Robert Popper, though it had earlier been introduced in the field of paleontology by E.P. Cox. The formula for calculating a district's Polsby–Popper score is PP(D) = \frac , where D is the district, P(D) is the perimeter of the district, and A(D) is the area of the district. A district's Polsby–Popper score will always fall within the interval of ,1/math>, with a score of 0 indicating complete lack of compactness and a score of 1 indicating maximal compactness. Compared to other measures that use dispersion to measure gerrymandering, the Polsby–Popper test is very sensitive to both physical geography (for instance, convoluted coastal borders) and map resolution. The method was chosen by Arizona's redistricting commission in 2000.Monorief, Gary FReapportionment and Redistri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compactness Measure Of A Shape
The compactness measure of a shape is a numerical quantity representing the degree to which a shape is compact. The meaning of "compact" here is not related to the topological notion of compact space. 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 t ... [...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] |
Daniel D
Daniel is a masculine given name and a surname of Hebrew origin. It means "God is my judge"Hanks, Hardcastle and Hodges, ''Oxford Dictionary of First Names'', Oxford University Press, 2nd edition, , p. 68. (cf. Gabriel—"God is my strength"), and derives from two early biblical figures, primary among them Daniel from the Book of Daniel. It is a common given name for males, and is also used as a surname. It is also the basis for various derived given names and surnames. Background The name evolved into over 100 different spellings in countries around the world. Nicknames (Dan, Danny) are common in both English and Hebrew; "Dan" may also be a complete given name rather than a nickname. The name "Daniil" (Даниил) is common in Russia. Feminine versions (Danielle, Danièle, Daniela, Daniella, Dani, Danitza) are prevalent as well. It has been particularly well-used in Ireland. The Dutch names "Daan" and "Daniël" are also variations of Daniel. A related surname developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Arizona
Arizona ( ; nv, Hoozdo Hahoodzo ; ood, Alĭ ṣonak ) is a state in the Southwestern United States. It is the 6th largest and the 14th most populous of the 50 states. Its capital and largest city is Phoenix. Arizona is part of the Four Corners region with Utah to the north, Colorado to the northeast, and New Mexico to the east; its other neighboring states are Nevada to the northwest, California to the west and the Mexican states of Sonora and Baja California to the south and southwest. Arizona is the 48th state and last of the contiguous states to be admitted to the Union, achieving statehood on February 14, 1912. Historically part of the territory of in New Spain, it became part of independent Mexico in 1821. After being defeated in the Mexican–American War, Mexico ceded much of this territory to the United States in 1848. The southernmost portion of the state was acquired in 1853 through the Gadsden Purchase. Southern Arizona is known for its desert cl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Redistricting In Arizona
The U.S. state of Arizona, in common with the other U.S. states, must redraw its congressional and legislative districts every ten years to reflect changes in the state and national populations. Redistricting normally follows the completion of the United States census, which is carried out by the federal government the first year of every decade; the most recent census took place in 2020. Historically, Arizona's legislature had control over the redistricting process. However, Proposition 106, passed in 2000, delegated the power to draw congressional and legislative boundaries to a bipartisan independent commission. The Arizona Independent Redistricting Commission (AIRC) comprises two Democrats, two Republicans, and one independent chair. County and local redistricting, which normally takes place along the same timeline as congressional and legislative redistricting, is carried out by the individual county and local governments rather than the AIRC. Background Reappor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isoperimetric Inequality
In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n-dimensional space \R^n the inequality lower bounds the surface area or perimeter \operatorname(S) of a set S\subset\R^n by its volume \operatorname(S), :\operatorname(S)\geq n \operatorname(S)^ \, \operatorname(B_1)^, where B_1\subset\R^n is a unit sphere. The equality holds only when S is a sphere in \R^n. On a plane, i.e. when n=2, the isoperimetric inequality relates the square of the circumference of a closed curve and the area of a plane region it encloses. '' Isoperimetric'' literally means "having the same perimeter". Specifically in \R ^2, the isoperimetric inequality states, for the length ''L'' of a closed curve and the area ''A'' of the planar region that it encloses, that : L^2 \ge 4\pi A, and that equality holds if and only if the curve is a circle. The isoperimetric problem is to determine a plane figure of the largest possible area whose ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
