Pi

The number π is a mathematical constant, the ratio of a circle's circumference to its diameter, commonly approximated as 3.14159. It has been represented by the Greek letter "π" since the mid-18th century, though it is also sometimes spelled out as "pi" (/paɪ/).

Being an irrational number, π cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed; however, to date, no proof of this has been discovered. Also, π is a transcendental number – a number that is not the root of any non-zero polynomial having rational coefficients. This transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge.

Ancient civilizations needed the value of π to be computed accurately for practical reasons. It was calculated to seven digits, using geometrical techniques, in Chinese mathematics and to about five in Indian mathematics in the 5th century CE. The historically first exact formula for π, based on infinite series, was not available until a millennium later, when in the 14th century the Madhava–Leibniz series was discovered in Indian mathematics. In the 20th and 21st centuries, mathematicians and computer scientists discovered new approaches that, when combined with increasing computational power, extended the decimal representation of π to, as of 2015, over 13.3 trillion (10¹³) digits. Practically all scientific applications require no more than a few hundred digits of π, and many substantially fewer, so the primary motivation for these computations is the human desire to break records. However, the extensive calculations involved have been used to test supercomputers and high-precision multiplication algorithms.

Pie (surname)

Pie is a surname. People with the surname include:

See also

Pie (game)

Pie or, Pieman, Pieman is an outdoor game for more than three children. Its origin is unknown. A variant exists called Easter Eggs.

Description

The game requires a seating area for the players (such as a flight of porch steps or a garden wall) which is designated the "Pie Shop" or "Bakery." Also required are a Goal distant from the seating area such as a tree, post or other object, and an expanse of lawn or field for a chase similar to the chase in the game of Tag.

One player is chosen Pieman, another Buyer, and the other players are Pies. The Buyer is sometimes designated Simple Simon following the Mother Goose rhyme:

To begin the game, the Buyer is sent to the Goal where he cannot see or hear the other players. The Pieman then names each Pie with a common pie filling such as Apple, Blueberry, Pumpkin, etc. When all the Pies have been named, the Pieman calls the Buyer to the Pie Shop.

The Buyer demands, "Pieman, Pieman, I would like a pie." The Pieman asks, "And what might that Pie be?" The Buyer then names a pie flavor such as Apple. If one of the Pies has been designated Apple, then he rushes from the Pie Shop to the Goal while the Buyer runs after him and attempts to tag him. Both the Pie and the Buyer must touch the Goal before running back to the Pie Shop. If the Pie returns to the Pie Shop without being tagged, he resumes his seat, and is renamed for another round. The chase may be complicated with dodging about lawn furniture, flower beds, clotheslines of drying laundry, or other obstacles in the path to and from the Goal.

City

A city is a large and permanent human settlement. Although there is no agreement on how a city is distinguished from a town in general English language meanings, many cities have a particular administrative, legal, or historical status based on local law.

Cities generally have complex systems for sanitation, utilities, land usage, housing, and transportation. The concentration of development greatly facilitates interaction between people and businesses, benefiting both parties in the process, but it also presents challenges to managing urban growth.

A big city or metropolis usually has associated suburbs and exurbs. Such cities are usually associated with metropolitan areas and urban areas, creating numerous business commuters traveling to urban centers for employment. Once a city expands far enough to reach another city, this region can be deemed a conurbation or megalopolis. In terms of population, the largest city proper is Shanghai, while the fastest-growing is Dubai.

Origins

There is not enough evidence to assert what conditions gave rise to the first cities. Some theorists have speculated on what they consider suitable pre-conditions and basic mechanisms that might have been important driving forces.

City government in Washington (state)

There are 281 municipalities in the U.S. state of Washington. State law determines the various powers its municipalities have.

City classes

Legally, a city in Washington can be described primarily by its class. There are five classes of cities in Washington:

First class cities are cities with a population over 10,000 at the time of reorganization and operating under a home rule charter. They are permitted to perform any function specifically granted them by Title 35 RCW (Revised Code of Washington). Among them are Seattle, Tacoma, Spokane, Vancouver, and Yakima.

Second class cities are cities with a population over 1,500 at the time of reorganization and operating without a home rule charter. Like first class cities, they are permitted to perform any function specifically granted them by Title 35 RCW. Among them are Port Orchard, Wapato, and Colville.

Towns are municipalities with a population of under 1,500 at the time of reorganization. Towns are not authorized to operate under a charter. Like the previously listed cities, they are permitted to perform any function specifically granted them by Title 35 RCW. Among them are Steilacoom, Friday Harbor, Eatonville, and Waterville. In 1994, the legislature made 1,500 the minimum population required to incorporate.

Administrative divisions of Texas

Texas has a total of 254 counties, many cities, and numerous special districts, the most common of which is the independent school district.

County

Texas has a total of 254 counties, by far the largest number of counties of any state.

Each county is run by a five-member Commissioners' Court consisting of four commissioners elected from single-member districts (called commissioner precincts) and a county judge elected at-large. The county judge does not have authority to veto a decision of the commissioners court; the judge votes along with the commissioners (being the tie-breaker in close calls). In smaller counties, the county judge actually does perform judicial duties, but in larger counties the judge's role is limited to serving on the commissioners court and certifying elections. Certain officials, such as the sheriff and tax collector, are elected separately by the voters, but the commissioners court determines their office budgets, and sets overall county policy. All county elections are partisan, and commissioner precincts are redistricted after each ten year Census both to equalize the voting power in each and in consideration of the political party preferences of the voters in each.