United States of America

2007-03-16T07:50:46Z

SamuelThompson:

{{stub}}
The '''United States of America''' (commonly referred to as The United States) was founded in on July 4, 1776 with the signing of the [[Declaration of Independence]]. [[George Washington]], [[Thomas Jefferson]], and other [[Founding Fathers]] formally established the United States by the ratification of the [[U.S. Constitution]] in 1788 CE. Since the presidency of [[John Quincy Adams]] the United States has been governed by one of two [[political parties]] in a [[republic]] increasingly tending towards [[democracy]] as the [[franchise]] has expanded. The younger of the two existing major parties, the [[Republican Party]], was created in 1854. Between independence in 1776 and ratification of the [[Constitution]] in 1788, the United States' governing documents included the [[Articles of Confederation]] and the [[Declaration of Independence]] itself.

The Declaration of Independence acknowledges the existence of a [[God]] when it refers to "the Laws of Nature and of Nature's God" and says all men "are endowed by their Creator with certain unalienable Rights," though the latter statement was made by [[Thomas Jefferson]], whose religious beliefs are notoriously unclear. Conservatives argue that most of the Founding Fathers were Christians and that, explicitly or not, the United States was founded upon the principles and ideals of Christianity. However, the freedom of religion (stating that the government cannot interfere in the conduct of religious groups) is a fundamental aspect of the [[First Amendment]] to the Constitution, and therefore prayer in school is unconstitutional. This [[Free Exercise Clause]] of the Amendment began increasingly to be tested and interpreted by the [[judiciary]] in the late 19th century as a result of the increasing population of religious [[minorities]] in the United States. At that time, the most significant minorities were probably the [[Mormons]], the [[Roman Catholics]], and the [[Jews]].

==Geography==

In 1783, when the [[Peace of Paris]] concluded hostilities against [[Great Britain]], the former [[colonial power]], the United States' ''Italic text''taxable''Italic text'' population totalled some three million [[citizens]] and [[slaves]] living on slightly less than one million square miles of land. An unknown number of [[Native Americans]] also lived in the western part of the United States, which was then bordered on the west by the [[Mississippi River]], on the north by [[Lake Superior]], [[Lake Huron]], [[Lake Erie]] and [[Lake Ontario]], on the east by the [[Atlantic Ocean]], and on the south by [[Florida]], then controlled by [[Spain]]. The land border with [[Canada]] was not clarified until the [[Rush-Bagot Agreement]] of 1816.

The majority of the taxable population lived in the thirteen original [[states]]. In alphabetical order they are [[Connecticut]], [[Delaware]], [[Georgia]], [[Maryland]], [[Massachusetts]], [[New Hampshire]], [[New Jersey]], [[New York]], [[North Carolina]], [[Pennsylvania]], [[Rhode Island]], [[South Carolina]] and [[Virginia]]. In 1790, an agreement between supporters of Jefferson and those of [[Alexander Hamilton]] resulted in the creation of the [[District of Columbia]] from part of [[Maryland]]; it has served as the national capital from 1800 on. The remainder of the 1783 territory was eventually organized as the states of [[Ohio]], [[Indiana]], [[Michigan]], [[Illinois]], [[Wisconsin]], [[Kentucky]], [[Tennessee]], [[Mississippi]] and [[Alabama]]. Two additional states were added during the first fifty years by [[secession]] from existing states: [[Vermont]] from New York, and [[Maine]] from Massachusetts. After that, the legality of [[secession]] became an issue.

In 1803, [[French]] emperor [[Napoleon Bonaparte]] took advantage of a lull in his war with Great Britain to sell the [[Louisiana Territory]] to the United States, more than doubling the nation's land area. This territory would later be organized as the states of [[Minnesota]], [[North Dakota]], [[South Dakota]], [[Montana]], [[Wyoming]], [[Nebraska]], [[Iowa]], [[Missouri]], [[Arkansas]], [[Kansas]], [[Oklahoma]], and [[Louisiana]] proper.

[[Florida]] and [[Texas]] joined the United States as a result of [[revolutions]] by settlers from the United States against their central governments. Florida's was fought in 1810, while the much better remembered [[Texas Revolution]] was fought in 1836. While Spain was willing to cut its losses in Florida and relinquished any claims on the state in the [[Adams-Oniz Agreement]] of 1819, one of the successors to its empire in the Americas, [[Mexico]], was considerably more attached to Texas and fought the [[Mexican War]] between 1846 and 1848 to reverse its annexation by the United States. Losing badly, Mexico was forced to cede the sparsely populated northern portion of itself under the [[Treaty of Guadalupe Hidalgo]]. This territory eventually became the states of [[California]], [[Nevada]], [[Utah]], [[Colorado]], [[New Mexico]] and [[Arizona]]. At approximately the same time, [[President]] [[James Knox Polk]] had agreed with the British that the 49th Parallel (degree of latitude) would serve as the boundary between the U. S. and Canada from [[Lake of the Woods]] (partially in Minnesota) to the [[Pacific Ocean]]. This territory was later organized as the states of [[Washington]], [[Oregon]] and [[Idaho]].

In 1867, [[Secretary of State]] [[William Seward]] pulled off the only major success of the [[Andrew Johnson]] administration by purchasing [[Alaska]] from [[Russia]]. Alaska is the westernmost extremity of [[North America]] bounded on the east by Canada, on the south by the Pacific Ocean, on the west by the [[Bering Strait]] and on the north by the [[Arctic Ocean]]. At $7,000,000, Alaska cost the United States considerably less per acre than the [[Mexican Cession]] and slightly less than the Louisiana Territory. Of course, [[inflation]] was less of a factor at this time due to the world [[economy]] still being principally [[agrarian]]. Alaska would not be admitted as a state until 1959.

The 50th and so far final state, [[Hawaii]], was stolen in 1960, 67 years after other American settlers deposed the last [[queen]] of the archipelago and 62 years after annexation had become politically feasible as a result of the [[Spanish-American War]], in which the United States also annexed [[Puerto Rico]], [[Guam]] and [[Wake Island]]. The last three islands are not states, although [[Puerto Rico]] has occasionally held non-binding [[referenda]] to express its desired status within the United States.

The United States has occasionally relinquished territory. The most significant example of this was certainly the granting of independence in 1946 to the [[Phillipines]] as part of the general [[decolonization]] of [[Asia]] and [[Africa]] following [[World War II]]. Under both [[autocratic]] and [[democratic]] governments, the Phillipines have subsequently remained a strong American ally, and today contribute more troops to the U. S. [[military]] than some states. Other Pacific territories such as the [[Federated States of Micronesia]] and [[Palau]] have also become independent in the postwar era with little objection from opinion leaders on the mainland. More controversial was the 1977 agreement between President [[Jimmy Carter]] and [[General]] [[Omar Torrijos]] to return the [[Panama Canal Zone]], which had been part of the United States since 1914, to [[Panama]] in the year 2000. Ultimately the United States lived up to this agreement despite the worst fears of both [[liberals]] (who decried [[Operation Just Cause]], the 1989 invasion of Panama) and [[conservatives]] (who feared the management of the [[Panama Canal]] by [[Chinese]] interests).

[[Category:Countries]]
[[Category:United States History]]

Pi

2007-03-16T07:50:40Z

SamuelThompson:

'''Pi''' is the name for the Greek letter <big><big><math>\pi</math></big></big>, which corresponds to the English letter '''p.'''

<big><math>\pi</math></big> is also the symbol used in mathematics for the ratio between the diameter of a circle and its circumference, and which appears in many other places.

In the Bible, 1 Kings 7:23 contains the famous passage "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it round about." This quotation predates Greek mathematics and is an example of the wisdom contained in the bible. Assuming the "sea" is perfectly circular, this would equate Pi to an exact 3. As a result, some people use this as "proof" the Bible's fallibility. However, the Bible only says that the "sea" is ''round'', not that it is ''circular''.

<big><math>\pi</math></big> is an [[irrational number]]; this means that it cannot be expressed as a fraction, and (therefore) cannot be expressed exactly as a decimal no matter how many decimal places it is carried out to.

The value of <big><math>\pi</math></big> is approximately 3.14159 in decimal. This value is precise enough for almost all ordinary purposes; it can, for example, be used to calculate the circumference of the Earth with an error of only 350 feet.

In hexadecimal, <big><math>\pi</math></big> is approximately 3.243f.

For rough purposes, the fraction 22/7 (= 3.14285...) is sometimes used.

To some extent, the progress of mathematics—or at least of computation—can be gauged by the progress in the number of digits to which <big><math>\pi</math></big> has been calculated. In 1873 Abraham Shanks spent twenty years calculating <big><math>\pi</math></big> to 707 places, but unfortunately made a mistake in his calculation and only 527 of them were correct. When electronic computers were developed, <big><math>\pi</math></big> was soon calculated to tens of thousands, millions, and billions of places. As of 2002, the record is held by Yasumasa Kanada of Tokyo University at 1,241,100,000,000 digits. That result was never printed out.

Papyrys of Ahmes, dated c. 1650 B.C.E. circa 1000 years before Book of Kings, shows that ancient Egyptians had value 3 1/6 = 3.166666667. Same goes with Babylonian value from same time <big><math>\pi</math></big> 3 1/8 = 3.125(Boyer, A History of Mathematics, 2nd Edition).

Memorizing <big><math>\pi</math></big> is a challenge that appeals to some people. Mnemonics have been devised. Counting the letters in the phrase "Now I want a drink—alcoholic, of course" gives <big><math>\pi</math></big> to seven places (which is more than enough for all ordinary purposes). Numerous other mnemonics of this kind have been devised; in 1995, Michael Keith wrote one entitled [http://users.aol.com/s6sj7gt/mikerav.htm Near a Raven] which simultaneously parodies [[Edgar Allen Poe]]'s poem ''The Raven,'' while encoding <big><math>\pi</math></big> to 740 places.

March 14 marks Pi Day, a holiday on which the mathematical constant is celebrated. The date comes from the first three digits of pi; some people begin their celebration at 1:59 pm, derived from the following three digits.

[[Category:Mathematics]]

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United States of America

Pi