text:
Bekenstein bound

In physics, the Bekenstein bound (named after Jacob Bekenstein) is an upper limit on the thermodynamic entropy S, or Shannon entropy H, that can be contained within a given finite region of space which has a finite amount of energy—or conversely, the maximum amount of information required to perfectly describe a given physical system down to the quantum level. It implies that the information of a physical system, or the information necessary to perfectly describe that system, must be finite if the region of space and the energy are finite.

Equations
The universal form of the bound was originally found by Jacob Bekenstein in 1981 as the inequality $$S \leq \frac{2 \pi k R E}{\hbar c},$$ where S is the entropy, k is the Boltzmann constant, R is the radius of a sphere that can enclose the given system, E is the total mass–energy including any rest masses, ħ is the reduced Planck constant, and c is the speed of light. Note that while gravity plays a significant role in its enforcement, the expression for the bound does not contain the gravitational constant G, and so, it ought to apply to quantum field theory in curved spacetime.

The Bekenstein–Hawking boundary entropy of three-dimensional black holes exactly saturates the bound. The Schwarzschild radius is given by $$r_{\rm s} = \frac{2 G M}{c^2},$$ and so the two-dimensional area of the black hole's event horizon is $$A = 4 \pi r_{\rm s}^2 = \frac{16 \pi G^2 M^2}{c^4},$$ and using the Planck length $$l_{\rm P}^2 = \hbar G/c^3,$$ the Bekenstein–Hawking entropy is $$S = \frac{kA}{4 \ l_{\rm P}^2} = \frac{4 \pi k G M^2}{\hbar c}.$$

One interpretation of the bound makes use of the microcanonical formula for entropy, $$S = k \log \Omega,$$ where $$\Omega$$ is the number of energy eigenstates accessible to the system. This is equivalent to saying that the dimension of the Hilbert space describing the system is $$\dim \mathcal{H} = \exp \left(\frac{2\pi R E}{\hbar c}\right).$$

The bound is closely associated with black hole thermodynamics, the holographic principle and the covariant entropy bound of quantum gravity, and can be derived from a conjectured strong form of the latter.

Origins
Bekenstein derived the bound from heuristic arguments involving black holes. If a system exists that violates the bound, i.e., by having too much entropy, Bekenstein argued that it would be possible to violate the second law of thermodynamics by lowering it into a black hole. In 1995, Ted Jacobson demonstrated that the Einstein field equations (i.e., general relativity) can be derived by assuming that the Bekenstein bound and the laws of thermodynamics are true. However, while a number of arguments were devised which show that some form of the bound must exist in order for the laws of thermodynamics and general relativity to be mutually consistent, the precise formulation of the bound was a matter of debate until Casini's work in 2008.

The following is a heuristic derivation that shows $$S \leq K\frac{kRE}{\hbar c} $$ for some constant $$K$$. Showing that $$K = 2\pi$$ requires a more technical analysis.

Suppose we have a black hole of mass $$M$$, then the Schwarzschild radius of the black hole is $$R_{bh} \sim \frac{GM}{c^2}$$, and the Bekenstein–Hawking entropy of the black hole is $$\sim \frac{kc^3 R_{bh}^2}{\hbar G} \sim \frac{kGM^2}{\hbar c}$$.

Now take a box of energy $$E$$, entropy $$S$$, and side length $$R$$. If we throw the box into the black hole, the mass of the black hole goes up to $$M+\frac{E}{c^2}$$, and the entropy goes up by $$\frac{kGME}{\hbar c^3}$$. Since entropy does not decrease, $$\frac{kGME}{\hbar c^3}\gtrsim S$$.

In order for the box to fit inside the black hole, $$R \lesssim \frac{GM}{c^2} $$. If the two are comparable, $$R \sim \frac{GM}{c^2} $$, then we have derived the BH bound: $$S \lesssim \frac{kRE}{\hbar c} $$.

Proof in quantum field theory
A proof of the Bekenstein bound in the framework of quantum field theory was given in 2008 by Casini. One of the crucial insights of the proof was to find a proper interpretation of the quantities appearing on both sides of the bound.

Naive definitions of entropy and energy density in Quantum Field Theory suffer from ultraviolet divergences. In the case of the Bekenstein bound, ultraviolet divergences can be avoided by taking differences between quantities computed in an excited state and the same quantities computed in the vacuum state. For example, given a spatial region $$V$$, Casini defines the entropy on the left-hand side of the Bekenstein bound as $$S_V = S(\rho_V) - S(\rho^0_V) = - \mathrm{tr}(\rho_V \log \rho_V) + \mathrm{tr}(\rho_V^0 \log \rho_V^0)$$ where $$S(\rho_V)$$ is the Von Neumann entropy of the reduced density matrix $$\rho_V$$ associated with $$V$$ in the excited state $$\rho$$, and $$S(\rho^0_V)$$ is the corresponding Von Neumann entropy for the vacuum state $$\rho^0$$.

On the right-hand side of the Bekenstein bound, a difficult point is to give a rigorous interpretation of the quantity $$2\pi R E$$, where $$R$$ is a characteristic length scale of the system and $$E$$ is a characteristic energy. This product has the same units as the generator of a Lorentz boost, and the natural analog of a boost in this situation is the modular Hamiltonian of the vacuum state $$K=-\log \rho_V^0$$. Casini defines the right-hand side of the Bekenstein bound as the difference between the expectation value of the modular Hamiltonian in the excited state and the vacuum state, $$ K_V = \mathrm{tr}(K \rho_V) - \mathrm{tr}(K \rho^0_V). $$

With these definitions, the bound reads $$ S_V \leq K_V, $$ which can be rearranged to give $$\mathrm{tr}(\rho_V \log \rho_V) - \mathrm{tr}(\rho_V \log \rho_V^0) \geq 0. $$

This is simply the statement of positivity of quantum relative entropy, which proves the Bekenstein bound.

However, the modular Hamiltonian can only be interpreted as a weighted form of energy for conformal field theories, and when V is a sphere.

This construction allows us to make sense of the Casimir effect where the localized energy density is lower than that of the vacuum, i.e. a negative localized energy. The localized entropy of the vacuum is nonzero, and so, the Casimir effect is possible for states with a lower localized entropy than that of the vacuum. Hawking radiation can be explained by dumping localized negative energy into a black hole.

title: Bekenstein bound


text:
About–Picard law

The 2001 About–Picard law [abu pika:r], officially Law No. 2001-504 of June 12, 2001, aimed at strengthening the prevention and repression of sectarian movements that undermine human rights and fundamental freedoms (loi n° 2001-504 du 12 juin 2001 tendant à renforcer la prévention et la répression des mouvements sectaires portant atteinte aux droits de l'homme et aux libertés fondamentales ) is French legislation passed by the National Assembly in 2000. The law is targeted at sects and movements deemed cultic (mouvements sectaires) that "undermine human rights and fundamental freedoms", as well as "mental manipulation". The law has caused controversy internationally, with some commentators alleging that it infringes on religious freedom while proponents contend that it reinforces religious freedom.

Background
Freedom of religion and separation of church and state have formed part of the French idea of the state since at least the French Revolution and in some ways long before, since the 16th-century period of the Reformation and of the Wars of Religion. Separation of religion and state in France takes the form of laïcité, by which political power avoids interference in the sphere of religious dogma, and religion avoids interference in public policies. The French understand "freedom of religion" primarily as the freedom of the individual to believe or not to believe what any religion teaches. Also, because of a long history of one single dominating church (the Catholic Church), the French state sees its duty less in protecting religion from state interference than in protecting the individual from interference by religion.

In the wake of the Order of the Solar Temple murders and suicides, the French Parliament established the Parliamentary Commission on Cults in France to investigate cults. In December 1995, the Commission delivered a report on cults which caused much controversy, some of it due to a list extracted from a report by the French National Police on purported cults.

Following the recommendations of the report, Prime Minister Alain Juppé set up in 1996 the "Interministerial Board of Observation of sects", followed in 1998 by the "Interministerial Mission in the Fight Against Sects" (MILS). In 2002 the "Interministerial Monitoring Mission Against Sectarian Abuses" (MIVILUDES) replaced MILS. Other action of the French government against potential abuses by cults resulted in the passing of the About–Picard law.

The About–Picard law
Commentators often refer to the Law 2001-504 of June 12, 2001 as the About–Picard law, from the name of its rapporteurs (parliamentarians who report upon the draft law), senator Nicolas About (UDF center-right party) and deputy Catherine Picard (PS center-left party).

The French parliament adopted the law with broad cross-party support under the government of center-right president Jacques Chirac and socialist prime minister Lionel Jospin.

Article 223-15-2 of Penal code: (Act no. 2001-504 of June 12, 2001, article 10 Official Journal of June 13, 2001; Ordinance No. 2000-916 of September 19, 2000, article 3 Official Journal of September 22, 2000, into force January 1, 2002)

"Fraudulently abusing the ignorance or state of weakness of a minor, or of a person whose particular vulnerability, due to age, sickness, infirmity, to a physical or psychological disability or to pregnancy, is apparent or known to the offender, or abusing a person in a state of physical or psychological dependency resulting from serious or repeated pressure or from techniques used to affect his judgement, in order to induce the minor or other person to act or abstain from acting in any way seriously harmful to him, is punished by three years' imprisonment and a fine of €375,000. Where the offence is committed by the legal or de facto manager of a group that carries out activities the aim or effect of which is to create, maintain or exploit the psychological or physical dependency of those who participate in them, the penalty is increased to five years' imprisonment and to a fine of €750,000."

The additional penalties that natural or legal persons may incur are mentioned in the following articles 223-15-3 and 4.

Main points
Notable new points introduced by the law include: The initial draft of the About–Picard law included the criminalization of "mental manipulation". Many organizations criticised this clause for its vagueness. Minister of Justice Élisabeth Guigou pushed for the removal of this clause, which the legislators excluded from the final version of the law. However, the law makes it a crime to defraud a person weakened by illness, old age, etc., but also of a person in a state of psychological or physical subjection resulting from grave or reiterated pressures or techniques able to alter judgement.
 * In the case of certain crimes, the law extends legal responsibility from individuals to organizations (corporations, associations, and other legal entities...).
 * Courts can order the dissolution of organizations if they or their executives have been found guilty of these crimes.

Application
There was one famous application of the law since its adoption: that of Arnaud Mussy, leader of the Néo-Phare (New Lighthouse) cult. Mussy, who claims that he is the Christ, had announced imminent apocalypse, resulting in the suicide of one of his followers and the attempted suicides of two others, who were severely wounded in 2001. The criminal court in Nantes sentenced him to three years in prison and 90,000 FF damages in November 2004. It ruled that he had "abused fraudulently the state of ignorance and weakness of several persons in the state of bodily or mental dependence". A higher court in Rennes confirmed the sentence in July 2005.

Criticism
The French government, when challenged on issues of religious discrimination, states that it has no concern in any way with religious doctrine per se. The government has taken the position that it will deal with the concrete consequences of cult affiliation, especially with respect to children. The government sees this as particularly important in the light of past abuse committed in some criminal cults, such as sexual slavery and mass suicide. According to government sources, none of the criteria listed in related government documents on sects discuss theology; they only focus on the actions and the methods of the groups.

Critics of the law see this as merely a semantic change and maintain that no empirical studies support claims of the use of techniques of coercive persuasion by NRMs.

Reactions inside France
The Bishop of Soissons, Marcel Herriot, defended the law on June 25, 2000, asserting it was necessary to protect by law persons, family, society and religions themselves from sects that are violating fundamental freedoms and human dignity.

Some groups claim that the Parliamentary Reports and the controversy surrounding the About–Picard law have created an unhealthy atmosphere, resulting in minority religious groups suffering from excessively strict, uneven, or even abusive discrimination in the application of other laws by local authorities. For example, the group Coordination des Associations et Particuliers pour la Liberté de Conscience (Co-ordination of Associations and Individuals for Freedom of Conscience) requested the repeal of the law, asserting laws should not specify groups as "sectarian" or "cultic" as, in a democracy. However, an OSCE report has described this group as a partisan

The umbrella association of French Jehovah's Witnesses sued the French government in the ECHR in case #53430/99, alleging that the publication of the parliamentary reports and the enactment of the About–Picard law infringed its civil rights. The court rejected the application.

In other cases (#53934/00), the Court affirmed that the publication of a Parliamentary Report disparaging to some groups did not constitute an infringement of human rights, even though these groups were not given a legal recourse for the removal of their name from the report.

Human rights activists dubbed the law "un délit d'opinion" (a thought crime).

Statements by the Council of Europe
Forty different religious and human-rights groups submitted a petition to the Council of Europe's Parliamentary Assembly. This petition led to a report (Report 9612 of the Committee on Legal Affairs and Human Rights of Europe) containing an expert paper by Swiss professor Joseph Voyame, who concluded:
 * "On the basis of the foregoing, I conclude that the French Law of 12 June 2001 is not incompatible with the Council of Europe’s values."

Voyame deduces that the law clearly responds to a need, that the measure of dissolution appears radical, but also effective and reliable, and that judicial guarantees surround it. He also discusses the title with its mentioning of "cultic groups", but comes to the conclusion that the uncertainty regarding the definition has little importance:

The title is undeniably part of the [Act], but has no legislative authority in itself. Although it may be useful for the purposes of interpretation, it cannot be used in making a ruling that runs counter to a clear legal provision ... . As we will see, [Sections] 1, 19 and 20 of this [Act] identify the targeted incorporated organizations and groups with the greatest possible precision. It is these standard-setting texts that are decisive.

The report discussed several objections regarding the word "secte" (cult):

... the word ‘sect’ has taken on an extremely pejorative connotation. In the eyes of the public, it stigmatises movements whose activities are dangerous either for their members or for society. Today, the world contains dozens, perhaps even hundreds, of groups both large and small, all with various beliefs and observances, which are not necessarily dangerous or prejudicial to freedom. It is true that among these groups are some which have committed criminal acts. Nevertheless, the existence of a few dangerous movements is not enough to condemn all the rest (...)

The report concluded:

The act for the most part simply reiterates existing provisions in the Criminal Code, the Code of Consumption, the Code of Public Health and the New Code of Civil Procedure and does so for a precise purpose in conformity with the European Convention on Human Rights, as we have just seen. Consequently, even if it had been possible to achieve the same objective by recourse to existing provisions, there is nothing to prevent the passing of an act which has the advantage of grouping together all the provisions necessary to achieve that objective.

In November 2002, the Council of Europe passed a resolution inviting the Government of France to reconsider the About–Picard Law and to clarify certain terms in the law. It referred, however, to the Recommendation 1412 (1999) on the illegal activities of sects, where it had concluded that it was "essential to ensure that the activities of groups, whatever religious, esoteric or spiritual description they adopted, were in keeping with the principles of democratic societies and, in particular, the provisions of Article 9 of the European Convention on Human Rights (ECHR)." and it stated that "ultimately, should the case arise, it will be for the European Court of Human Rights, and it alone, to say whether or not this law is compatible with the European Convention on Human Rights.".

Reactions outside of France
In an open letter dated June 2000 to Alain Vivien about religious freedom in France, Aaron Rhodes, Executive Director of the International Helsinki Federation for Human Rights (IHFHR), wrote:

We question ourselves how such a law can claim to guarantee human rights when it goes against the rights of association, expression, religion and conscience; when it puts in danger the right of minorities and maintains prejudices that are so incompatible with the concept of tolerance intrinsic to that of human rights. France must deal with its responsibilities and obligations as a signatory for the International Conventions and respect the European laws and its interpretation by the Court of Strasbourg, before one of its citizens become a victim of discrimination due to the law which you propose.

Alain Vivien responded: "[The IHFHR] seems today to have passed into the hands of Scientologists and perhaps other transnational organizations". Aaron Rhodes then acknowledged that the Moscow office of the IHFHR had received funding from the Church of Scientology to print a leaflet about religious freedom in Russia, and voiced his astonishment at the charge. Rhodes voiced his embarrassment: "[...]for you and your fellow French citizens by your recourse to methods of denunciations and insinuations that remind us of those sometimes used by totalitarian and backward regimes."

Reaction of the government of the United States of America
Some groups sought the help of their governments to fight what they saw as religious intolerance in France. In the United States, the Church of Scientology utilised pressure groups against the French government, and had some success with the Clinton administration, which repeatedly brought the matter before the French government.

According to pastor Jean-Arnold de Clermont, head of the French Protestant federation and himself a strong critic of the first draft of the law, the complaints originating in the United States concerning religious freedom in France were largely based on biased, poor information.

According to a newspaper article published in The Guardian in June 2000, the French government considered American interference regarding religious freedom in France as unwarranted meddling by the US government in France's internal affairs. Paul Webster wrote that President Jacques Chirac told Clinton that religious freedom would no longer be a subject for bilateral presidential talks, "in the light of what has been officially described as 'shocking' White House support for Scientologists and Moonies". The French government also described the United States Congress's introduction of laws protecting religious freedom internationally as "an unacceptable intrusion into internal affairs". Alain Vivien, former chairman of the French ministerial mission to combat the influence of cults (MILS), and the president of the Centre Contre les Manipulations Mentales (Centre Against Mental Manipulation), said many observers believed that Clinton was making his peace with big religious movements, "because they offer an indispensable source of political financing", and that with the help of Scientologists, cults were infiltrating UN and European human rights associations and collaborating on virulent reports against France's policies.

The French did not alter their law following these requests; and the claims and actions of the US government regarding the religious situation in France largely ceased with the Bush administration.

Some critics of French legislation have voiced concerns that countries which do not have the same legal safeguards and constitutional rights as France may emulate this legislation. In the words of a US official:

Yet the law itself remains problematic not only because of the threat the language carries in France, but because it is even now being considered for emulation by countries that lack France’s commitment to rule of law and human rights. Such a model serves only too well as cover for those nations who persecute under the guise of law enforcement.

On September 15, 2006, the United States Bureau of Democracy, Human Rights, and Labor released a report on religious freedom in France. This report noted that "The constitution provides for freedom of religion, and the Government generally respected this right in practice." It reported mostly anonymous concerns over repression of religious freedom in France, notably in regards to what the report referred to in one case as "cult groups", as well as the law banning religious symbols in schools, and rising anti-semitism in France.

Opinions

 * Baker, Eileen, Religious Movements: Cult and Anticult Since Jonestown, Annual Review of Sociology, Vol. 12: pp. 329–346, 1986
 * Introvigne, Massimo and Richardson, James T., "Western Europe, Postmodernity, and the Shadow of the French Revolution: A Response to Soper and Robbins", Symposium on Government Policy Toward Unconventional Religions in Europe, Journal for the Scientific Study of Religion, Vol. 40 I.2 p. 181, June 2001
 * Introvigne, Massimo. & Richardson, James T., "Brainwashing" Theories in European Parliamentary and Administrative Reports on "Cults" and "Sects, Symposium on Government Policy Toward Unconventional Religions in Europe, Journal for the Scientific Study of Religion, Vol. 40 I.2 p. 43, June 2001
 * Palmer, Susan J. The secte Response to Religious Discrimination: Subversives, Martyrs, or Freedom Fighters in the French Sect Wars?, article published in the book edited by Phillip Charles Lucas and Thomas Robbins: New Religious Movements in the 21st Century published by Routledge (2004) ISBN 0-415-96577-2
 * Wybraniec, John & Finke Roger, Religious Regulation and the Courts: The Judiciary's Changing Role in Protecting Minority Religions from Majoritarian Rule, Journal for the Scientific Study of Religion, Vol.40 I.3 p. 427, September 2001
 * Marci Hamilton: Why the U.S.'s International Religious Freedom Commission Is Harming Its Status In the World Community
 * Dominique Decherf: French Views of Religious Freedom
 * Stephen A. Kent: The French and German versus American Debate Over New Religions, Scientology, and Human Rights
 * Robert Jacques: Religious liberty and French secularism
 * Marci Hamilton: Why the U.S.'s International Religious Freedom Commission Is Harming Its Status In the World Community

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: About–Picard law


text:
Cuna

Cuna may refer to:

 * Credit Union National Association
 * CUNA Credit Union, a defunct credit union based in Madison, Wisconsin
 * CUNA Mutual Group, a mutual insurance company based in Madison, Wisconsin
 * Kuna (people), of Panama and Colombia
 * Kuna language, spoken by the Kuna people
 * Cuna (bivalve), a genus of bivalve mollusc

title: Cuna


text:
Talk:Multiverse Authority

I'm the person that created this article and I created the wikipedia version before I did the other Joinee version. Therefore it must stay on this encyclopedia. -- Yulaw 18:27, 8 Feb 2005 (UTC)

title: Talk:Multiverse Authority


text:
User talk:Mine15

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:28, 8 Feb 2005 (UTC)

Welcome
--Slowking Man 01:52, Feb 9, 2005 (UTC)

title: User talk:Mine15


text:
User talk:Katie04

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:30, 8 Feb 2005 (UTC)

Welcome
--Slowking Man 01:55, Feb 9, 2005 (UTC)

title: User talk:Katie04


text:
Warrosquyoake Shire

Warrosquoake Shire (with numerous variant spellings, including Warrascoyack, Warrascocke and "Warwick Squeak") was officially formed in 1634 in the Virginia colony, but had already been known as "Warascoyack County" before this. It was named for an Algonquian-speaking tribe that was part of the Powhatan Confederacy. The county was renamed Isle of Wight County in 1637, after an island in the English Channel.

History
Shortly after the establishment of Jamestown in 1607, English settlers explored and began settling areas adjacent to Hampton Roads. The shoreline region of the Warrascoyack River was occupied by the Warraskoyak tribe of the Powhatan Confederacy, under their weroance, Tackinekintaco. In December 1608, Captain John Smith left his page Samuel Collier with Tackinekintaco to learn the language.

The main Warraskoyak village was located where present-day Smithfield, Virginia developed. A satellite village called Mokete was at Pagan Point, and another called Mathomank was on Burwell's Bay, led by a sub-weroance named Sasenticum.

The first English plantation in the region, dating to 1618, was that of Puritan merchant Christopher Lawne. Several other Puritans also settled nearby. Edward Bennett, an English merchant and a free member of the London Company, was among those who got a land patent and founded his plantation in 1621. He named his plantation Warrosquoake, after the river which the indigenous people called by that name. His plantation suffered high fatalities of colonists in the Great Massacre of 1622, losing 53 persons. A total of the 347 colonists were killed that day, as the Powhatan tribes tried to kill and expel the English.

The surviving English retreated to a small number of plantations near Jamestown until an expedition was mounted against the Warraskoyak and Nansemond peoples. The colony built a fort nearby Bennett's plantation. In reprisals during the following years, they drove off the Native Americans from their villages. A census of settlers at Bennett's plantation on 16 February 1623 showed a total of "33, including 4 negroes", with 20 settlers recorded at nearby Basse's Choice. A year later, a census showed a total population of 31 settlers for the region.

Two of Bennett's brothers had managed his plantation and died in the colony, in 1624 and 126. Edward Bennett finally went to Virginia himself for a time, representing his plantation in the 1628 House of Burgesses, then returned to England.

His nephew Richard Bennett came out to manage the plantation, and stayed in the colony. He became a large landowner and eventually governor of the colony. In 1629, the "County of Warascoyack" was represented in the House of Burgeses was represented by Richard Bennett, Captain Nathaniel Basse (who owned Basse's Choice), Thomas Jordan and two others, all Puritans. This was the Puritans' strongest representation in a colony dominated by members of the Anglican Church.

By 1634, by order of the King of England, Charles I, eight shires of Virginia were formed, with a total population of 4,914 settlers. Warrosquoake Shire included 522 persons at the time. It and Accomac Shire were the only shires given Native-American names, honoring the friendly tribes nearby. In 1637 the English renamed it Isle of Wight County, after an island of the same name in the English channel between England and France. They also renamed the Warrosquoake river the Pagan River.

During the three years when it was officially Warrosquoake Shire, Richard Bennett led the small Puritan community to neighboring Nansemond. They later moved to Maryland when under religious pressure in Virginia. He returned during the Cromwellian period with a Parliamentary Commission to take over from the Royalist government and served as Governor of Virginia.

As population increased, land was drawn from Warrosquoake Shire and Isle of Wight County to form many other counties to the immediate southwest, in the region now defined as Southside Virginia. The counties of Isle of Wight, Southampton, Greensville and Brunswick were all created within the limits of what had been Warrosquoake Shire.

title: Warrosquyoake Shire


text:
Wikipedia:Articles for deletion/Shane Turner

 This page is an archive of the discussion about the proposed deletion of the article below. This page is no longer live. Further comments should be made on the article's talk page rather than here so that this page is preserved as an historic record. The result of the debate was speedy delete. —Korath (Talk) 21:01, Feb 17, 2005 (UTC)

Shane Turner
Vanity page for a non-notable drummer from Ontario. Carrp | Talk 18:31, 8 Feb 2005 (UTC)
 * Delete He's tough to Google, sharing a name with both a baseball player and the bassist from Brundlefly. Since the anonymous user who wrote this article has a long history of vandalism, including replacing whole articles with curse words and telling wikipedia to go F*** itself, it would seem to follow that this is likely vandalism too, or at least not notable. Andrew Lenahan - St ar bli nd  19:13, Feb 8, 2005 (UTC)
 * Delete, aside from the PoV, article provides no evidence of the encyclopedic claims made. Wyss 19:15, 8 Feb 2005 (UTC)
 * Delete, unless someone (i) can verify that he's played with at least one notable band, and (ii) deletes the nonsense on the current page and replaces it with real information. CJCurrie 22:42, 8 Feb 2005 (UTC)
 * Delete Seems like a candidate for speedy deletion. Spinboy 22:46, 8 Feb 2005 (UTC)
 * Delete. I would have speedy deleted it, since it's a recreation, except nothing in this version is the same as the last version except for their both being Canadian.  RickK 00:29, Feb 9, 2005 (UTC)
 * Delete, not notable, possible artist vanity. Megan1967 01:42, 9 Feb 2005 (UTC)
 * Not notable + every other edit made by the user who created this article was vandalism. I've speedied. Bearcat 05:35, 9 Feb 2005 (UTC)

This page is now preserved as an archive of the debate and, like some other VfD subpages, is no longer 'live'. Subsequent comments on the issue, the deletion, or the decision-making process should be placed on the relevant 'live' pages. Please do not edit this page.


text:
User talk:Jubes09

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:32, 8 Feb 2005 (UTC)

Welcome
--Slowking Man 01:57, Feb 9, 2005 (UTC)

title: User talk:Jubes09


text:
User talk:B-rad

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:33, 8 Feb 2005 (UTC)

Welcome
--Slowking Man 01:58, Feb 9, 2005 (UTC)

title: User talk:B-rad


text:
User talk:Woodchuck19

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:34, 8 Feb 2005 (UTC)

Welcome
--Slowking Man 01:58, Feb 9, 2005 (UTC)

title: User talk:Woodchuck19


text:
Castorama

Castorama is a French retailer of DIY and home improvement tools and supplies, headquartered in Templemars, France, and is part of the British group Kingfisher plc, which has 101 stores in France and 90 in Poland. The company became a subsidiary of Kingfisher plc in May 2002, along with Castorama's own subsidiary Brico Dépôt.

Some outlets have been converted or relocated under the Brico Dépôt format "DIY warehouse", based on the B&Q Warehouse fascia in the United Kingdom. In February 2009, Kingfisher sold 31 stores of Castorama in Italy to French retailer Leroy Merlin.

In 1969, Christian Dubois founded in Englos, near Lille, France's first large-scale (5000 m2) DIY store. The rapid expansion of the chain meant that 20 years later Castorama had 80 stores in France.

A second store opened in 1972, followed by a third in 1973. In 1975, Castorama set up shop in Plaisir (Yvelines), outside its home region. In 1977, Castorama launched its famous slogan "Chez Casto, y a tout ce qu'il faut!", a phrase coined by Lucky Blondo and taken up two years later by Pierre Perret.

title: Castorama


text:
Real coordinate space

In mathematics, the real coordinate space or real coordinate n-space, of dimension $n$, denoted $R^{n}$ or $\R^n$, is the set of all ordered $n$-tuples of real numbers, that is the set of all sequences of $n$ real numbers, also known as coordinate vectors. Special cases are called the real line $R^{1}$, the real coordinate plane $R^{2}$, and the real coordinate three-dimensional space $R^{3}$. With component-wise addition and scalar multiplication, it is a real vector space.

The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension $n$, $E^{n}$ (Euclidean line, $E$; Euclidean plane, $E^{2}$; Euclidean three-dimensional space, $E^{3}$) form a real coordinate space of dimension $n$.

These one to one correspondences between vectors, points and coordinate vectors explain the names of coordinate space and coordinate vector. It allows using geometric terms and methods for studying real coordinate spaces, and, conversely, to use methods of calculus in geometry. This approach of geometry was introduced by René Descartes in the 17th century. It is widely used, as it allows locating points in Euclidean spaces, and computing with them.

Definition and structures
For any natural number $n$, the set $R^{n}$ consists of all $n$-tuples of real numbers ($R$). It is called the "$n$-dimensional real space" or the "real $n$-space".

An element of $R^{n}$ is thus a $n$-tuple, and is written $$(x_1, x_2, \ldots, x_n)$$ where each $x_{i}$ is a real number. So, in multivariable calculus, the domain of a function of several real variables and the codomain of a real vector valued function are subsets of $R^{n}$ for some $n$.

The real $n$-space has several further properties, notably:
 * With componentwise addition and scalar multiplication, it is a real vector space. Every $n$-dimensional real vector space is isomorphic to it.
 * With the dot product (sum of the term by term product of the components), it is an inner product space. Every $n$-dimensional real inner product space is isomorphic to it.
 * As every inner product space, it is a topological space, and a topological vector space.
 * It is a Euclidean space and a real affine space, and every Euclidean or affine space is isomorphic to it.
 * It is an analytic manifold, and can be considered as the prototype of all manifolds, as, by definition, a manifold is, near each point, isomorphic to an open subset of $R^{n}$.
 * It is an algebraic variety, and every real algebraic variety is a subset of $R^{n}$.

These properties and structures of $R^{n}$ make it fundamental in almost all areas of mathematics and their application domains, such as statistics, probability theory, and many parts of physics.

The domain of a function of several variables
Any function $f(x_{1}, x_{2}, ..., x_{n})$ of $n$ real variables can be considered as a function on $R^{n}$ (that is, with $R^{n}$ as its domain). The use of the real $n$-space, instead of several variables considered separately, can simplify notation and suggest reasonable definitions. Consider, for $n = 2$, a function composition of the following form: $$ F(t) = f(g_1(t),g_2(t)),$$ where functions $g_{1}$ and $g_{2}$ are continuous. If then $F$ is not necessarily continuous. Continuity is a stronger condition: the continuity of $f$ in the natural $∀x_{1} ∈ R : f(x_{1}, ·)$ topology (discussed below), also called multivariable continuity, which is sufficient for continuity of the composition $F$.
 * $x_{2}$ is continuous (by $∀x_{2} ∈ R : f(·, x_{2})$)
 * $x_{1}$ is continuous (by $R^{2}$)

Vector space
The coordinate space $R^{n}$ forms an $n$-dimensional vector space over the field of real numbers with the addition of the structure of linearity, and is often still denoted $R^{n}$. The operations on $R^{n}$ as a vector space are typically defined by $$\mathbf x + \mathbf y = (x_1 + y_1, x_2 + y_2, \ldots, x_n + y_n)$$ $$\alpha \mathbf x = (\alpha x_1, \alpha x_2, \ldots, \alpha x_n).$$ The zero vector is given by $$\mathbf 0 = (0, 0, \ldots, 0)$$ and the additive inverse of the vector $x$ is given by $$-\mathbf x = (-x_1, -x_2, \ldots, -x_n).$$

This structure is important because any $n$-dimensional real vector space is isomorphic to the vector space $R^{n}$.

Matrix notation
In standard matrix notation, each element of $R^{n}$ is typically written as a column vector $$\mathbf x = \begin{bmatrix} x_1 \\ x_2 \\ \vdots \\ x_n \end{bmatrix}$$ and sometimes as a row vector: $$\mathbf x = \begin{bmatrix} x_1 & x_2 & \cdots & x_n \end{bmatrix}.$$

The coordinate space $R^{n}$ may then be interpreted as the space of all $n × 1$ column vectors, or all $1 × n$ row vectors with the ordinary matrix operations of addition and scalar multiplication.

Linear transformations from $R^{n}$ to $R^{m}$ may then be written as $m × n$ matrices which act on the elements of $R^{n}$ via left multiplication (when the elements of $R^{n}$ are column vectors) and on elements of $R^{m}$ via right multiplication (when they are row vectors). The formula for left multiplication, a special case of matrix multiplication, is: $$(A{\mathbf x})_k = \sum_{l=1}^n A_{kl} x_l$$

Any linear transformation is a continuous function (see below). Also, a matrix defines an open map from $R^{n}$ to $R^{m}$ if and only if the rank of the matrix equals to $m$.

Standard basis
The coordinate space $R^{n}$ comes with a standard basis: $$\begin{align} \mathbf e_1 & = (1, 0, \ldots, 0) \\ \mathbf e_2 & = (0, 1, \ldots, 0) \\ & {}\;\; \vdots \\ \mathbf e_n & = (0, 0, \ldots, 1) \end{align}$$

To see that this is a basis, note that an arbitrary vector in $R^{n}$ can be written uniquely in the form $$\mathbf x = \sum_{i=1}^n x_i \mathbf{e}_i.$$

Orientation
The fact that real numbers, unlike many other fields, constitute an ordered field yields an orientation structure on $R^{n}$. Any full-rank linear map of $R^{n}$ to itself either preserves or reverses orientation of the space depending on the sign of the determinant of its matrix. If one permutes coordinates (or, in other words, elements of the basis), the resulting orientation will depend on the parity of the permutation.

Diffeomorphisms of $R^{n}$ or domains in it, by their virtue to avoid zero Jacobian, are also classified to orientation-preserving and orientation-reversing. It has important consequences for the theory of differential forms, whose applications include electrodynamics.

Another manifestation of this structure is that the point reflection in $R^{n}$ has different properties depending on evenness of $n$. For even $n$ it preserves orientation, while for odd $n$ it is reversed (see also improper rotation).

Affine space
$R^{n}$ understood as an affine space is the same space, where $R^{n}$ as a vector space acts by translations. Conversely, a vector has to be understood as a "difference between two points", usually illustrated by a directed line segment connecting two points. The distinction says that there is no canonical choice of where the origin should go in an affine $n$-space, because it can be translated anywhere.

Convexity

In a real vector space, such as $(n + 1)$, one can define a convex cone, which contains all non-negative linear combinations of its vectors. Corresponding concept in an affine space is a convex set, which allows only convex combinations (non-negative linear combinations that sum to 1).

In the language of universal algebra, a vector space is an algebra over the universal vector space $(n + 1)$ of finite sequences of coefficients, corresponding to finite sums of vectors, while an affine space is an algebra over the universal affine hyperplane in this space (of finite sequences summing to 1), a cone is an algebra over the universal orthant (of finite sequences of nonnegative numbers), and a convex set is an algebra over the universal simplex (of finite sequences of nonnegative numbers summing to 1). This geometrizes the axioms in terms of "sums with (possible) restrictions on the coordinates".

Another concept from convex analysis is a convex function from $R^{n}$ to real numbers, which is defined through an inequality between its value on a convex combination of points and sum of values in those points with the same coefficients.

Euclidean space
The dot product $$\mathbf{x}\cdot\mathbf{y} = \sum_{i=1}^n x_iy_i = x_1y_1+x_2y_2+\cdots+x_ny_n$$ defines the norm $R^{∞}$ on the vector space $R^{n}$. If every vector has its Euclidean norm, then for any pair of points the distance $$d(\mathbf{x}, \mathbf{y}) = \|\mathbf{x} - \mathbf{y}\| = \sqrt{\sum_{i=1}^n (x_i - y_i)^2}$$ is defined, providing a metric space structure on $|x| = √x ⋅ x$ in addition to its affine structure.

As for vector space structure, the dot product and Euclidean distance usually are assumed to exist in $R^{n}$ without special explanations. However, the real $n$-space and a Euclidean $n$-space are distinct objects, strictly speaking. Any Euclidean $n$-space has a coordinate system where the dot product and Euclidean distance have the form shown above, called Cartesian. But there are many Cartesian coordinate systems on a Euclidean space.

Conversely, the above formula for the Euclidean metric defines the standard Euclidean structure on $R^{n}$, but it is not the only possible one. Actually, any positive-definite quadratic form $q$ defines its own "distance" $R^{n}$, but it is not very different from the Euclidean one in the sense that $$\exist C_1 > 0,\ \exist C_2 > 0,\ \forall \mathbf{x}, \mathbf{y} \in \mathbb{R}^n: C_1 d(\mathbf{x}, \mathbf{y}) \le \sqrt{q(\mathbf{x} - \mathbf{y})} \le C_2 d(\mathbf{x}, \mathbf{y}). $$ Such a change of the metric preserves some of its properties, for example the property of being a complete metric space. This also implies that any full-rank linear transformation of $R^{n}$, or its affine transformation, does not magnify distances more than by some fixed $√q(x − y)$, and does not make distances smaller than $R^{n}$ times, a fixed finite number times smaller.

The aforementioned equivalence of metric functions remains valid if $C_{2}$ is replaced with $1 / C_{1}$, where $M$ is any convex positive homogeneous function of degree 1, i.e. a vector norm (see Minkowski distance for useful examples). Because of this fact that any "natural" metric on $√q(x − y)$ is not especially different from the Euclidean metric, $M(x − y)$ is not always distinguished from a Euclidean $R^{n}$-space even in professional mathematical works.

In algebraic and differential geometry
Although the definition of a manifold does not require that its model space should be $R^{n}$, this choice is the most common, and almost exclusive one in differential geometry.

On the other hand, Whitney embedding theorems state that any real differentiable $m$-dimensional manifold can be embedded into $n$.

Other appearances
Other structures considered on $R^{n}$ include the one of a pseudo-Euclidean space, symplectic structure (even $n$), and contact structure (odd $n$). All these structures, although can be defined in a coordinate-free manner, admit standard (and reasonably simple) forms in coordinates.

$R^{2m}$ is also a real vector subspace of $R^{n}$ which is invariant to complex conjugation; see also complexification.

Polytopes in Rn
There are three families of polytopes which have simple representations in $R^{n}$ spaces, for any $n$, and can be used to visualize any affine coordinate system in a real $n$-space. Vertices of a hypercube have coordinates $C^{n}$ where each $x_{k}$ takes on one of only two values, typically 0 or 1. However, any two numbers can be chosen instead of 0 and 1, for example and 1. An $n$-hypercube can be thought of as the Cartesian product of $n$ identical intervals (such as the unit interval $[0,1]$) on the real line. As an $n$-dimensional subset it can be described with a system of $R^{n}$ inequalities: $$\begin{matrix} 0 \le x_1 \le 1 \\ \vdots \\ 0 \le x_n \le 1 \end{matrix}$$ for $[0,1]$, and $$\begin{matrix} \vdots \\ \end{matrix}$$ for $[−1,1]$.
 * x_1| \le 1 \\
 * x_n| \le 1

Each vertex of the cross-polytope has, for some $k$, the $x_{k}$ coordinate equal to ±1 and all other coordinates equal to 0 (such that it is the $k$th standard basis vector up to sign). This is a dual polytope of hypercube. As an $n$-dimensional subset it can be described with a single inequality which uses the absolute value operation: $$\sum_{k=1}^n |x_k| \le 1\,,$$ but this can be expressed with a system of $(x_{1}, x_{2}, ..., x_{n})$ linear inequalities as well.

The third polytope with simply enumerable coordinates is the standard simplex, whose vertices are $n$ standard basis vectors and the origin $2n$. As an $n$-dimensional subset it is described with a system of $2^{n}$ linear inequalities: $$\begin{matrix} 0 \le x_1 \\ \vdots \\ 0 \le x_n \\ \sum\limits_{k=1}^n x_k \le 1 \end{matrix}$$ Replacement of all "≤" with "<" gives interiors of these polytopes.

Topological properties
The topological structure of $(0, 0, ..., 0)$ (called standard topology, Euclidean topology, or usual topology) can be obtained not only from Cartesian product. It is also identical to the natural topology induced by Euclidean metric discussed above: a set is open in the Euclidean topology if and only if it contains an open ball around each of its points. Also, $n + 1$ is a linear topological space (see continuity of linear maps above), and there is only one possible (non-trivial) topology compatible with its linear structure. As there are many open linear maps from $R^{n}$ to itself which are not isometries, there can be many Euclidean structures on $R^{n}$ which correspond to the same topology. Actually, it does not depend much even on the linear structure: there are many non-linear diffeomorphisms (and other homeomorphisms) of $R^{n}$ onto itself, or its parts such as a Euclidean open ball or the interior of a hypercube).

$R^{n}$ has the topological dimension $n$.

An important result on the topology of $R^{n}$, that is far from superficial, is Brouwer's invariance of domain. Any subset of $R^{n}$ (with its subspace topology) that is homeomorphic to another open subset of $R^{n}$ is itself open. An immediate consequence of this is that $R^{n}$ is not homeomorphic to $R^{n}$ if $R^{m}$ – an intuitively "obvious" result which is nonetheless difficult to prove.

Despite the difference in topological dimension, and contrary to a naïve perception, it is possible to map a lesser-dimensional real space continuously and surjectively onto $R^{n}$. A continuous (although not smooth) space-filling curve (an image of $m ≠ n$) is possible.

n ≤ 1
Cases of $R^{n}$ do not offer anything new: $R^{1}$ is the real line, whereas $R^{0}$ (the space containing the empty column vector) is a singleton, understood as a zero vector space. However, it is useful to include these as trivial cases of theories that describe different $n$.

n = 2

The case of (x,y) where x and y are real numbers has been developed as the Cartesian plane P. Further structure has been attached with Euclidean vectors representing directed line segments in P. The plane has also been developed as the field extension $$\mathbf{C}$$ by appending roots of X2 + 1 = 0 to the real field $$\mathbf{R}.$$ The root i acts on P as a quarter turn with counterclockwise orientation. This root generates the group $$\{i, -1, -i, +1\} \equiv \mathbf{Z}/4\mathbf{Z}$$. When (x,y) is written x + y i it is a complex number.

Another group action by $$\mathbf{Z}/2\mathbf{Z}$$, where the actor has been expressed as j, uses the line y=x for the involution of flipping the plane (x,y) ↦ (y,x), an exchange of coordinates. In this case points of P are written x + y j and called split-complex numbers. These numbers, with the coordinate-wise addition and multiplication according to jj=+1, form a ring that is not a field.

Another ring structure on P uses a nilpotent e to write x + y e for (x,y). The action of e on P reduces the plane to a line: It can be decomposed into the projection into the x-coordinate, then quarter-turning the result to the y-axis: e (x + y e) = x e since e2 = 0. A number x + y e is a dual number. The dual numbers form a ring, but, since e has no multiplicative inverse, it does not generate a group so the action is not a group action.

Excluding (0,0) from P makes [x : y] projective coordinates which describe the real projective line, a one-dimensional space. Since the origin is excluded, at least one of the ratios x/y and y/x exists. Then [x : y] = [x/y : 1] or [x : y] = [1 : y/x]. The projective line P1(R) is a topological manifold covered by two coordinate charts, [z : 1] → z or [1 : z] → z, which form an atlas. For points covered by both charts the transition function is multiplicative inversion on an open neighborhood of the point, which provides a homeomorphism as required in a manifold. One application of the real projective line is found in Cayley–Klein metric geometry.

n = 4

$0 ≤ n ≤ 1$ can be imagined using the fact that points $R^{1}$, where each $x_{k}$ is either 0 or 1, are vertices of a tesseract (pictured), the 4-hypercube (see above).

The first major use of $R^{0}$ is a spacetime model: three spatial coordinates plus one temporal. This is usually associated with theory of relativity, although four dimensions were used for such models since Galilei. The choice of theory leads to different structure, though: in Galilean relativity the $t$ coordinate is privileged, but in Einsteinian relativity it is not. Special relativity is set in Minkowski space. General relativity uses curved spaces, which may be thought of as $R^{2}$ with a curved metric for most practical purposes. None of these structures provide a (positive-definite) metric on $R^{3}$.

Euclidean $R^{4}$ also attracts the attention of mathematicians, for example due to its relation to quaternions, a 4-dimensional real algebra themselves. See rotations in 4-dimensional Euclidean space for some information.

In differential geometry, $(x_{1}, x_{2}, x_{3}, x_{4})$ is the only case where $R^{4}$ admits a non-standard differential structure: see exotic R4.

Norms on $R^{4}$
One could define many norms on the vector space $R^{4}$. Some common examples are

 * the p-norm, defined by $\|\mathbf{x}\|_p := \sqrt[p]{\sum_{i=1}^n|x_i|^p}$ for all $$\mathbf{x} \in \mathbf{R}^n$$ where $$p$$ is a positive integer. The case $$p = 2$$ is very important, because it is exactly the Euclidean norm.
 * the $$\infty$$-norm or maximum norm, defined by $$\|\mathbf{x}\|_\infty:=\max \{x_1,\dots,x_n\}$$ for all $$\mathbf{x} \in \mathbf{R}^n$$. This is the limit of all the p-norms: $\|\mathbf{x}\|_\infty = \lim_{p \to \infty} \sqrt[p]{\sum_{i=1}^n|x_i|^p}$.

A really surprising and helpful result is that every norm defined on $R^{4}$ is equivalent. This means for two arbitrary norms $$\|\cdot\|$$ and $$\|\cdot\|'$$ on $n = 4$ you can always find positive real numbers $$\alpha,\beta > 0$$, such that $$\alpha \cdot \|\mathbf{x}\| \leq \|\mathbf{x}\|' \leq \beta\cdot\|\mathbf{x}\|$$ for all $$\mathbf{x} \in \R^n$$.

This defines an equivalence relation on the set of all norms on $R^{n}$. With this result you can check that a sequence of vectors in $R^{n}$ converges with $$\|\cdot\|$$ if and only if it converges with $$\|\cdot\|'$$.

Here is a sketch of what a proof of this result may look like:

Because of the equivalence relation it is enough to show that every norm on $R^{n}$ is equivalent to the Euclidean norm $$\|\cdot\|_2$$. Let $$\|\cdot\|$$ be an arbitrary norm on $R^{n}$. The proof is divided in two steps:

\leq \sqrt{\sum_{i=1}^n \|e_i\|^2} \cdot \sqrt{\sum_{i=1}^n |x_i|^2} = \beta \cdot \|\mathbf{x}\|_2,$$ where $\beta := \sqrt{\sum_{i=1}^n \|e_i\|^2}$.
 * We show that there exists a $$\beta > 0$$, such that $$\|\mathbf{x}\| \leq \beta \cdot \|\mathbf{x}\|_2$$ for all $$\mathbf{x} \in \mathbf{R}^n$$. In this step you use the fact that every $$\mathbf{x} = (x_1, \dots, x_n) \in \mathbf{R}^n$$ can be represented as a linear combination of the standard basis: $\mathbf{x} = \sum_{i=1}^n e_i \cdot x_i$ . Then with the Cauchy–Schwarz inequality $$\|\mathbf{x}\| = \left\|\sum_{i=1}^n e_i \cdot x_i \right\|\leq \sum_{i=1}^n \|e_i\| \cdot |x_i|
 * Now we have to find an $$\alpha > 0$$, such that $$\alpha\cdot\|\mathbf{x}\|_2 \leq \|\mathbf{x}\|$$ for all $$\mathbf{x} \in \mathbf{R}^n$$. Assume there is no such $$\alpha$$. Then there exists for every $$k \in \mathbf{N}$$ a $$\mathbf{x}_k \in \mathbf{R}^n$$, such that $$\|\mathbf{x}_k\|_2 > k \cdot \|\mathbf{x}_k\|$$. Define a second sequence $$(\tilde{\mathbf{x}}_k)_{k \in \mathbf{N}}$$ by $\tilde{\mathbf{x}}_k := \frac{\mathbf{x}_k}{\|\mathbf{x}_k\|_2}$ . This sequence is bounded because $$\|\tilde{\mathbf{x}}_k\|_2 = 1$$. So because of the Bolzano–Weierstrass theorem there exists a convergent subsequence $$(\tilde{\mathbf{x}}_{k_j})_{j\in\mathbf{N}}$$ with limit $$\mathbf{a} \in$$ $R^{n}$. Now we show that $$\|\mathbf{a}\|_2 = 1$$ but $$\mathbf{a} = \mathbf{0}$$, which is a contradiction. It is $$\|\mathbf{a}\| \leq \left\|\mathbf{a} - \tilde{\mathbf{x}}_{k_j}\right\| + \left\|\tilde{\mathbf{x}}_{k_j}\right\| \leq \beta \cdot \left\|\mathbf{a} - \tilde{\mathbf{x}}_{k_j}\right\|_2 + \frac{\|\mathbf{x}_{k_j}\|}{\|\mathbf{x}_{k_j}\|_2} \ \overset{j \to \infty}{\longrightarrow} \ 0,$$ because $$\|\mathbf{a}-\tilde{\mathbf{x}}_{k_j}\| \to 0$$ and $$0 \leq \frac{\|\mathbf{x}_{k_j}\|}{\|\mathbf{x}_{k_j}\|_2} < \frac{1}{k_j}$$, so $$\frac{\|\mathbf{x}_{k_j}\|}{\|\mathbf{x}_{k_j}\|_2} \to 0$$. This implies $$\|\mathbf{a}\| = 0$$, so $$\mathbf{a}= \mathbf{0}$$. On the other hand $$\|\mathbf{a}\|_2 = 1$$, because $$\|\mathbf{a}\|_2 = \left\| \lim_{j \to \infty}\tilde{\mathbf{x}}_{k_j} \right\|_2 = \lim_{j \to \infty} \left\| \tilde{\mathbf{x}}_{k_j} \right\|_2 = 1$$. This can not ever be true, so the assumption was false and there exists such a $$\alpha > 0$$.

title: Real coordinate space


text:
User talk:FrozenRose

Hi, So, as I explained in class, your first Project is to create a slide-show presentation on any particular still-camera (not video) produced prior to 1950. Information you should include in your presentation includes:

 * Full name of camera
 * Creator of your selected model
 * Manufacturer
 * Type of film used
 * Picture of the specific model
 * Years of production
 * Important features
 * Specifications
 * Popularity
 * Intended market: Amature or Professional photographers
 * Original selling price
 * Value today
 * Current availability of film stock
 * Limitations of this particular model
 * Example of a current equivalent model

Please use multiple sources for your research, and as always, if you have questions.... ask. Weaponofmassinstruction 18:35, 8 Feb 2005 (UTC)

Oh hey there
Oh hey, haha imma just checkin to see if this actually works. kinda weird but whatever its all good ight, haha yup BYE Katie04 21:37, 9 Feb 2005 (UTC)

title: User talk:FrozenRose


text:
Euclidean topology

In mathematics, and especially general topology, the Euclidean topology is the natural topology induced on $$n$$-dimensional Euclidean space $$\R^n$$ by the Euclidean metric.

Definition
The Euclidean norm on $$\R^n$$ is the non-negative function $$\|\cdot\| : \R^n \to \R$$ defined by $$\left\|\left(p_1, \ldots, p_n\right)\right\| ~:=~ \sqrt{p_1^2 + \cdots + p_n^2}.$$

Like all norms, it induces a canonical metric defined by $$d(p, q) = \|p - q\|.$$ The metric $$d : \R^n \times \R^n \to \R$$ induced by the Euclidean norm is called the Euclidean metric or the Euclidean distance and the distance between points $$p = \left(p_1, \ldots, p_n\right)$$ and $$q = \left(q_1, \ldots, q_n\right)$$ is $$d(p, q) ~=~ \|p - q\| ~=~ \sqrt{\left(p_1 - q_1\right)^2 + \left(p_2 - q_2\right)^2 + \cdots + \left(p_i - q_i\right)^2 + \cdots + \left(p_n - q_n\right)^2}.$$

In any metric space, the open balls form a base for a topology on that space. The Euclidean topology on $$\R^n$$ is the topology by these balls. In other words, the open sets of the Euclidean topology on $$\R^n$$ are given by (arbitrary) unions of the open balls $$B_r(p)$$ defined as $$B_r(p) := \left\{x \in \R^n : d(p,x) < r\right\},$$ for all real $$r > 0$$ and all $$p \in \R^n,$$ where $$d$$ is the Euclidean metric.

Properties
When endowed with this topology, the real line $$\R$$ is a T5 space. Given two subsets say $$A$$ and $$B$$ of $$\R$$ with $$\overline{A} \cap B = A \cap \overline{B} = \varnothing,$$ where $$\overline{A}$$ denotes the closure of $$A,$$ there exist open sets $$S_A$$ and $$S_B$$ with $$A \subseteq S_A$$ and $$B \subseteq S_B$$ such that $$S_A \cap S_B = \varnothing.$$

title: Euclidean topology


text:
Talk:All-terrain vehicle

editor comment
Nothing new in this article though it has some historical tit bits here and there. For example, the year 3 wheeled ATV seized to be sold can be got from this sentence. "In 1987, the agency sued ATV manufacturers, declaring the vehicles an imminently hazardous consumer product. The suit was settled a year later, with the companies agreeing to stop selling the three-wheel ATV models the agency considered highly unstable." Sales figure for ATV in some past years come out in this sentence "According to the industry, 884,000 ATVs were sold in 2003, up from 447,000 in 1998." Other historical data "The popularity of ATVs has been increasing, with 6.2 million four-wheel vehicles in use in 2003, double the number in 1998. Injuries have been rising steadily every year, according to agency statistics. In 2003, there were 125,500 injuries, up from 67,800 in 1998. About 31 percent of those injured in 2003 were younger than 16, compared with 37 percent in 1998." gathima 18:37, 8 Feb 2005 (UTC)

Citation sought (ATV Price ranges)
"Engine sizes of ATVs currently for sale (as of 2006) range from 50cc to 800cc. They range in price from about $2000 to nearly $8000." I am wonder where this info applies. USA? It is why I would like to seek a citation.--Jusjih 06:24, 5 May 2006 (UTC)

 * As you can see, I added the citation to the CPSC research giving the market data in question. It is for the US. My apologies for not giving the region initially. --Lynne Jorgensen 02:20, 10 May 2006 (UTC)

 * I have corrected this information back to what it was originally as cited in the article. While it may be true some ATV's retail for $12,000 this is no representative of the market, and will need a citation to prove such information.--Budlight 05:02, 22 September 2006 (UTC)

 * I changed the cost info back to the original (from $13000 to $8000) because that is what the citation gives. If someone is going to change it to $13000, please give a correct citation for it. The CPSC citation does not contain a reference to the upper end of the ATV cost range as being $13000. Please see the Wikipedia policy on citing references and verifiability of information at WP:V. Lynne Jorgensen 01:42, 6 November 2006 (UTC)

Non trail usage?
Wondering if it would be prudent to make note of non-typical usages of ATVs. For example, they are a familiar sight driving down city streets in phildelphia and can be seen with rims and other such adornments.--Ron 19:50, 27 July 2006 (UTC)

 * Curious! I've never heard of widespread inner-city use, though I have seen some on the outskirts of Miami. Nothing like what you describe, however. I would think this would be a good addition to the article -- very educational, and I thought I'd seen and heard a lot about ATVs to this point. Thanks for your expertise! Lynne Jorgensen 02:17, 30 July 2006 (UTC)

 * Yes, people actually use them for drag racing (complete with wagering) in inner cities. However, I would have to be convinced that it's a "familiar sight" in urban Philadelphia. --Don Williams 22:01, 1 August 2006 (UTC)

 * There have been articles in the Philadelphia Inquirer newspaper on the illegal use of ATV's in city parks and on city streets- and on the Philadelphia Police efforts to reduce these.-Sept. 2012 see http://www.philly.com/philly/news/Phillys_bike_life_culture.html[User: Mi.Lee.Hu.] — Preceding unsigned comment added by Mi.Lee.Hu (talk • contribs) 04:16, 22 October 2012 (UTC)

 * In several countries in Europe ATVs are legal to use on the street and are considered an automobile. Japanese and North American manufacturers have to convert ATVs sold to Europe for the market. This includes having the foot brake operate all four wheels, reinforce the ignition to guard against theft, place engine restrictions (if the particular market calls for them) and adding turn signals and reflectors. Also, it is legal to ride 2-Up on a one-person machine. I rode in the French Alps and it was quite an experience riding on the streets of the French towns. If I can find any photos I will consider adding them. There are also several American communities that have made it legal to ride on streets in order to facilitate business growth around trail use and to connect trails. One place that comes to mind is the city of Logan, W.V. that is in the heart of the Hatfield-McCoy Trails.Alf rules 21:34, 16 November 2006 (UTC)

Some work needs to be done on expanding the classifications of ATVs. While the 2WD "sport" quad is well understood, they are limited in application, due to the lack of 4WD. Originally, 4x4 "utility" machines were focused on, well, utility. They were often used by farmers for working lands, and by hunters by accessing distant hunting areas and game retrieval. Their use has migrated to a much greater focus on recreation in recent years, with a greater emphasis on performance and comfort. In addition, the "sport 4x4" class, pioneered by the Polaris Scrambler, and built upon by the Yamaha Wolverine and Can-Am Renegade. (BPD) — Preceding unsigned comment added by 208.94.87.21 (talk) 04:03, 28 December 2011 (UTC)

Name
I just wanted to mention that where I live in Canada, ATVs are almost always referred to as "four-wheelers" or "three-wheelers", and almost never ATVs. Is this the common term anywhere else?Thomasiscool 16:34, 16 September 2006 (UTC)Thomasiscool

 * Well, if you look at the magazines, you have ATV Action, ATV Sport and ATV Illustrated. Don Williams 07:06, 2 October 2006 (UTC)

 * There is also Quad, Dirt Wheels, and many more that dont have ATV in the name, That is a very shity point. "four-wheeler" and "three-wheeler" are the most common here to. — Preceding unsigned comment added by 216.250.12.60 (talk) 06:32, 31 October 2006 (UTC)

 * Thank you for your highly inarticulate contribution. Don Williams 00:49, 19 November 2006 (UTC)

 * I have to just mention I laughed out loud seeing Don's deadpan response above to the 'shity' crticism comment. —Preceding unsigned comment added by 79.70.12.104 (talk) 23:57, 27 June 2009 (UTC)

Where I live in Canada it usually depends on the level of education of the individual, and whether or not they use the machines. I know several avid users who even call them "bikes". OHV ("off-highway vehicle") is the official term in Nova Scotia. — Preceding unsigned comment added by Naymetayken (talk • contribs) 15:48, 17 March 2013 (UTC)

Tone
I find the overall tone of this article to be decidely anti-ATV. Especially the section regarding injuries and deaths. While it is worth noting that there are people killed and injured on ATVs each year, it is also worth noting that the accident rate per hour of use is actually decreasing. The more ATVs are sold, the more people will ride them. And the more ATVs are ridden, the more accidents will happen. Just something to think about, I believe. I will research sources to back up my claims. Alf rules 21:28, 16 November 2006 (UTC)

 * I find the article excessively PRO 4-wheeler, without discussion of noise pollution, pollution from mud runoff, property invasion, and habitat destruction. Mudholes become mosquito breeding grounds. —Preceding unsigned comment added by 72.195.138.125 (talk) 18:54, 15 October 2010 (UTC)

ATV ROAD
Can you ride an ATV on the road and What is so bad about three wheelers?PendoFSX 00:34, 5 February 2007 (UTC)Pendo 4

 * About road riding: In some states, South Dakota, for instance, ATVs with a displacement of 250CC or greater can be licensed as a motorcycle for road use. However the machine must have a rear-view mirror and horn. BTW, in the Black Hills of South Dakota, more than 80% of the 1.4-million-acre Black Hills National Forest, is open for ATV users. Additonally, BLM land, national grasslands and state lands are also open to ATV users.Dab1066 04:48, 17 February 2007 (UTC)

more about roads
"Three wheelers" can actually be made street legal in the United States due to loop holes for three wheel vehicles to be classified as motorcycles, allowing "meter-maid" vehicles and the such. Conversion kits are available to convert some sport ATV's to a single rear wheel, thus allowing them to be licensed with the afor mentioned horn, mirror, turn signal additions. Four wheel ATV's cannot be made street legal in most states because they are then classified as cars and do not pass Federal safety standards (side impact, etc.). Road legal quads abound in Europe and the quad magazines regularly do articles on them. RustyATV 04:24, 28 February 2007 (UTC)

 * Street use of ATVs is legal in several states. In Idaho, they are registered with a "limited use" plate, which permits operation on all county and local (city) roads/streets, unless specifically prohibbited by that county or city.  Operation on state and interstate highways is not permitted.  Requirements include brake lights, mirror and horn.  Turn signal lights are not required.  —Preceding unsigned comment added by 50.37.75.110 (talk) 15:01, 27 April 2011 (UTC)

Reference Needed (Weasel Words - Overwhelming?)
"the overwhelming evidence of human growth patterns upon the landscape indicates damage to the sensitive habitats are caused by unmitigated growth of single-family housing planning and extractive industries" 207.216.216.119 03:45, 30 April 2007 (UTC)

Factual Error - Number of Injuries
I found this article to be incredibly slanted in favor of ATV's. But that aside the claim of 500 accidents a year is preposterous. In 2003 the state of Minnesota has reports of 254 ATV accidents, 228 people injured and 18 deaths, this in just one state that has 1.6% of the total US population.

here is the link to the Minnesota data files.dnr.state.mn.us/enforcement/incident_reports/atvaccidents03.pdf

whoever wrote this article mislabeled tha data, in the link that they provide for this data (2) it says there 470 DEATHS in 2004, but in the text of the article they said "There are only about 500 injuries from Quads each year all from misuse by very young drivers from the age of five to ten.[2]"

Would be nice if they read the actual article they are citing in their faulty statistics.

In 2004 there were more than 136,000 injuries treated in Emergency Rooms, God know how many there were total, also only 33% of these injuries were in persons less than 16 years of age, whereas in the articles the author says that the majority of the 500 injuries were riders between 5 and 10.

I hope someone can clean this article up so that there are some factual injury statistics. 192.240.46.60 20:38, 14 May 2007 (UTC)

 * I took out all of that convoluted "information". Don Williams 18:05, 15 May 2007 (UTC)

 * Gee, those statistics were not only accurate, but highly relevant to the article. Don, am I misinterpreting what you took out? Did you take out the 136,100 injuries in 2004 and 470 deaths in 2003? User 192.240.46.60 should indeed read the referenced work. Those are not numbers of accidents but victims. Minnesota's 18 deaths contributed to the US total of 470. There's nothing about that that doesn't add up (except that they're from different years, but you get the idea).
 * The second statement, "There are only about 500 injuries from Quads each year... age five to ten." that User 192.240.46.60 makes was not made by me, though it appears someone is attributing it to the source I used for the other statistics. That source does not include this information, and I believe this statement is not true for the US. Perhaps it is true for some other country?
 * It appears that someone mucked up the stats section after I wrote it and it got all haywire with other numbers so that it didn't make sense anymore. I restored my original paragraph and updated it using CPSC's latest statistics. Lynne Jorgensen 01:30, 16 May 2007 (UTC)

 * Works for me. I just knew that it wasn't accurate and needed to be removed, then replaced when fixed. But, I do have a problem with this: "Statistics released by CPSC show that in 2005, there were an estimated 136,700 injuries associated with ATVs treated in US hospital emergency rooms -- more than double the number of injuries treated in the last year of the consent decrees." It needs the context of injuries-per-user or injuries-per-hours-of-use. Just a flat number doesn't tell you if injury rate is up or down. Either add that info, or I'm going to yank it as incomplete. Don Williams 00:02, 17 May 2007 (UTC)

 * I added risk per ATVs in use figures from CPSC's report, which is the only research available on the subject. The statement that injuries have doubled is based on sound statistical methodology (read the report). Rate/Risk is another matter altogether and it wasn't what I was originally citing. If you yank it I'll ask for mediation. Lynne Jorgensen 19:30, 17 May 2007 (UTC)

Injury statistics are important and a useful tool for someone considering the sport. However, they must be put in perspective. In comparision, how many injuries and deaths occur from other recreational activities? Bicycling comes to mind as a suitable comparison (BPD) — Preceding unsigned comment added by 208.94.87.21 (talk) 03:55, 28 December 2011 (UTC)

Adding a link
I work for the America's Most Wanted Safety Center, a new department of America's Most Wanted getting away from the capturing of criminals, and branching out to all aspects of safety. I feel a link to our post about ATV safety would be appropriate and mutually beneficial, particularly because it prominently features an exciting video narrated by Julie Vallese of the Consumer Products Safety Commission. The link is http://www.amw.com/safety/?p=57 please consider it. Jrosenfe 15:45, 22 June 2007 (UTC)

I would like to see a link added for the site EscargoTracks http://escargotracks.com They are a new company in Canada that has built custom tracks for several types of ATV which allows the argo to be more flexible and access greater amounts of terrain type. It appears to be the first track to allow extreme all terrain access. There is alot of interest in this new track on Youtube and argo users around the world. The site offers video footage of various argo's in different terrain. —Preceding unsigned comment added by 17:17, 27 July 2007 (talk • contribs) 66.206.244.155

 * External links should be added to dmoz, see EL. Is this thing working? (talk) 01:24, 27 December 2007 (UTC)

Land usage
The land usage section is slanted and biased AGAINST ATV riders pretty badly. — Preceding unsigned comment added by 64.80.110.50 (talk) 13:46, 26 June 2007 (UTC)

 * I cannot disagree more strongly with the above statement. Quad bikes (as well as motorbikes) tear up soft trails and make mudholes (in non-desert areas), Many, if not most, 4-wheelers regularly ride on private land in Maine. I tink this article is remarkably positive to neutral, without regard to the environmental destruction they cause. —Preceding unsigned comment added by Krementz (talk • contribs) 19:04, 15 October 2010 (UTC)

 * I have to agree, citing "studies" without a reference to the study is pretty blatant. I can reference "studies" that the authors of various parts of this article are morons.  What, you don't believe me?  I said studies didn't I?  What further proof do you need?  All kidding aside, the tone of most of this article is decidedly anti-ATV.
 * "In some countries where fencing is not common, such as the US, Canada and Australia, a small percentage of ATV riders knowingly cross privately owned property in rural areas and travel over public/private properties, where their use is explicitly limited to trails." - No reference, no quote, nothing...  Without references, Wikipedia is far more dangerous than it is useful.  This is PR, pure and simple.
 * The vast majority of the points made could be applied to just about any off-road vehicle. All vehicles create ruts when traveling through soft wet ground (I've actually seen far worse damage from off road motorcycles than quads, at least the quads balance their weight on 4 wheels.
 * Unfortunately this article is spreading across the internet just like the invasive species the article references. All you have to do is Google "Studies have also shown that ATVs may help in the spread of invasive species" and you'll see this article replicated almost in it's entirety without even the discussion page.  Anti-ATV propaganda at it's best...  —Preceding unsigned comment added by 71.133.34.33 (talk) 21:52, 1 July 2010 (UTC)

 * Everything is relative. It is worth noting that horses and pack animals typically do greater damage (on a per-use basis) than ATVs. A typical ATV weights about 600 lbs, with that supported on 4 wide, soft, low pressure tires, and that load is carried by rolling of the tires. A 1200 lb horse carries it's weight on 4 hard (often shod) hooves, with that weight carried by only 2-3 as they are moving. As such, the "ground pressure" of horses is several times that of ATVs. Adding to their damage is their "emmissions", which contribute to polution of the trails, waterways and the spread of noxious weeds. — Preceding unsigned comment added by 208.94.87.21 (talk • contribs) 03:50, 28 December 2011 (UTC)

 * Additional editing should be done concerning the positive economic benefit that ATV/OHV recreation provides to local communities. Many small, rural communities in my state benefit considerably, and are very supportive of the sport.  One area that gets significant publicity is the Paiute Trail in Utah.  The trail system is some 900 miles, connects many small communities and is a common vacation destination for those involved in the sport.
 * The access to our public lands that ATVs provide should also be mentioned. At a time when a very small percentage of the population recreates on forest service and BLM lands, ATV (and other OHV operation) in increasing and offering more people opportunities to experience these lands.  In addition, these users are among the few that provide funding for multiple use trail systems, through registration and permits.  OHV use also funds the Recreational Trails Program, through fuel tax on off-highway fuel.  This program benefits both motorized and non-motorized trails. (BPD)  — Preceding unsigned comment added by 208.94.87.21 (talk) 04:13, 28 December 2011 (UTC)

Citation?
"Nationally, the US Forest Service considers managed ATV use to be a legitimate activity in national forests, yet it also lists their unregulated use as one of the four greatest threats to long term forest management. The US Forest Service recently released a national travel management plan designed to minimize the negative environmental impacts of ATVs while providing a safe, sustainable and enjoyable opportunity for ATV users." --It seems to me that a statement like that should require some kind of citation. 76.208.9.104 14:30, 4 July 2007 (UTC)

 * The quote is used here in 2003: http://www.powersportsforums.com/atvs-quads/ —Preceding unsigned comment added by Kathleenatkins (talk • contribs) 06:48, 2 September 2009 (UTC)

erosion photo
"Unverified?" Those are obviously ATV tracks, and obviously eroded. The only further verification you could have is to have a wider angle to get a better idea of whether there is in fact no erosion surrounding the track. Can we NOT be ridiculous about this?Andy Christ 19:21, 27 July 2007 (UTC)

vandalism
i knoticed their was some vandalism on the page. ive taken care of that. Atvrider1919 21:18, 24 October 2007 (UTC)

Grossly Biased
This article really needs a cleanup to bring it to NPOV. An example sentence that either needs to be cited or removed is: "Since the late 1980s, ATVs are used for sex and underage drinking. This has led to greater conflict between ATV users and child-safety advocates, rural landowners, fellow outdoor recreationalists and environmentalists."

Laplie 01:33, 31 October 2007 (UTC)

The History section is wrong
Royal Enfield invented a powered Quaracycle in 1893 that both resembles a modern Quadbike and operates in a similar manner. This Article is also too US centric and doesn't have any infomation about what other governments reconise as a Quadbike or about not ATV quads (EG cars classified as motorbikes like the G-wiz and the reliant robin). TBH the article could do with a complete overhaul.(Morcus (talk) 02:39, 31 March 2008 (UTC))

 * those are cars classified as motorcycles though, not ATVs, they have their own catigory anyway three wheelers — Preceding unsigned comment added by 64.235.83.23 (talk) 22:03, 13 May 2012 (UTC)

Quad bikes and redirects
Quad Bike redirects here but I feel a second page specifically about Powered Quadracycles should exist under Quad bike. There are many Quads that are not ATV's and this article doesn't contain info on them, also this article is far too US centric with half the Article filled with infomation about critisms and observations that are irrelevent in the UK and most likely in other places, The first paragraph gives a deffinition of what an ATV is wich is diferent to the DVLA's deffinition of what a quadracycle is (A 4 wheeled Vehicle below a certain weight). There would be the potential for alot of cross over but I feel it is nessessary whilst this article remains in this format.(Morcus (talk) 02:33, 13 April 2008 (UTC))

 * A quadricycle is specifically a vehicle powered by a human, so I'm not sure at all what you mean. In any case, most of what is on the page you helped create is replicated here or is uncited. Alastairward (talk) 11:35, 4 August 2008 (UTC)

 * Had a look at the Quad bike article and I reinstated the redirect. The lead paragraph of that article had confusing information, whereby the license category that a driver of an ATV in the UK was used as a definition of such a vehicle. Other than that the rest of the article is a simple replication of what is here or is uncited. Alastairward (talk) 11:56, 4 August 2008 (UTC)

I would like to contribute with some editorial and link to the UK Quad Bike Industry. We have a communication with some well known celebrities who have been involved in accidents relating to Quad Bikes. We would appreciate if you could let us know as soon as you have read this posting and question. My name is Darren and I work for a company called [www.myquadbike.com]and we are a website that could contribute towards Quad Bike safety within the uk, along side EASi [www.quadsafety.org]. —Preceding unsigned comment added by Myquadbike (talk • contribs) 15:44, 20 November 2008 (UTC)

Lousy Article
This sounds like it was written by someone with an axe to grind. Weasel words abound. Opinion does not belong in an encyclopedia article period. Article is twice as long as it should be. —Preceding unsigned comment added by 76.204.195.101 (talk) 02:39, 12 May 2009 (UTC)

 * The Emissions sections is particularly troublesome. Lawn mowers produce far more "harmful" emissions than ATV's.   Plus there is a broken link on a significant claim that ATV's are harmful to the environment, despite their low incident of use.  What a bunch of BS.--96.244.247.130 (talk) 02:08, 11 September 2011 (UTC)

Neutrality
There are now a number of complaints about neutrality on the talk page. This page currently contains four major non-reference sections ("Safety Issues in the U.S.", "Emissions", "Land Usage", and "Sport Usage"), of which at least the first three would really constitute the "Criticism" section of a typical WP article. Reading them is like reading a debate -- "almost immediately realized alarming injury rates" followed by "mainly due to improper and irresponsible use". A decent chunk of a Times article arguing for change is excerpted into the article. In the article body, after the lead-in, there are really only three sentences (the "Sport Competition" section) that aren't related to arguing for or against ATVs. Mark7-2 (talk) 13:00, 13 May 2009 (UTC)

 * Please fell free to add more sourced data "not against" ATVs.
 * BTW, the "Safety" section is not "Against" BUT "About" ATVs.Randroide (talk) 07:58, 15 October 2009 (UTC)

Quad bike?
OK, this is not the place to change things, Wikipedia is describing what is but I cannot resist... "bike" = bi-cycle = 2 circles. A "quad bike" must then be 4 * 2 circles, it must have eight wheels =) bi-bike, that's what it is!! (compare to trike, it got three wheels) —Preceding unsigned comment added by 213.89.240.124 (talk) 06:07, 14 May 2009 (UTC)

USA Emphasis
I am not terribly interested in this subject but reading the page it appears almost as if the subject is not "quadbikes" but "quadbikes in the USA", this is especially true of the first few paragraphs and makes for a bit odd reading reiknir (talk) 07:52, 30 July 2009 (UTC)

 * I agree and have removed the US bias from this article - perhaps if there are some relevant issues for quadbikes in the US, then they could form part of an existing section, but right now it seems as if this article is only concerned with quads in USA. 119.173.81.176 (talk) 08:40, 11 October 2009 (UTC)

 * can people please contribute to this talk page, before this descends into an edit war? 119.173.81.176 (talk) 08:49, 11 October 2009 (UTC)

 * As no one is contributing, any objections if I remove the US only section? 119.173.81.176 (talk) 16:42, 12 October 2009 (UTC)

 * Please do NOT remove SOURCED data. I also fail to see any rationale to remove any "U.S. only" section, specially if we take into account the simple fact that (AFAIK) all the existing studies about the safety (or lack of it) of ATVs have been made in the USA English speaking countries.
 * And please, please (please...) avoid this kind of edits . If you are going to make controversial edits, please make them step by step to facilitate overseeing and communication with other editors.
 * OTOH you were absolutely right about the unsourced blocks of text you removed. I carefully respected those edits you made Randroide (talk) 17:31, 14 October 2009 (UTC)

 * "all the existing studies about the safety (or lack of it) of ATVs have been made in the USA English speaking countries." Nonsense, Loads of research into the safety of quads in Northern Europe after they firs came onto the market in the 70/80's after a large number of serious accidents, especially in Sweden, these contraptions are heavily used in Scandinavia by farmers after all. This research led to them being banned, at the least temporarily, in a number of countries and trike variants outlawed in some instances altogether. Did you mean to write "no existing studies in a language I can understand" ?. reiknir (talk) 12:33, 30 November 2009 (UTC)

 * Could you please reference those studies?. It is a pity I can not read Swedish Randroide (talk) 16:50, 1 December 2009 (UTC)

 * I was under the impression that cited data can be removed if (as in this case) it contributes towards undue weight. Oh and be a little more careful with reverting, your revert removed a huge section on this history and development of ATVs, try putting the information back manually, rather than just hitting the revert button. 119.173.81.176 (talk) 18:44, 14 October 2009 (UTC)

 * Your impression is absolutely correct: Sourced data can and should be removed if creates a case of undue weight. But I fail to see the WP:DUE case you see so clear. Could you please be more specific about where do you see UW?.
 * Sorry my unintended deletion of the sections you mentioned. Please note that the edit you made I reverted was an extremely complex one . Once I checked you deleted sourced (and IMHO highly relevant) data I decided to revert your contribution. Please make "step by step" edits and I guarantee you I shall never delete well sourced contributions. Thank you. Randroide (talk) 07:42, 15 October 2009 (UTC)

While this article is certainly USA centric--unfortunately this reflects current research on the topic. As the top page of this edit page shows (motorcycles, cars, and trucks), ATV's tend to fall through motor vehicle regulation gaps and data on their safety is not especially easy to obtain. While the US has (especially in the past 10 years) started to focus research data to correcting this, there are few published peer reviewed articles on ATV safety from much of the world. As I am an ATV researcher, I will be adding global sources as soon as I am aware of their existence. I will make note that there was quite the research splurge in the early 70's when ATV's were first made available to the public in large quantities, but current safety data is hard to find. (129.255.1.225 (talk) 21:02, 7 September 2011 (UTC))

Safety
About this edit

The editor removed 2 links revelant to the subject and 8 sourced facts. Could you please explain your reasons for this edit?. We could trim/condense the list, if you wish. But a total blanking seem unacceptable to me. Uh: And your blanking left a picture with an unsourced claim. Randroide (talk) 16:51, 25 October 2009 (UTC)

 * This article seems overly negative regarding ATVs - it should be rename "ATVs and why they suck" the safety/emissions/etc sections should be much smaller. 119.173.81.176 (talk) 07:31, 3 November 2009 (UTC)

 * The article presents sourced facts about ATVs, and by now those are the facts available for these machines. This is an encyclopedia, not a fan forum. If you want to add to the article sourced positive facts (whatever they are) about ATVs (as much positive sourced facts as you want), you have all my blessings.
 * There´s no reason at all to make any section "smaller". Please read.
 * I restored the safety section you deleted. I suppose you deleted that section because it was unsourced (I deleted the sources in a n edit error weeks ago). I restored section and sources.
 * If you really want to delete the (IMO crucial) fact that valid sources indicate that ATVs are as risky as motorcycles, I think it would be much better for us if we go now to a Dispute Resolution process (WP:DR). Sorry but with me there is going to be no consensus to delete this fact, so I suggest to move to a DR now.
 * I also suggest you going to a Third opinion.
 * Sorry, but I decided to revert all your edits once I saw this  Randroide (talk) 13:43, 3 November 2009 (UTC)

 * Edits reverted again tonight. Blanking of cited and ref'd material. - 4twenty42o (talk) 05:21, 4 November 2009 (UTC)

Useless Article.
It's been a while since I've read this and its useless, for a start its to US centric and the history is all wrong. Royal Enfield Built a Quad in the 1800 yet the history starts in the 70's.(Morcus (talk) 19:10, 4 May 2010 (UTC))

 * could you please site Enfield's first bike? While ATV's may have existed before the 60's, major sales to the public began in the late 60's to early 70's. (Gibbs 1995) They started becoming commonplace in the early 80's coinciding with popular mechanics articles and increased sales (Rodgers 1990). (129.255.1.225 (talk) 21:20, 7 September 2011 (UTC))

New major ATV manufacturers
I added Argo to the list, since they are also pretty big in the industry. Since they do not have an article on wikipedia, I simply linked it to their homepage. Is that cool with everyone? —Preceding unsigned comment added by 216.16.227.118 (talk) 19:27, 30 June 2010 (UTC)

opps! forgot to put it in alphabetical order! Changed it tho. —Preceding unsigned comment added by 216.16.227.118 (talk) 19:33, 30 June 2010 (UTC)

 * Rather than link to their home page -- which merely proves they exist -- it would be better to link to a story in a book or magazine or news outlet which focuses on the company itself, which would demonstrate that they are a major manufacturer. For example, a story in Business Week or the New York Times or whatever which states, "Argo is a major ATV manufacturer" or something like that. But I can't seem to find any independent sources which say that. Are they really that big? --Dbratland (talk) 20:05, 30 June 2010 (UTC)

No Mention of Electric ATVs?
It would be helpful to at least mention electric ATVs, perhaps in the "Emissions" section to present a zero-emissions alternative.

Here is a quick link which, being from How Stuff Works, may not be citation-worthy but still offers some good general information for a party savvy in the subject matter area to build upon: http://adventure.howstuffworks.com/outdoor-activities/off-roading/off-road-atvs4.htm  — Preceding unsigned comment added by Harris.thomasj (talk • contribs) 14:12, 31 August 2011 (UTC)

Merger
Info regarding the proposed merger can be found here. Also, please follow the link and reply to my comment if you want to discuss the merger. Passengerpigeon (talk) 02:47, 18 November 2012 (UTC)

removing POV tag with no active discussion per Template:POV
I've removed an old neutrality tag from this page that appears to have no active discussion per the instructions at Template:POV:
 * This template is not meant to be a permanent resident on any article. Remove this template whenever:
 * There is consensus on the talkpage or the NPOV Noticeboard that the issue has been resolved
 * It is not clear what the neutrality issue is, and no satisfactory explanation has been given
 * In the absence of any discussion, or if the discussion has become dormant.

Since there's no evidence of ongoing discussion, I'm removing the tag for now. If discussion is continuing and I've failed to see it, however, please feel free to restore the template and continue to address the issues. Thanks to everybody working on this one! -- Khazar2 (talk) 02:41, 14 June 2013 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 1 one external link on All-terrain vehicle. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive https://web.archive.org/20070128081640/http://www.cpsc.gov:80/library/atv2005.pdf to http://www.cpsc.gov/library/atv2005.pdf

When you have finished reviewing my changes, please set the checked parameter below to true to let others know.

Cheers. —cyberbot II  Talk to my owner :Online 01:49, 9 September 2015 (UTC)

External links modified
Hello fellow Wikipedians,

I have just added archive links to 2 one external links on All-terrain vehicle. Please take a moment to review my edit. If necessary, add after the link to keep me from modifying it. Alternatively, you can add to keep me off the page altogether. I made the following changes:
 * Added archive http://web.archive.org/web/20081010150303/http://www.dvla.gov.uk:80/media/pdf/leaflets/inf45.pdf to http://www.dvla.gov.uk/media/pdf/leaflets/inf45.pdf/
 * Added archive http://web.archive.org/web/20040730233904/http://www.epa.gov:80/otaq/regs/nonroad/largesi/f00051.pdf to http://www.epa.gov/otaq/regs/nonroad/largesi/f00051.pdf

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at Sourcecheck).

Cheers.—cyberbot II  Talk to my owner :Online 07:08, 28 February 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on All-terrain vehicle. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20080909234652/http://www.cpsc.gov/library/atv2005.pdf to http://www.cpsc.gov/library/atv2005.pdf

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.— InternetArchiveBot  (Report bug) 14:50, 9 October 2016 (UTC)

External Link about ATV Touring in West Virginia
I added a link that regards ATV tourism in West Virginia: https://wvexplorer.com/recreation/atv-touring/

Then I saw the note about discussing it first. I'll be happy to remove it pronto, if need be. — Preceding unsigned comment added by Dsibray (talk • contribs) 01:02, 25 February 2017 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 4 external links on All-terrain vehicle. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20150909014952/http://bicycledeport.com/2015/04/royal-enfield-owners-club/ to http://bicycledeport.com/2015/04/royal-enfield-owners-club/
 * Added archive https://web.archive.org/web/20100705100056/http://www.svia.org/ASI/ASI.aspx to http://www.svia.org/ASI/ASI.aspx
 * Added archive https://web.archive.org/web/20111105153858/http://www.hwsa.org.au/files/documents/Activities%20-%20Current%20Campaigns/6eec848e-c9d7-41a4-a9d5-fe243eef93f2.pdf to http://www.hwsa.org.au/files/documents/Activities%20-%20Current%20Campaigns/6eec848e-c9d7-41a4-a9d5-fe243eef93f2.pdf
 * Added archive https://web.archive.org/web/20090820005306/http://www.fim-live.com/en/sport/quads-cross-country-rallies/winners/ to http://www.fim-live.com/en/sport/quads-cross-country-rallies/winners/

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

Cheers.— InternetArchiveBot  (Report bug) 01:09, 2 July 2017 (UTC)

title: Talk:All-terrain vehicle


text: User talk:66.131.38.51

title: User talk:66.131.38.51