Conservapedia - User contributions [en]

World treasures

2009-02-14T03:17:36Z

JosephineP: /* America */ change to "The Americas"; more countries are reflected here than just ours :)

<CENTER> World Treasures

Gallery
 </CENTER>

=== [[Africa]] ===
<center>
<gallery perrow="5">
Image:Kasbah of Algiers Mosque.jpg|'''Kasbah of Algiers Mosque''' [[Algeria]]
Image:5457e.jpg|'''The Sphinx and Khafra Pyramid ''' [[Egypt]]
Image:Mt Nimba.jpg|'''Mt. Nimba''' [[Guinea]]
Image:Royal Palaces of Abomey.jpg|'''Royal Palaces of Abomey''' [[Benin]]
Image:Elephant Jose Tello.jpg|'''Manovo-Gounda St Floris National Park''' [[Central African Republic]]
</gallery>
</center>

=== [[Americas|The Americas]] ===
<center>
<gallery perrow="5">

Image:Stuart George Washington portrait.jpg|[[George Washington]] '''portrait by''' [[Gilbert Stuart]] [[US]]
Image:DcLincMor.JPG|'''Lincoln Memorial''' [[US]]
Image:Golden Gate Bridge.jpg|'''Golden Gate Bridge''' [[US]]
Image:Statue of Liberty.jpg|'''[[Statue of Liberty]]''' [[US]]
Image:Grand Canyon2.jpg|'''[[Grand Canyon]]''' [[US]]
Image:Alaska Mt. McKinley.jpg|'''Mt. McKinley''' [[US]]
Image:Calakmul 2.jpg|'''[[Calakmul]]''' [[Mexico]]
Image:Uxmal 2.jpg|'''Uxmal''' [[Mexico]]
Image:Kukulcan3.jpg|'''[[Chichen Itza]]''' [[Mexico]]
Image:Bellas Artes.jpg|'''[[The Fine Arts Palace]]''' [[Mexico]]
Image:Canada-cn-tower.jpg|'''[[CN Tower]]''' [[Canada]]
Image:Tikal.JPG|'''[[Tikal]]''' [[Guatemala]]
Image:Cartegna Colombia.jpg|'''Cartegna''' [[Colombia]]
Image:AMAZONAS Venezuela.png|'''Jungle region''' [[Venezuela]]
Image:Galapagos islands Ecuador.JPG|'''[[Galápagos Islands|Galapagos islands]]''' [[Ecuador]]
Image:Cristo Redentor Río de Janeiro.jpg|'''Christ the Redeemer''' [[Brazil]]
Image:Iguazu Falls.jpg|'''Iguazu Falls''' [[Argentina]] / [[Brazil]]
Image:Machu Picchu.jpg|'''[[Machu Picchu]]''' [[Peru]]
Image:Andes chilenos.gif|'''Andes''' [[Chile]]
Image:Moai Rano.jpg|'''Moai''', '''Easter Island''' [[Chile]]

</gallery>
</center>

=== [[Asia]] ===
<center>
<gallery perrow="5">
Image:Meenakshi temple.jpg|'''Meenakshi temple''' [[India]]
Image:Taj Mahal...jpg|'''Taj Mahal''' [[India]]
Image:China Wall.jpg|'''Great Wall of [[China]]'''
Image:Daibutsu - Buddha.jpg|'''Daibutsu - [[Buddha]]''' [[Japan]]
Image:Japan Miyajima s.jpg|'''The gate of [[Itsukushima Shrine]] ''' [[Japan]]
Image:Buddha Korea.jpg|'''[[Buddha]]''' [[Korea]]
Image:Siem Reap, Cambodia.jpg|'''Angkor temples''' [[Cambodia]]
Image:Silver Pagoda Cambodia.jpg|'''Silver Pagoda''' [[Cambodia]]
Image:Lak Muang Bangkok.jpg|'''Lak Muang''' [[Thailand]]
Image:Petronas towers at night.jpg|'''Petronas towers''' [[Malaysia]]
Image:Petra.jpg|'''El Khazneh - Petra''' [[Jordan]]
Image:Fatima al Masouma.jpg|'''Fatima al Masouma''' [[Iran]]
Image:Omayyad Mosque Damascus Syria.jpg|'''Omayyad Mosque''' [[Syria]]
Image:Saint Sophia.jpg|'''Saint Sophia''' [[Turkey]]
Image:Nazareth.jpg|'''Basilica of the Annunciation''' [[Israel]]
</gallery>
</center>

=== [[Australasia]] ===
<center>
<gallery perrow="5">
Image:Sidney opera house.jpg|'''Sydney Opera House''' [[Australia]]
Image:Great Barrier Reef.jpg|'''Great Barrier Reef''' [[Australia]]
Image:Barriere corail.jpg|'''Barrier Corail''' [[Australia]]
Image:Royal exhibition building.jpg|'''Royal Exhibition Building''' [[Australia]]

Image:Te Papa.jpg|'''Te Papa, Museum of New Zealand''' [[New Zealand]]

</gallery>
</center>
=== [[Europe]] ===
<center>
<gallery perrow="5">

Image:The Tower of Belem.jpg|'''The Tower of Belem''' [[Portugal]]
Image:Valencia.jpg|'''Valencia''' [[Spain]]
Image:Gutenburg1.jpg|'''Gutenberg [[Bible]]''' [[Germany]]
Image:Cosmographia.jpg|'''Map from Ptolemy's Geographia''' [[Greece]]
Image:Acropolis.gif|'''Acropolis''' [[Greece]]
Image:Colosseum.jpg|'''[[Colosseum]]''' [[Italy]]
Image:Michelangelopieta.jpg|'''Pieta''' [[Italy]]
Image:Da Vinci The Last Supper.jpg|'''[[Last Supper|The Last Supper, Da Vinci]]''' [[Italy]]
Image:Tower of Pisa.jpg|'''[[Tower of Pisa]]''' [[Italy]]
Image:Rembrandt Nightwatch.jpg|'''Nightwatch Rembrandt''' [[Netherlands]]
Image:Notre Dame.jpg|'''[[Notre Dame]]''', [[France]]
Image:Tour - Eiffel.jpg|'''[[Eiffel Tower]]''' [[France]]
Image:Miranda.jpg|'''Miranda''' [[John William Waterhouse|Waterhouse]] [[United Kingdom]]
Image:Tower bridge London.jpg|'''[[London Tower Bridge|Tower bridge]]''' [[United Kingdom]]
Image:Big Ben - England.jpg|'''Big Ben''' [[United Kingdom]]

</gallery>
</center>

== Guest treasure ==

[[Image:El Escorial.jpg|400px]]

''' El Escorial '''

{{Clear}}

:::::::::::::::::::::: [[World treasures II|Continue to Part II]]

== See also ==
[[Image:Basilica of San Vicente, Avila.jpg|thumb|Basilica of San Vicente, Avila, [[Spain]].]]
*[[List of World Heritage Sites in Africa]]
*[[List of World Heritage Sites in the Americas]]
*[[World Heritage Site]]
*[[Famous Architects]]
*[[Famous American artists]]
*[[Famous Cathedrals]]
*[[Famous Sculptures]]

== External links ==

*[http://www.nla.gov.au/worldtreasures/html/intro.html National Library of Australia]
*[http://www.worldtreasures.org/ Museum of World Treasures]
*[http://www.loc.gov/exhibits/world/world-record.html World Treasures of the Library of Congress]
*[http://www.metmuseum.org/toah/splash.htm Timeline of Art History] The Metropolitan Museum of Art.
*[http://whc.unesco.org/en/list World Heritage List] UNESCO.

[[Category:Art]][[Category:Culture]][[Category:History]][[Category:Geography]]
[[Category:Tourist Attractions]]

Secret ballot

2009-02-14T03:16:03Z

JosephineP: New page: The '''secret ballot''' is a major feature of the United States voting system. A secret ballot is unable to be inspected by anyone else after it has been cast (with the obvious exc...

The '''secret ballot''' is a major feature of the [[United States]] [[voting system]]. A secret ballot is unable to be inspected by anyone else after it has been cast (with the obvious exception of poll employees during [[recount]]s). While the secret ballot is [[mandate]]d by the U.S. [[Constitution]], some [[expert]]s consider it a poor choice. In particular, the lack of [[accountability]] attached to a secret ballot means that voters in an election may not feel the same level of [[personal responsibility]] as voters in a more [[open]] [[society]]. The beneficial [[peer pressure]] attached to an open ballot, in contrast, helps to ensure that a few [[antisocial]] voters do not overturn [[community standards]].

[[Category:Politics]]

Arrow's Theorem

2009-02-14T03:10:48Z

JosephineP: sp., possibily -> possibly

'''Arrow's Theorem''', also known as '''Arrow's impossibility theorem''' or '''Arrow's paradox''', is a seemingly [[paradox]]ical [[result]] in the [[mathematics|mathematical]] [[science]] of [[voting theory]]. The theorem was invented by the economist [[Kenneth Arrow]] in 1951, and applied the following year in the [[1952 Presidential Election]].

The theorem states, quite simply, that no [[representative]] voting system can simultaneously be "[[fair]]" and satisfy the following five [[condition]]s:

# ''Unrestricted domain.'' This condition means that the entire set of leaders (or whatever is being voted upon) must be decided by the voting system. It would clearly be both fair and satisfactory if the election, instead of determining the next [[President]], were to determine a Cabinet of 350 million people, a system known technically as [[direct democracy]] or [[referendum]]. This is not the situation being considered when we talk about Arrow's Theorem.
# ''Non-imposition.'' Non-imposition means, quite simply, that nobody is ''imposed upon'' to vote (or, contrariwise, not to vote). In the [[United States]], this criterion is satisfied by the [[secret ballot]].
# ''Non-dictatorship.'' Clearly this condition is satisfied as well.
# ''Positive association,'' also known as the ''Peter principle.'' Now we come to one of the trickier principles. The criterion of positive association means that if one voter — call him Alice — prefers Bush to Obama, then the final ranking of candidates will reflect that preference in some way. This condition was intended by Arrow to reflect real-world concerns regarding the protection of minority rights.
# ''Independence of irrelevant alternatives'' (known jocularly as the ''Nader corollary''). This condition means that a third-party candidate (such as [[Ralph Nader]] in the 2000 primaries) should not be able to "swing" the election to one side or another. In particular, a third party should be unable to draw votes away from the primary candidates, as Nader did to [[Al Gore]] in 2000, or as [[Pat Buchanan]] did to [[George W. Bush|Bush]]. This condition is perhaps the most relevant to the state of elections in the [[United States]] today.

In 1951, Kenneth Arrow proved that no system of voting, however so fair, can possibly satisfy all five of these constraints. For example, the [[Electoral College]] system used in the United States satisfies all of them except the last two (and in fact even the first, unrestricted domain, is questionable, since [[federal judge]]s are not elected by the people, but rather ''appointed'' by the bench).

The 1952 Presidential election demonstrated beyond doubt the correctness of Arrow's vision; incumbent [[Dwight D. Eisenhower]] beat his "egghead" Democratic challenger [[Adlai Stevenson]] in the largest landslide in human history. Nevertheless, the [[West Virginia]] Democratic primary was won by [[Averell Harriman]], who had never before held any elected office. This abnomaly led to closer investigation of Arrow's results. For his work on modern voting metholodgy, Arrow was awarded the 1972 [[Nobel Prize]] in [[Economics]].

[[Category:Mathematics]]

Arrow's Theorem

2009-02-14T03:10:26Z

JosephineP: Undo revision 550337 by CSGuy (Talk)

'''Arrow's Theorem''', also known as '''Arrow's impossibility theorem''' or '''Arrow's paradox''', is a seemingly [[paradox]]ical [[result]] in the [[mathematics|mathematical]] [[science]] of [[voting theory]]. The theorem was invented by the economist [[Kenneth Arrow]] in 1951, and applied the following year in the [[1952 Presidential Election]].

The theorem states, quite simply, that no [[representative]] voting system can simultaneously be "[[fair]]" and satisfy the following five [[condition]]s:

# ''Unrestricted domain.'' This condition means that the entire set of leaders (or whatever is being voted upon) must be decided by the voting system. It would clearly be both fair and satisfactory if the election, instead of determining the next [[President]], were to determine a Cabinet of 350 million people, a system known technically as [[direct democracy]] or [[referendum]]. This is not the situation being considered when we talk about Arrow's Theorem.
# ''Non-imposition.'' Non-imposition means, quite simply, that nobody is ''imposed upon'' to vote (or, contrariwise, not to vote). In the [[United States]], this criterion is satisfied by the [[secret ballot]].
# ''Non-dictatorship.'' Clearly this condition is satisfied as well.
# ''Positive association,'' also known as the ''Peter principle.'' Now we come to one of the trickier principles. The criterion of positive association means that if one voter — call him Alice — prefers Bush to Obama, then the final ranking of candidates will reflect that preference in some way. This condition was intended by Arrow to reflect real-world concerns regarding the protection of minority rights.
# ''Independence of irrelevant alternatives'' (known jocularly as the ''Nader corollary''). This condition means that a third-party candidate (such as [[Ralph Nader]] in the 2000 primaries) should not be able to "swing" the election to one side or another. In particular, a third party should be unable to draw votes away from the primary candidates, as Nader did to [[Al Gore]] in 2000, or as [[Pat Buchanan]] did to [[George W. Bush|Bush]]. This condition is perhaps the most relevant to the state of elections in the [[United States]] today.

In 1951, Kenneth Arrow proved that no system of voting, however so fair, can possibily satisfy all five of these constraints. For example, the [[Electoral College]] system used in the United States satisfies all of them except the last two (and in fact even the first, unrestricted domain, is questionable, since [[federal judge]]s are not elected by the people, but rather ''appointed'' by the bench).

The 1952 Presidential election demonstrated beyond doubt the correctness of Arrow's vision; incumbent [[Dwight D. Eisenhower]] beat his "egghead" Democratic challenger [[Adlai Stevenson]] in the largest landslide in human history. Nevertheless, the [[West Virginia]] Democratic primary was won by [[Averell Harriman]], who had never before held any elected office. This abnomaly led to closer investigation of Arrow's results. For his work on modern voting metholodgy, Arrow was awarded the 1972 [[Nobel Prize]] in [[Economics]].

[[Category:Mathematics]]

Diagram

2009-02-14T03:06:01Z

JosephineP: Redirecting to Graph

#REDIRECT [[Graph]]

Compass and straightedge

2009-02-14T03:05:25Z

JosephineP: add header

'''Compass and straightedge constructions''' played an important role in the [[history]] of [[mathematics]]. Some constructions accomplished by the ancients led to revolutionary developments in abstract mathematics. Other construction problems posed in antiquity remain unsolved even today.

==Description==
A compass-and-straightedge construction is a [[diagram]] drawn freehand with only the aid of a [[compass]] and a [[ruler]] from which the markings have been erased, also known as a "straight edge". Part of the finished diagram should display the solution to a particular given problem. For example, if the problem is "Trisect a [[line]]," the solution might consist of the given line with three Xs constructed over it at even [[interval]]s.

The art of compass-and-straightedge construction was invented by the [[Ancient Greeks]] in the centuries before [[Christ]]. The Greeks were not only excellent [[mathematician]]s, but also accomplished [[navigation|navigators]] — so it perhaps seemed natural to them that their mathematical drawings should involve the use of compasses. The straightedge was a later embellishment; straight edges were plentiful in the ancient world (for example: sword edges, [[oar]]s, and the foundations of [[building]]s), and the concept of a straight edge was pleasing and [[aesthetic]] to the ancient Greek mind. Many popular constructions were collected in the ''[[Element]]s'' of [[Euclid]].

In modern times, compass-and-straightedge constructions were rediscovered by [[Euler]], who [[resurrected]] them from the pages of his namesake's ''Elements'' and found that their simple geometric [[truth]]s were a pleasant diversion from the [[calculus wars]] then raging between the [[Newton]]ian British and the [[Leibniz]]ian German mathematical communities. In the twentieth century, compass-and-straightedge methods have become a popular form of [[recreational mathematics]], and the technique is taught as a one-week [[unit]] in many [[middle school]] [[math]] [[class]]es.

==Unsolved problems==
The Ancident Greeks solved all their problems with compass and straightedge. There were, however, three problems which they could not solve: [[cube|doubling the cube]], [[square|completing the square]], and [[angle|trisecting the angle]]. [[Pythagoras]] himself was said to have remarked that trisecting the angle was the hardest thing he had ever attempted. [[Archimedes]] attempted a "[[rationalism|rationalistic]]" approach to trisecting the angle, in which he repeatedly ''bisected'' the angle until the number of divisions became a multiple of 3; however, this does not work for most angles, and in any event it is only physically possible to bisect most angles seven or eight times, so Archimedes' approach does not [[scale]].

[[Category:Plane Geometry]]

Compass and straightedge

2009-02-14T03:04:52Z

JosephineP: New page: '''Compass and straightedge constructions''' played an important role in the history of mathematics. Some constructions accomplished by the ancients led to revolutionary developmen...

'''Compass and straightedge constructions''' played an important role in the [[history]] of [[mathematics]]. Some constructions accomplished by the ancients led to revolutionary developments in abstract mathematics. Other construction problems posed in antiquity remain unsolved even today.

A compass-and-straightedge construction is a [[diagram]] drawn freehand with only the aid of a [[compass]] and a [[ruler]] from which the markings have been erased, also known as a "straight edge". Part of the finished diagram should display the solution to a particular given problem. For example, if the problem is "Trisect a [[line]]," the solution might consist of the given line with three Xs constructed over it at even [[interval]]s.

The art of compass-and-straightedge construction was invented by the [[Ancient Greeks]] in the centuries before [[Christ]]. The Greeks were not only excellent [[mathematician]]s, but also accomplished [[navigation|navigators]] — so it perhaps seemed natural to them that their mathematical drawings should involve the use of compasses. The straightedge was a later embellishment; straight edges were plentiful in the ancient world (for example: sword edges, [[oar]]s, and the foundations of [[building]]s), and the concept of a straight edge was pleasing and [[aesthetic]] to the ancient Greek mind. Many popular constructions were collected in the ''[[Element]]s'' of [[Euclid]].

In modern times, compass-and-straightedge constructions were rediscovered by [[Euler]], who [[resurrected]] them from the pages of his namesake's ''Elements'' and found that their simple geometric [[truth]]s were a pleasant diversion from the [[calculus wars]] then raging between the [[Newton]]ian British and the [[Leibniz]]ian German mathematical communities. In the twentieth century, compass-and-straightedge methods have become a popular form of [[recreational mathematics]], and the technique is taught as a one-week [[unit]] in many [[middle school]] [[math]] [[class]]es.

==Unsolved problems==
The Ancident Greeks solved all their problems with compass and straightedge. There were, however, three problems which they could not solve: [[cube|doubling the cube]], [[square|completing the square]], and [[angle|trisecting the angle]]. [[Pythagoras]] himself was said to have remarked that trisecting the angle was the hardest thing he had ever attempted. [[Archimedes]] attempted a "[[rationalism|rationalistic]]" approach to trisecting the angle, in which he repeatedly ''bisected'' the angle until the number of divisions became a multiple of 3; however, this does not work for most angles, and in any event it is only physically possible to bisect most angles seven or eight times, so Archimedes' approach does not [[scale]].

[[Category:Plane Geometry]]

User:JosephineP

2009-02-14T03:01:52Z

JosephineP: New page: This user enjoys mathematics! I'm here to help.

This user enjoys mathematics! I'm here to help.

Manifold

2009-02-14T03:01:25Z

JosephineP: copy-edit

[[Image:Mobius.png|right|thumb|The [[Möbius strip]] is an example of a 2-manifold.]]
An ''n''-[[dimension]]al '''manifold''' (or ''n''-manifold) ''M'' is a [[topological space]] such that every point in ''M'' has a [[neighbourhood]] that is [[homeomorphism|homeomorphic]] to <math>\mathbb{R}^n</math>. These homeomorphisms induce a [[coordinatization]] of ''M'', and it is further required that the coordination is continuous.

An alternate definition constructs the manifolds over the [[complex numbers]] instead of the [[real numbers]]. An ''n''-dimensional complex manifold ''N'' is a [[topological space]] such that every point in ''N'' has a neighbourhood that is homeomorphic to '''C'''''n'' and whose coordinatization by these homeomorphisms is [[holomorphic]] ([[analytic]]).

Manifolds have [[Hausdorff space|Hausdorff]] dimension and are [[2nd-countable space|2-countable]].

==Constructing new manifolds from old==

*Suppose that <math>f:R^n \rightarrow R^m</math> is a differentiable function. Then <math>f^{-1}(y)</math> is a smooth manifold if ''y'' is a regular value of ''f''.

[[Category: Topology]]

Exterior derivative

2009-02-14T02:59:43Z

JosephineP: sp.

Let <math>f:M\rightarrow \mathbb{R}</math> be a [[smooth]] [[function]] on a [[manifold]]. The '''differential''' (or '''exterior derivative'''), <math>df</math>, is a [[covector field]] on ''M'' defined as follows: for ''v'' a [[tangent]] [[vector]] at a point <math>p</math>

<math>
df(v) = D_{v}(f)
</math>

i.e., <math>df(v)</math> is the [[directional derivative]] of ''f'' in the direction ''v''.

Note that if <math>x_1,...,x_n</math> are a local [[coordinate system]] for ''M'' at ''p'', then <math>dx_1,...,dx_n</math> define a local co-frame near ''p''. Thus, near ''p'', we may write the differential of ''f'' as a [[linear combination]]:

<math>
df = g_1 dx_1 +...+ g_n dx_n
</math>

In fact, since <math>dx_i(\frac{\partial}{\partial x_j}) = \delta^i_j</math>, we get that:

<math>
df = \frac{\partial f}{\partial x_1} dx_1 + ... + \frac{\partial f}{\partial x_n} dx_n
</math>

==Exterior derivative of differential forms==

If <math>\omega</math> is a [[differential form|differential k-form]] (i.e., a smooth section of <math>\Lambda^k T^*M</math>), the exterior derivative <math>d\omega</math> is a differential (k+1)-form defined as follows:

If we can write <math>\omega</math> in local coordinates as

<math>
f_{i_1\cdots i_k} dx_{i_1}\wedge\cdots\wedge dx_{i_k}
</math>

then in this coordinate system, <math>d\omega</math> equals

<math>
df_{i_1\cdots i_k}\wedge dx_{i_1}\wedge\cdots\wedge dx_{i_k}
</math>

More generally, we define the differential <math>d\omega</math> by extending the above definition by [[linearity]].

==Cosmological properties of the differential==

The [[operator]] ''d'' has the important property that <math>d\circ d = 0</math>. This essentially follows from the equality of mixed [[partial derivative]]s. The following simplest example illustrates the general proof: Let <math>f(x,y)</math> be a smooth function in two variables. Then

<math>
df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy
</math>

Thus

<math>
d^2 f = \frac{\partial^2 f}{\partial y\partial x}dy\wedge dx + \frac{\partial^2 f}{\partial x\partial y}dx\wedge dy
</math>

Since <math>dx\wedge dy = -dy\wedge dx</math>, the equality of mixed partials shows that <math>d^2 f = 0</math>.

[[Category:Mathematics]]