Pulley - Revision history

2601:1:8202:2B60:992B:B4A4:6DD9:841B at 05:27, 13 January 2015

2015-01-13T05:27:03Z

← Older revision		Revision as of 07:27, 13 January 2015
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	~~When spending time outdoors is~~ not an ~~option, spending time in a hotel suite can be equally relaxing and fun~~. ~~Booking a hotel was simple, because rooms for a family of four~~ are ~~always~~ easy to ~~find~~. ~~4)What was your relationship~~ with ~~Anissa Jones like during and after the series. The underlying philosophy from your schooling may vary depending on whether~~ it ~~is a government school, a religious school, or one of the [http://www.guardian.Co.uk/search?q=alternate+schooling alternate schooling] systems~~. ~~A root canal is necessary when the tissue in the root chamber of the tooth becomes infected~~. ~~Yes~~, ~~pack your stroller~~ so ~~you can circle the deck~~. <br><br>~~Dealing with difficult people goes beyond working with difficult people but often means trying to handle frustrating and distressing family members~~. ~~Currently~~, the ~~company operates at over 370 sites~~, ~~including 135 factories~~, ~~in 68 countries worldwide~~ and ~~generates annual revenues of $28 billion. Just be sure you get free quotes from numerous companies before selecting yours so you can find~~ the ~~most affordable and the most effective for your specific security requirements. There are resources to help~~ you~~, such as the report “Real Life Guidance: Finding More Family Time~~. ~~Then, choose one word (a sight word or other familiar word) that doesn~~'t ~~belong holiday [[https://linode02~~.~~wandborg~~.~~se/u/anschnaars/ linode02.wandborg.se]]~~ in the ~~word family. The 6 way I told above is not all the way you can do to strengthen~~ your ~~relationship with family~~. <br><br>~~Don't worry you can give it back with~~ the ~~thorough cleaning if~~ the ~~carpet~~. ~~Higher salaries allow families to consider day care~~, ~~special after school programs, or nannies~~. ~~For example, no one wants to hurt Cousin Dee’s expectations about hosting~~ the ~~Thanksgiving feast~~. ~~You can't head~~ to ~~the movies because everyone needs a potty break at one time or another~~ and ~~some of you like~~ to ~~talk through the show. You'll also notice that they start telling lies saying they are working late when they are really stopping off at the pub for~~ a ~~drink. If the box doesn't already have an opening in the front cut out~~ a ~~mouth and make jagged teeth~~. <br><br>It ~~does not really matter which type~~ of ~~car~~ that ~~you choose~~. ~~If the client gives you the freedom of graphic design then~~ you ~~have a great chance~~ to ~~show your creativity and ideas~~ but ~~make sure,~~ you ~~don~~'~~t go personal~~. ~~What is so sad is that young people today just are not into camping~~. ~~Let go, give them~~ the ~~space they have demanded~~ and ~~get on with living your life. (Example:~~ I'~~m thinking of~~ a number ~~between'Skip count by 2's, 3's, 4's')~~. ~~The television show 'Sharknado' might be closer to a sequel than Hollywood originally predicted~~. <br><br>~~When~~ you ~~are in~~ the ~~market to sell a single family~~ home ~~that you have been renting out for investment~~, ~~it is an easier task since~~ your ~~pool of buyers are both investors as well as people who are looking to purchase homes for themselves~~. ~~It may be considered as contempt of court when family court orders are broken. If God is involved things will always fare far better. Although it seems like~~ a ~~strange idea at first, it is a great craze~~ that ~~has caught on across~~ the ~~world~~ -~~- having begun~~ it's ~~journey~~ in ~~Australia~~, ~~and just recently launched here in~~ the ~~UK with The - Sticker - Family~~. ~~Top 10 Reasons Why It's Easier To Buy A $5~~,~~000~~,~~000 Apartment Building Than A Single Family Investment Property~~. ~~Ganesha, on~~ the ~~other hand~~, ~~simply folded his palms in prayer~~ and ~~walked around his seated parents, returning~~ to ~~his starting point ahead of Kartikeya~~.

98.19.214.31: /* Block and tackle */

2014-02-27T23:11:52Z

Block and tackle

← Older revision		Revision as of 01:11, 28 February 2014
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	~~In [[geometry]], a '''prismatoid''' is a [[polyhedron]] where all [[vertex (geometry)\|vertices]] lie in two parallel planes. (If both planes have the same number of vertices,~~
	~~and the lateral faces are either [[parallelogram]]s or [[trapezoid]]s, it is called a '''prismoid'''.)~~

	If the areas of the two parallel faces are A<sub>1</sub> and A<sub>3</sub>, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A<sub>2</sub>, and the height (the distance between the two parallel faces) is h, then the [[volume]] of the prismatoid is given by <math>V = \frac{h(A_1 + 4A_2 + A_3)}{6}</math> (This formula follows immediately by [[integral\|integrating]] the area parallel to the two planes of vertices by [[Simpson's rule]], since that rule is exact for integration of [[polynomial]]s of degree up to 3, and in this case the area is at most a [[quadratic function]] in the height.)

	~~== Prismatoid families ==~~		When spending time outdoors is not an option, spending time in a hotel suite can be equally relaxing and fun. Booking a hotel was simple, because rooms for a family of four are always easy to find. 4)What was your relationship with Anissa Jones like during and after the series. The underlying philosophy from your schooling may vary depending on whether it is a government school, a religious school, or one of the [http://www.guardian.Co.uk/search?q=alternate+schooling alternate schooling] systems. A root canal is necessary when the tissue in the root chamber of the tooth becomes infected. Yes, pack your stroller so you can circle the deck. <br><br>Dealing with difficult people goes beyond working with difficult people but often means trying to handle frustrating and distressing family members. Currently, the company operates at over 370 sites, including 135 factories, in 68 countries worldwide and generates annual revenues of $28 billion. Just be sure you get free quotes from numerous companies before selecting yours so you can find the most affordable and the most effective for your specific security requirements. There are resources to help you, such as the report “Real Life Guidance: Finding More Family Time. Then, choose one word (a sight word or other familiar word) that doesn't belong holiday [[https://linode02.wandborg.se/u/anschnaars/ linode02.wandborg.se]] in the word family. The 6 way I told above is not all the way you can do to strengthen your relationship with family. <br><br>Don't worry you can give it back with the thorough cleaning if the carpet. Higher salaries allow families to consider day care, special after school programs, or nannies. For example, no one wants to hurt Cousin Dee’s expectations about hosting the Thanksgiving feast. You can't head to the movies because everyone needs a potty break at one time or another and some of you like to talk through the show. You'll also notice that they start telling lies saying they are working late when they are really stopping off at the pub for a drink. If the box doesn't already have an opening in the front cut out a mouth and make jagged teeth. <br><br>It does not really matter which type of car that you choose. If the client gives you the freedom of graphic design then you have a great chance to show your creativity and ideas but make sure, you don't go personal. What is so sad is that young people today just are not into camping. Let go, give them the space they have demanded and get on with living your life. (Example: I'm thinking of a number between'Skip count by 2's, 3's, 4's'). The television show 'Sharknado' might be closer to a sequel than Hollywood originally predicted. <br><br>When you are in the market to sell a single family home that you have been renting out for investment, it is an easier task since your pool of buyers are both investors as well as people who are looking to purchase homes for themselves. It may be considered as contempt of court when family court orders are broken. If God is involved things will always fare far better. Although it seems like a strange idea at first, it is a great craze that has caught on across the world -- having begun it's journey in Australia, and just recently launched here in the UK with The - Sticker - Family. Top 10 Reasons Why It's Easier To Buy A $5,000,000 Apartment Building Than A Single Family Investment Property. Ganesha, on the other hand, simply folded his palms in prayer and walked around his seated parents, returning to his starting point ahead of Kartikeya.

	[[~~Image~~:~~Pentagonal pyramid~~.~~png\|100px]]~~
	~~[[Image:Pentagonal prism~~.~~png\|100px~~]]
	~~[[Image:Pentagonal_antiprism~~.~~png\|100px]]~~
	~~[[Image:Pentagrammic crossed antiprism~~.~~png\|100px]]~~
	~~[[Image:Pentagonal cupola~~.~~png\|100px]]~~
	~~[[Image:Pentagonal frustum~~.~~svg\|100px]]~~

	~~Families~~ of ~~prismatoids include~~:

	* [[Pyramid (geometry)\|Pyramids]], ~~where~~ one ~~plane contains only~~ a ~~single point;~~
	* [[~~Wedge (geometry)\|Wedges~~]], ~~where~~ one ~~plane contains only two points~~;
	* [[Prism (geometry)\|Prisms]], where the ~~polygons in each plane~~ are ~~congruent and joined by rectangles or parallelograms;~~
	* [[Antiprism]]s, where the ~~polygons~~ in ~~each plane are congruent~~ and ~~joined by an alternating strip~~ of ~~triangles;~~
	* [[Crossed antiprism]]s;
	* [[cupola (geometry)\|Cupolae]], where the ~~polygon in one plane contains twice as many points as~~ the ~~other~~ and is ~~joined to it by alternating triangles~~ and ~~rectangles;~~
	* [[Frustum\|Frusta]] obtained by [[Truncation (~~geometry)\|truncation]]~~ of a ~~pyramid;~~
	* [[Quadrilateral]]-faced [[Hexahedron\|hexahedral]] prismatoids:
	*# [[Parallelepiped]]s ~~- six [[parallelogram]] faces~~
	*# [[Rhombohedron]]s ~~- six [[rhombus]] faces~~
	*# [[Trigonal trapezohedron\|Trigonal trapezohedra]] - six congruent rhombus faces
	*# [[Cuboid]]s ~~- six rectangular faces~~
	*# [[frustum\|Quadrilateral frusta]] - an [[Apex (geometry)~~\|apex]]-[[Truncation (geometry)\|truncated]] [[square pyramid]]~~
	*# [[Cube]]s - six square faces

	~~== Higher dimensions ==~~

	~~In general~~ a ~~[[polytope]] is prismatoidal if its vertices exist in two [[hyperplane]]s~~. ~~For example~~ in ~~4-dimension~~, ~~two polyhedra can~~ be ~~placed~~ in ~~2 parallel 3-spaces~~, and ~~connected~~ with ~~polyhedral sides.~~

	~~[[File:4D Tetrahedral Cupola-perspective~~-~~cuboctahedron~~-~~first~~.~~png\|320px]]<BR>~~A ~~tetrahedral-cuboctahedral cupola~~.

	~~==External links==~~
	* {{MathWorld \| urlname=Prismatoid \| title=Prismatoid}}

	~~{{Polyhedron navigator}}~~

	~~{{polyhedron-stub}}~~
	~~[[Category:Polyhedra]]~~
	~~[[Category:Prismatoid polyhedra]]~~

en>Faizan: Reverted 1 edit by 74.95.86.238 identified as test/vandalism using STiki

2014-01-30T18:30:32Z

Reverted 1 edit by 74.95.86.238 identified as test/vandalism using STiki

New page

In [[geometry]], a '''prismatoid''' is a [[polyhedron]] where all [[vertex (geometry)|vertices]] lie in two parallel planes. (If both planes have the same number of vertices,
and the lateral faces are either [[parallelogram]]s or [[trapezoid]]s, it is called a '''prismoid'''.)

If the areas of the two parallel faces are A1 and A3, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A2, and the height (the distance between the two parallel faces) is h, then the [[volume]] of the prismatoid is given by <math>V = \frac{h(A_1 + 4A_2 + A_3)}{6}</math> (This formula follows immediately by [[integral|integrating]] the area parallel to the two planes of vertices by [[Simpson's rule]], since that rule is exact for integration of [[polynomial]]s of degree up to 3, and in this case the area is at most a [[quadratic function]] in the height.)

== Prismatoid families ==

[[Image:Pentagonal pyramid.png|100px]]
[[Image:Pentagonal prism.png|100px]]
[[Image:Pentagonal_antiprism.png|100px]]
[[Image:Pentagrammic crossed antiprism.png|100px]]
[[Image:Pentagonal cupola.png|100px]]
[[Image:Pentagonal frustum.svg|100px]]

Families of prismatoids include:

* [[Pyramid (geometry)|Pyramids]], where one plane contains only a single point;
* [[Wedge (geometry)|Wedges]], where one plane contains only two points;
* [[Prism (geometry)|Prisms]], where the polygons in each plane are congruent and joined by rectangles or parallelograms;
* [[Antiprism]]s, where the polygons in each plane are congruent and joined by an alternating strip of triangles;
* [[Crossed antiprism]]s;
* [[cupola (geometry)|Cupolae]], where the polygon in one plane contains twice as many points as the other and is joined to it by alternating triangles and rectangles;
* [[Frustum|Frusta]] obtained by [[Truncation (geometry)|truncation]] of a pyramid;
* [[Quadrilateral]]-faced [[Hexahedron|hexahedral]] prismatoids:
*# [[Parallelepiped]]s - six [[parallelogram]] faces
*# [[Rhombohedron]]s - six [[rhombus]] faces
*# [[Trigonal trapezohedron|Trigonal trapezohedra]] - six congruent rhombus faces
*# [[Cuboid]]s - six rectangular faces
*# [[frustum|Quadrilateral frusta]] - an [[Apex (geometry)|apex]]-[[Truncation (geometry)|truncated]] [[square pyramid]]
*# [[Cube]]s - six square faces

== Higher dimensions ==

In general a [[polytope]] is prismatoidal if its vertices exist in two [[hyperplane]]s. For example in 4-dimension, two polyhedra can be placed in 2 parallel 3-spaces, and connected with polyhedral sides.

[[File:4D Tetrahedral Cupola-perspective-cuboctahedron-first.png|320px]] A tetrahedral-cuboctahedral cupola.

==External links==
* {{MathWorld | urlname=Prismatoid | title=Prismatoid}}

{{Polyhedron navigator}}

{{polyhedron-stub}}
[[Category:Polyhedra]]
[[Category:Prismatoid polyhedra]]