The Coal Question - Revision history

en>Motekov at 17:24, 12 November 2014

2014-11-12T17:24:12Z

← Older revision		Revision as of 19:24, 12 November 2014
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	~~{{use British English\|date=September 2013}}~~		Hello and welcome. My title is Figures Wunder. My day occupation is a meter reader. One of the extremely best things in the world for me is to do aerobics and now I'm attempting to earn money with it. For many years he's been residing in North Dakota and his family enjoys it.<br><br>Here is my webpage: [http://www.lankaclipstv.com/user/SFergerso at home std test]
	~~[[File:squircle2.svg\|thumb\|A squircle]]~~

	~~A '''squircle''' is a mathematical [[shape]] with properties between those of a [[Square (geometry)\|square]]~~ and ~~those of a [[circle]]~~. It is ~~a special case of [[superellipse]]~~. ~~The word "squircle"~~ is a ~~[[portmanteau]] of the words "square" and "circle"~~.

	~~==Equation==~~
	~~In a [[Cartesian coordinate system]], the squircle centered on the point (''a'', ''b'') with axes parallel to the coordinate axes is described by the equation:~~

	~~: <math>\left( x - a \right)^4 + \left( y - b \right)^4 = r^4</math>~~

	~~where ''r'' is the minor radius~~ of the ~~squircle ([[cf.]] [[Circle#Equations\|equation of a circle]]).~~

	~~==Generalisation==~~
	~~The squircle is a specific case (found by setting ''n'' = 4) of~~ the ~~class of shapes known as "supercircles", which have the equation~~

	~~:<math>\left\| x - a \right\|^n + \left\| y - b \right\|^n = \|r\|^n.\,</math>~~

	~~Unfortunately, the [[Taxonomy (general)\|taxonomy]]~~ is ~~not consistent - some authors refer~~ to the class as "supercircles" and the specific case as a squircle, while others adopt the opposite naming convention. Supercircles in turn are a subset of the even more general "[[superellipse]]s", which have the equation

	~~:<math>\left\|\frac{x - a}{r_a}\right\|^n\! + \left\|\frac{y - b}{r_b}\right\|^n\! = 1,\,</math>~~

	~~where ''r''<sub>''a''</sub>~~ and ''r''<sub>''b''</sub> are the [[Semi-major axis\|semi-major]] and [[Semi-minor axis\|semi-minor]] axes. Superellipses were extensively studied and popularised by the [[Denmark\|Danish]] [[mathematician]] [[Piet Hein (Denmark)\|Piet Hein]].

	~~== Similar shapes ==~~
	~~[[File:squircle rounded square.svg\|thumb\|A squircle (blue) compared~~ with ~~a rounded square (red)~~. ~~[[:File:squircle rounded square.svg\|~~'~~''(Larger image)''' ]] ]]~~

	A shape similar to a squircle, called a ''rounded square'', may be generated by arranging four quarters of a circle and connecting their loose ends with straight lines. Such a shape is very similar but not identical to the squircle. Although constructing a rounded square may be conceptually and physically simpler, the squircle has the simpler equation and can be generalised much more easily. One consequence of this is that the squircle and other superellipses can be scaled up or down quite easily. This is useful where, for example, one wishes to create nested squircles.

	~~[[File:Simple squircles.jpg\|thumb\|Various forms of a truncated circle]]~~
	Another similar shape is defined as the [[constructive solid geometry\|boolean intersection]] of a square and a concentric circle whose diameter is greater than the length of the side of the square, but less than the length of the diagonal of the square. Such truncated circle shapes lack the tangent continuity possessed by both superellipses and rounded squares.

	~~==Uses==~~
	Squircles are useful in [[optics]]. If light is passed through a two-dimensional square aperture, the central spot in the [[diffraction]] pattern can be closely modelled by a squircle or supercircle. If a rectangular aperture is used, the spot can be approximated by a [[superellipse]].<ref>{{cite journal \|journal=[[Optik (journal)\|Optik]] \|volume=116 \|pages=265–269 \|year=2005 \|url=http://investigacion.izt.uam.mx/mfg/pub/lcdpix_optik05.pdf \|accessdate=20 November 2006 \|doi=10.1016/j.ijleo.2005.01.018 \|title=LCD pixel shape and far-field diffraction patterns \|issue=6 \|author1=M. Fernández Guasti \|author2=A. Meléndez Cobarrubias \|author3=F.J. Renero Carrillo \|author4=A. Cornejo Rodríguez}}</ref>

	~~Squircles have also~~ been used to construct [[Plate (dishware)\|dinner plate]]s. A squircular plate has a larger area (and can thus hold more food) than a circular one with the same radius, but still occupies the same amount of space in ~~a rectangular or square [[cupboard]]. The same is true of a square plate, but there are various problems (such as fragility,~~ and difficulty of wiping up sauce) associated with the corners of square plates.<ref>{{cite web \|publisher=Kitchen Contraptions \|url=http://www.kitchencontraptions.com/archives/006830.php \|title=Squircle Plate \|accessdate=20 November 2006}}</ref>

	[[Sumvision]] manufactures an [[Secure Digital\|SD card]]-based [[Digital audio player\|MP3 player]] named Squircle for the budget market. It is not, however, a genuine squircle, although vaguely similar in shape.<ref>{{cite web \|publisher=Advanced MP3 Players \|url=http://www.advancedmp3players.co.uk/shop/product_info.php?products_id=1092 \|title=Squircle SD Card MP3 Player \|accessdate=20 November 2006}}</ref>

	~~[[Nokia]] is closely associated with the squircle, having used~~ it ~~as a touchpad button in many phones~~.<~~ref~~>~~Nokia Designer Mark Delaney mentions the squircle in a video regarding classic Nokia phone designs:~~<br>~~{{cite video \|url=http~~://conversations.nokia.com/2009/06/17/nokia-6700-the-little-black-dress-of-phones/ \|title=Nokia 6700 – The little black dress of phones \|quote=See 3:13 in video \|accessdate=9 December 2009}}</ref><ref>{{cite web \|title=Clayton Miller evaluates shapes on mobile phone platforms \|url=http://interuserface.net/2011/06/own-a-shape/ \|accessdate=2 July 2011}}</ref>

	~~==See also==~~
	* [[Superegg]]
	* [[Ellipse]]
	* [[Astroid]]
	* [[Ellipsoid]]
	* [[Oval]]
	* [[Lp_space\|L<sup>p</sup> spaces]]

	~~==References==~~
	~~{{Reflist\|colwidth=25em}}~~

	~~==External links==~~
	* [http://www.~~procato~~.com/~~superellipse~~/ ~~Online Calculator for supercircle and super-ellipse]~~
	* [http://www.webcitation.org/query?url=http://www.geocities.com/dougtclark/mySquircle.html&date=2009-10-25+21:04:33 Web based supercircle generator]



	~~[[Category:Geometric shapes]]~~
	~~[[Category:Curves]]~~
	~~[[Category:Algebraic curves]~~]

en>BD2412: Fixing links to disambiguation pages, replaced: overpopulation → overpopulation using AWB

2013-12-31T17:19:15Z

Fixing links to disambiguation pages, replaced: overpopulation → overpopulation using AWB

← Older revision		Revision as of 19:19, 31 December 2013
Line 1:		Line 1:
	The ~~name~~ of the ~~author~~ is ~~Jayson~~. ~~I am presently~~ a ~~travel agent~~. ~~Alaska~~ is the ~~only location I~~'~~ve been residing in~~ but ~~now I'm considering~~ other ~~choices~~. ~~The favorite hobby~~ for ~~him~~ and ~~his children~~ is to ~~perform lacross~~ and ~~he'll be starting some thing else along~~ with it.<br><br>~~Also visit my site~~ - [http://~~modenpeople~~.co.kr/~~modn~~/~~qna~~/~~292291 online psychics~~]		{{use British English\|date=September 2013}}
			[[File:squircle2.svg\|thumb\|A squircle]]

			A '''squircle''' is a mathematical [[shape]] with properties between those of a [[Square (geometry)\|square]] and those of a [[circle]]. It is a special case of [[superellipse]]. The word "squircle" is a [[portmanteau]] of the words "square" and "circle".

			==Equation==
			In a [[Cartesian coordinate system]], the squircle centered on the point (''a'', ''b'') with axes parallel to the coordinate axes is described by the equation:

			: <math>\left( x - a \right)^4 + \left( y - b \right)^4 = r^4</math>

			where ''r'' is the minor radius of the squircle ([[cf.]] [[Circle#Equations\|equation of a circle]]).

			==Generalisation==
			The squircle is a specific case (found by setting ''n'' = 4) of the class of shapes known as "supercircles", which have the equation

			:<math>\left\| x - a \right\|^n + \left\| y - b \right\|^n = \|r\|^n.\,</math>

			Unfortunately, the [[Taxonomy (general)\|taxonomy]] is not consistent - some authors refer to the class as "supercircles" and the specific case as a squircle, while others adopt the opposite naming convention. Supercircles in turn are a subset of the even more general "[[superellipse]]s", which have the equation

			:<math>\left\|\frac{x - a}{r_a}\right\|^n\! + \left\|\frac{y - b}{r_b}\right\|^n\! = 1,\,</math>

			where ''r''<sub>''a''</sub> and ''r''<sub>''b''</sub> are the [[Semi-major axis\|semi-major]] and [[Semi-minor axis\|semi-minor]] axes. Superellipses were extensively studied and popularised by the [[Denmark\|Danish]] [[mathematician]] [[Piet Hein (Denmark)\|Piet Hein]].

			== Similar shapes ==
			[[File:squircle rounded square.svg\|thumb\|A squircle (blue) compared with a rounded square (red). [[:File:squircle rounded square.svg\|'''(Larger image)''' ]] ]]

			A shape similar to a squircle, called a ''rounded square'', may be generated by arranging four quarters of a circle and connecting their loose ends with straight lines. Such a shape is very similar but not identical to the squircle. Although constructing a rounded square may be conceptually and physically simpler, the squircle has the simpler equation and can be generalised much more easily. One consequence of this is that the squircle and other superellipses can be scaled up or down quite easily. This is useful where, for example, one wishes to create nested squircles.

			[[File:Simple squircles.jpg\|thumb\|Various forms of a truncated circle]]
			Another similar shape is defined as the [[constructive solid geometry\|boolean intersection]] of a square and a concentric circle whose diameter is greater than the length of the side of the square, but less than the length of the diagonal of the square. Such truncated circle shapes lack the tangent continuity possessed by both superellipses and rounded squares.

			==Uses==
			Squircles are useful in [[optics]]. If light is passed through a two-dimensional square aperture, the central spot in the [[diffraction]] pattern can be closely modelled by a squircle or supercircle. If a rectangular aperture is used, the spot can be approximated by a [[superellipse]].<ref>{{cite journal \|journal=[[Optik (journal)\|Optik]] \|volume=116 \|pages=265–269 \|year=2005 \|url=http://investigacion.izt.uam.mx/mfg/pub/lcdpix_optik05.pdf \|accessdate=20 November 2006 \|doi=10.1016/j.ijleo.2005.01.018 \|title=LCD pixel shape and far-field diffraction patterns \|issue=6 \|author1=M. Fernández Guasti \|author2=A. Meléndez Cobarrubias \|author3=F.J. Renero Carrillo \|author4=A. Cornejo Rodríguez}}</ref>

			Squircles have also been used to construct [[Plate (dishware)\|dinner plate]]s. A squircular plate has a larger area (and can thus hold more food) than a circular one with the same radius, but still occupies the same amount of space in a rectangular or square [[cupboard]]. The same is true of a square plate, but there are various problems (such as fragility, and difficulty of wiping up sauce) associated with the corners of square plates.<ref>{{cite web \|publisher=Kitchen Contraptions \|url=http://www.kitchencontraptions.com/archives/006830.php \|title=Squircle Plate \|accessdate=20 November 2006}}</ref>

			[[Sumvision]] manufactures an [[Secure Digital\|SD card]]-based [[Digital audio player\|MP3 player]] named Squircle for the budget market. It is not, however, a genuine squircle, although vaguely similar in shape.<ref>{{cite web \|publisher=Advanced MP3 Players \|url=http://www.advancedmp3players.co.uk/shop/product_info.php?products_id=1092 \|title=Squircle SD Card MP3 Player \|accessdate=20 November 2006}}</ref>

			[[Nokia]] is closely associated with the squircle, having used it as a touchpad button in many phones.<ref>Nokia Designer Mark Delaney mentions the squircle in a video regarding classic Nokia phone designs:<br>{{cite video \|url=http://conversations.nokia.com/2009/06/17/nokia-6700-the-little-black-dress-of-phones/ \|title=Nokia 6700 – The little black dress of phones \|quote=See 3:13 in video \|accessdate=9 December 2009}}</ref><ref>{{cite web \|title=Clayton Miller evaluates shapes on mobile phone platforms \|url=http://interuserface.net/2011/06/own-a-shape/ \|accessdate=2 July 2011}}</ref>

			==See also==
			* [[Superegg]]
			* [[Ellipse]]
			* [[Astroid]]
			* [[Ellipsoid]]
			* [[Oval]]
			* [[Lp_space\|L<sup>p</sup> spaces]]

			==References==
			{{Reflist\|colwidth=25em}}

			==External links==
			* [http://www.procato.com/superellipse/ Online Calculator for supercircle and super-ellipse]
			* [http://www.webcitation.org/query?url=http://www.geocities.com/dougtclark/mySquircle.html&date=2009-10-25+21:04:33 Web based supercircle generator]



			[[Category:Geometric shapes]]
			[[Category:Curves]]
			[[Category:Algebraic curves]]

en>INeverCry: border

2012-07-16T18:19:07Z

border

New page

The name of the author is Jayson. I am presently a travel agent. Alaska is the only location I've been residing in but now I'm considering other choices. The favorite hobby for him and his children is to perform lacross and he'll be starting some thing else along with it.<br><br>Also visit my site - [http://modenpeople.co.kr/modn/qna/292291 online psychics]