The Coal Question: Difference between revisions

Revision as of 19:19, 31 December 2013

A squircle

A squircle is a mathematical shape with properties between those of a 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:

{(x - a)}^{4} + {(y - b)}^{4} = r^{4}

where r is the minor radius of the squircle (cf. 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

{| x - a |}^{n} + {| y - b |}^{n} = | r |^{n} .

Unfortunately, the 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 "superellipses", which have the equation

{| \frac{x - a}{r_{a}} |}^{n} + {| \frac{y - b}{r_{b}} |}^{n} = 1,

where r_a and r_b are the semi-major and semi-minor axes. Superellipses were extensively studied and popularised by the Danish mathematician Piet Hein.

Similar shapes

File:Squircle rounded square.svg

A squircle (blue) compared with a rounded square (red). (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

Various forms of a truncated circle

Another similar shape is defined as the 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.^[1]

Squircles have also been used to construct dinner plates. 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.^[2]

Sumvision manufactures an SD card-based MP3 player named Squircle for the budget market. It is not, however, a genuine squircle, although vaguely similar in shape.^[3]

Nokia is closely associated with the squircle, having used it as a touchpad button in many phones.^[4]^[5]

References

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External links

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Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Template:Cite web
↑ Template:Cite web
↑ Nokia Designer Mark Delaney mentions the squircle in a video regarding classic Nokia phone designs:
Template:Cite video
↑ Template:Cite web

[1] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] Template:Cite web

[3] Template:Cite web

[4] Nokia Designer Mark Delaney mentions the squircle in a video regarding classic Nokia phone designs:
Template:Cite video

[5] Template:Cite web

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-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'',&nbsp;''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''&nbsp;=&nbsp;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]]

The Coal Question: Difference between revisions

en>BD2412

Revision as of 19:19, 31 December 2013

Contents

Equation

Generalisation

Similar shapes

Uses

See also

References

External links

Navigation menu

The Coal Question: Difference between revisions

en>BD2412

Revision as of 19:19, 31 December 2013

Equation

Generalisation

Similar shapes

Uses

See also

References

External links

Navigation menu

Search