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[[File:Perles configuration.svg|thumb|The Perles configuration]]
In geometry, the '''Perles configuration''' is a configuration of 9 points and 9 lines that can be realized in the [[Euclidean plane]] but for which every realization has at least one [[irrational number]] as one of its coordinates. It is not a [[projective configuration]], however, because its points and lines do not all have the same number of incidences as each other. It was introduced by [[Micha Perles]] in the 1960s.


One way of constructing the Perles configuration is to start with a regular [[pentagon]] and its five diagonals, which form the sides of a smaller regular pentagon within the initial one. The nine points of the configuration consist of four out of the five vertices of each pentagon and the shared center of the two pentagons; the two missing pentagon vertices are chosen to be collinear with the center. The nine lines of the configuration consist of the five lines that are diagonals of the outer pentagon and sides of the inner pentagon, and the four lines that pass through the center and through corresponding pairs of vertices from the two pentagons.


Feminism is fashionable. That's the statement we are never supposed to utter, within earshot of either feminists or fashion editors.<br><br>That's because feminists understandably rail against the co-opting of their cause as a "trend", while editors, the press and some fashion designers rankle at the implication that their brave stance for womankind is viewed on a par with the ensemble cast of Sex and the City 2 performing Helen Reddy's empowering 1971 anthem "I Am Woman".<br><br>But feminism is fashionable, insomuch as it is being name-checked by the fashion industry with a striking frequency. Miuccia Prada's spring/summer 2014 collection was based on "the multiplicity of guises that women assume in the course of a day, a lifetime", a notion interpreted by many as fundamentally feminist.<br>For once, however, this feeling didn't start with Miuccia Prada: over the past few years, any female fashion designer or editor seems to be asked their views on the topic. Collections by every designer from Donatella Versace, to Phoebe Philo at C�line, to the London duo Meadham Kirchhoff, have been interpreted as feminist - whether the designers intended it or not.<br><br>Last November, British Elle began a campaign to "rebrand" feminism, inviting feminist publications Vagenda and Feminist Times to work with advertising agencies to rework the terminology.<br>Prada spring/summer 2014 fashion show <br>"What we did was ask, 'Does the word need rebranding?' The only thing that seemed an issue was the word," says Lorraine Candy, Elle's editor-in-chief. "We just asked a question." The response to Elle's question was staggering: a reach of 135 million on Twitter for the campaign, which Candy emphasises "is the biggest thing we've had engagement in, on Twitter, it's extraordinary� I was slightly taken aback by the force of opinion, the need from young women to talk about it� It struck me that this is a debate that everyone is having at the moment," Candy state<br><br>
Every realization of this configuration in the real [[projective plane]] is equivalent, under a [[projective transformation]], to a realization constructed in this way from a regular pentagon. Therefore, in every realization, there are four points having the same [[cross-ratio]] as the cross-ratio of the four collinear points in the realization derived from the regular pentagon. But, these four points have <math>1+\varphi</math> as their cross-ratio, where <math>\varphi</math> is the [[golden ratio]], an irrational number. Every four collinear points with rational coordinates have a rational cross ratio, so the Perles configuration cannot be realized by rational points. [[Branko Grünbaum]] has conjectured that every configuration that can be realized by irrational but not rational numbers has at least nine points; if so, the Perles configuration would be the smallest possible irrational configuration of points and lines.<ref>{{harvtxt|Grünbaum|2003}}.</ref>
"If you look at women's magazines in the last year, you'll see the word being used more than I think it ever has been<br>
In itself, this was the motivation for Elle to tackle the terminology head-on. "I feel it excludes younger women," says Candy. "Younger women felt they wouldn't know enough to be a feminist, if you haven't read Germaine Greer or Marilyn French� I think there is still a lot of confusion around it, and I think the word remains quite contentiou<br><br>


Elle sought to unpick the meaning behind the word, rather than just splashing it across its front-page. However, the issue with feminism in fashion for some is exactly that: the use of the term for simple, superficial sloganeering. "It absolutely has become a buzzword," says Reni Eddo-Lodge, a journalist and contributing editor to the website Feminist Times, "and a lot of the time there is a lot of confusion about what it means. There isn't a huge, joined-up movement like there was 30 or 40 years ago. There's no agreement." For Eddo-Lodge, this is an enormous iss<br><br>
Perles used his configuration to construct an eight-dimensional [[convex polytope]] with twelve vertices that can similarly be realized with real coordinates but not with rational coordinates. [[Ernst Steinitz]]'s proof of [[Steinitz's theorem]] can be used to show that every three-dimensional polytope can be realized with rational coordinates, but it is now known that there exist irrational polytopes in four dimensions.<ref>{{harvtxt|Grünbaum|2003}}, p. 96a.</ref>


"The word is meaningless if there are no politics to back it up� Ultimately feminism is a political moveme<br>."
==Notes==
Politics are often rinsed from fashionable feminism. It's understandable: fashion is primarily visual, so aesthetic elements do the talking, unless you're literally sloganeering, in the manner of Katharine Hamnett in the 1980s. "This collection really became about female power," said the jewellery designer Eddie Borgo of his spring 2014 collection. "It gives [women] strength." The collection could easily have been interpreted as punk, with its zip-teeth and razor-sharp ed<br><br>
{{reflist}}


But punk is very 2013. Generally, designers scrabble after the same grab-bag of "feminist" signifiers: clich�s of the "tough woman" or "power dressing," big shoulders, high heels, zips and studs. "Some people consider feminism to be climbing into the boardroom, becoming Sheryl Sandberg," says Eddo-Lo<br>e.
==References==
"Feminism for me is about liberation from structural power." That's much more difficult to evoke in a skirt-s<br>t.
*{{Citation | last1=Berger | first1=Marcel | author1-link=Marcel Berger | title=Geometry revealed | url=http://dx.doi.org/10.1007/978-3-540-70997-8 | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-70996-1 | doi=10.1007/978-3-540-70997-8 | id={{MR|2724440}} | year=2010}}
Other designers' work can be more unexpectedly interpreted as feminist: the fact that JW Anderson cross-pollinates the wardrobes of men and women, for instance, to the extent that he cut his winter 2013 menswear trousers without a phallocentric masculine bu<br><br>
*{{citation
| last = Grünbaum | first = Branko | authorlink = Branko Grünbaum
| edition = Second
| isbn = 0-387-00424-6
| location = New York
| mr = 1976856
| pages = 93–95
| publisher = Springer-Verlag
| series = Graduate Texts in Mathematics
| title = Convex polytopes
| volume = 221
| year = 2003}}.


He may not approach fashion with a strictly feminist intent, but it is easy to interpret Anderson's [http://Www.Google.de/search?q=clothes clothes] as such. The same is true of Phoebe Philo, arguably the spark that ignited the feminism and fashion debate. She left her previous role at Chlo� to focus on her personal life, and moved the C�line studio to London when she took over the house's reins in <br><br>.
[[Category:Configurations]]
 
[[Category:Polyhedral combinatorics]]
[http://www.pcs-systems.co.uk/Images/celinebag.aspx Cheap Celine Bags]'s designer, Pheobe <br>ilo
"One of the things we share is the reality that the clothes we design are actually worn," says fellow designer Stella McCartney about Philo's output. That reality of dressing working women with a sense of the practical, as well as the fashionable, is often seen as femi<br><br>.
 
"The flat shoe has been a big trend," adds Candy. "Those cripplingly high shoes aren't coming through anymore. Maybe it's a subconscious thing - of just being nicer to women!" What could be more feminist than <br>at?
My own issues with feminism and fashion are simple: fashion is an industry, and feminism, as Eddo-Lodge succinctly puts it, is a political movement with distinct aims for equality between the sexes. The trouble with tying such noble aims to fashion is that it can look like you're trying to tug on heartstrings to hawk somet<br><br>.
 
"As a fashion magazine, a lot of criticism around us was 'How dare you engage with this?' - given that a lot of what we do is about make-up, and nail polish and handbags," says Candy of Elle's rebranding campaign. "How could we say that when we place so much emphasis on how women look? But how women look is incredibly important to their day-to-day li<br>s."
Activists of the feminist movement FEMEN protest on the catwalk as models present creations for Nina Ricci during the 2014 Spring/Summer ready-to-wear collection fashion <br><br>
 
Some argue that simply raising the profile of the word, and stimulating discussion of feminism in popular culture, is valuable enough. Eddo-Lodge has other feelings. "Wishy-washy awareness-raising is good, but it almost adds to the confusion. What does it mean? What are the politics behind it?" But for Candy, engagement with the "Rebranding Feminism" campaign has fundamentally altered the way she w<br>ks.
"Are we patronising women? Are we doing things that are accidentally sexist? Are we writing in the right language?" These are questions she throws out to herself, rather than at the world at l<br><br>.
 
There is even an argument that the mere act of embracing the fashion industry is intrinsically feminist. "Feminine things like fashion and beauty are often considered less worthy pursuits," reasons Eddo-Lodge. "Some feminists talk about 'fem phobia', of heaping disgust on things that are seen as traditionally feminine, so in a way I think embracing fashion can be hugely liberating for women and men." That's a resolutely modern idea of feminism: "I was a feminist in the sixties," stated Miuccia Prada in <br><br>.
 
"Can you imagine? The worst thing I could have done was to be in fashion." Not any more.

Revision as of 12:21, 12 August 2013

The Perles configuration

In geometry, the Perles configuration is a configuration of 9 points and 9 lines that can be realized in the Euclidean plane but for which every realization has at least one irrational number as one of its coordinates. It is not a projective configuration, however, because its points and lines do not all have the same number of incidences as each other. It was introduced by Micha Perles in the 1960s.

One way of constructing the Perles configuration is to start with a regular pentagon and its five diagonals, which form the sides of a smaller regular pentagon within the initial one. The nine points of the configuration consist of four out of the five vertices of each pentagon and the shared center of the two pentagons; the two missing pentagon vertices are chosen to be collinear with the center. The nine lines of the configuration consist of the five lines that are diagonals of the outer pentagon and sides of the inner pentagon, and the four lines that pass through the center and through corresponding pairs of vertices from the two pentagons.

Every realization of this configuration in the real projective plane is equivalent, under a projective transformation, to a realization constructed in this way from a regular pentagon. Therefore, in every realization, there are four points having the same cross-ratio as the cross-ratio of the four collinear points in the realization derived from the regular pentagon. But, these four points have 1+φ as their cross-ratio, where φ is the golden ratio, an irrational number. Every four collinear points with rational coordinates have a rational cross ratio, so the Perles configuration cannot be realized by rational points. Branko Grünbaum has conjectured that every configuration that can be realized by irrational but not rational numbers has at least nine points; if so, the Perles configuration would be the smallest possible irrational configuration of points and lines.[1]

Perles used his configuration to construct an eight-dimensional convex polytope with twelve vertices that can similarly be realized with real coordinates but not with rational coordinates. Ernst Steinitz's proof of Steinitz's theorem can be used to show that every three-dimensional polytope can be realized with rational coordinates, but it is now known that there exist irrational polytopes in four dimensions.[2]

Notes

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

References

  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

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    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
  • Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

    Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

    In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

    Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

    Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

    15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

    To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
  1. ↑ Template:Harvtxt.
  2. ↑ Template:Harvtxt, p. 96a.
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