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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.


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>
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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>
 
==Notes==
{{reflist}}
 
==References==
*{{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}}
*{{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}}.
 
[[Category:Configurations]]
[[Category:Polyhedral combinatorics]]

Latest revision as of 19:30, 22 November 2014


Citizens of Toronto have set up a trend of hiring a personal injury lawyer. Spending this extra time preparing applications, filling out activity forms, managing the consultative exam process does not always guarantee a favorable decision at the initial or reconsideration levels, but allows the attorney to help his or her clients win more claims at the ALJ level. However, it is not advisable to choose the very first lawyer you find. We all know this, of course, yet as life rolls along so many of us put off creating a Will, often until it. Prior experience in Social Security Disability, Workers Compensation or Personal Injury law is preferred.

If the words "severe", "chronic", or "recurrent" do not appear anywhere in your medical records, the examiner will assume your condition is not any of those. But they would not tell us that magic number, I had to find that out through my own research. Basic details such as your name, current and previous addresses, date of birth and social security number. Speak up in college when you have something to contribute to the conversation or have a question. The two types of social security disability benefit programs that comes under the Social Security System is the Social Security Disability Insurance (SSDI) that provides benefits to workers who have contributed enough through payroll taxes to be covered and who become significantly disabled before reaching full retirement age.

There were no safeguards for filling out the form with a stated age of less than 13, and by popping up instantly, it was seen as likely that many would lie or have another non-parent fill it out. Ensure you use spyware programs and of course that you keep up on all the security updates for these programs as well. 00 penalty for a second offense late report and $500 for conspiracy in South Carolina. With this help, you can learn not only how to qualify but if your case is likely to qualify for disability. Rather, claims are most often denied because the accompanying form was not properly filled out or because supporting documentation for the claim was either not included or was insufficient.

The administrative judge is absolutely meticulous with the details of his client and so one must consult with a Social Security Disability Attorney to avoid the problems of rejection of a claim. Social Security may locate that you are disabled on the basis of your fibromyalgia if you can easily present ALL of the following:. The lawyer will help build a case appealing for withholding tax cut on benefits if the individual is for some reason unable to meet his youtube.com/watch?v=5e0A5wBbpfA [please click the next post] expenses. They will represent you in court to prove that you deserve to get the benefits. Be honest with your attorney - Do not hide anything from your lawyer.

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