Papyrus 31: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Charles Matthews
m typos
en>Trappist the monk
m →‎Description: Fix CS1 deprecated coauthor parameter errors; using AWB
 
Line 1: Line 1:
{{unreferenced|date=February 2010}}
[[Image:Equilateral pentagon.SVG|thumb|right|250px|Equilateral pentagon built with four equal circles disposed in a chain.]]


In [[geometry]] an '''equilateral pentagon''' is a [[polygon]] with five sides of equal length. Its five internal angles, in turn, can take a range of sets of values, thus permitting it to form a family of pentagons. In contrast, the [[regular pentagon]] is unique, because it is equilateral and moreover its five angles are equal.


Four intersecting equal circles arranged in a closed chain are sufficient to determine an equilateral pentagon. Each circle's center is one of four vertices of the pentagon. The remain vertex is determined by the intersection of the first and the last circle of the chain.
It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner. <br><br>purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. This plugin allows a blogger get more Facebook fans on the related fan page. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring. <br><br>Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help.  If you enjoyed this post and you would like to obtain additional information relating to [http://ll.my/wordpressdropboxbackup18455 wordpress backup plugin] kindly visit the web page. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. Enough automated blog posts plus a system keeps you and your clients happy. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way. <br><br>Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white. <br><br>Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. Automated deal feed integration option to populate your blog with relevant deals. It's not a secret that a lion share of activity on the internet is takes place on the Facebook. If this is not possible you still have the choice of the default theme that is Word - Press 3. I have never seen a plugin with such a massive array of features, this does everything that platinum SEO and All In One SEO, also throws in the functionality found within SEO Smart Links and a number of other plugins it is essentially the swiss army knife of Word - Press plugins.
 
It is possible to describe any equilateral pentagon with only two angles α and β with α ≥ β provided the fourth angle (δ) is the smallest of the rest of the angles. Thus the general equilateral pentagon can be regarded as a bivariate function ''f(α, β)'' where the rest of the angles can be obtained by using trigonometric relations. The equilateral pentagon described in this manner will be unique up to a rotation in the plane.
 
== Internal angles ==
[[Image:Equilateral pentagon triangulated.SVG|thumb|right|250px|Equilateral Pentagon dissected into 3 triangles which helps to calculate the value of angle δ as a function of α and β.]]
When the equilateral pentagon is dissected into triangles, two of them appear as [[isosceles]] (triangles in orange and blue) while the other one is more general (triangle in green).
 
According to the [[law of sines]] the length of the line dividing the green and blue triangles is:
 
: <math>a = 2\sin\left(\frac{\beta}{2}\right)</math>
 
The square of the length of the line dividing the orange and green triangles is:
 
: <math>
\begin{align}
b^2 & = 1 + a^2 - 2(1)(a)\cos\left(\alpha - \frac{\pi}{2} + \frac{\beta}{2} \right)\\
    & = 1 + 4\sin^2\left(\frac{\beta}{2}\right)
        - 4\sin\left(\frac{\beta}{2}\right)\sin\left(\alpha+\frac{\beta}{2}\right)\\
\end{align}
</math>
 
According to the [[law of cosines]], the cosine of δ can be seen from the figure:
 
: <math>\cos(\delta) = \frac{1^2 + 1^2 - b^2}{2(1)(1)}\ . </math>
 
Simplifying, δ is obtained as function of α and β:
 
: <math>
\delta = \arccos\left[\cos(\alpha) + \cos(\beta) - \cos(\alpha + \beta) - \frac{1}{2}      \right]
</math>
 
== Two dimensional mapping ==
[[Image:Equilateral pentagons plot.svg|thumb|right|400px|All the equilateral pentagons plotted within the area delimited by the condition α ≥ β ≥ δ. Three regions for each of three types of pentagons are shown: stellated, concave and convex]]
 
The equilateral pentagon as a function of two variables can be plotted in the two-dimensional [[Plane (geometry)|plane]]. Each pair of values (α, β) maps to a single point of the plane and also maps to a single pentagon.
 
The periodicity of the values of α and β and the condition α ≥ β ≥ δ permit the size of the mapping to be limited. In the plane with coordinate axes α and β, '''α = β''' is a line dividing the plane in two parts (south border shown in orange in the drawing). '''δ = β''' as a curve divides the plane into different sections (north border shown in blue).
 
Both borders enclose a continuous region of the plane whose points map to unique equilateral pentagons. Points outside the region just map to repeated pentagons—that is, pentagons that when rotated or reflected can match others already described. Pentagons that map exactly onto those borders have a [[line of symmetry]].
 
Inside the region of unique mappings there are three types of pentagons: stellated, concave and convex, separated by new borders.
 
=== Stellated ===
 
The [[stellated]] pentagons have sides intersected by others. A common example of this type of pentagon is the [[pentagram]]. A condition for a pentagon to be stellated, or self-intersecting, is to have 2α + β ≤ 180°. So, in the mapping, the line '''2α + β = 180°''' (shown in orange at the north) is the border between the regions of stellated and non-stellated pentagons. Pentagons which map exactly to this border have a vertex touching another side.
 
=== Concave ===
 
The [[Concave polygon|concave]] pentagons are non-stellated pentagons having at least one angle greater than 180°. The first angle which opens wider than 180° is γ, so '''γ = 180°''' (border shown in green at right) is a curve which is the border of the regions of concave pentagons and others, called convex. Pentagons which map exactly to this border have at least two consecutive sides appearing as a double length side, which resembles a pentagon degenerated to a quadrilateral.
 
=== Convex ===
 
The [[Convex polygon|convex]] pentagons have all of their five angles smaller than 180° and no sides intersecting others. A common example of this type of pentagon is the [[regular pentagon]].
 
{{DEFAULTSORT:Equilateral Pentagon}}
[[Category:Polygons]]

Latest revision as of 14:31, 21 July 2014


It depends on the quality of the Wordpress theme but even if it's not a professional one you will be able to average 50-60$ EACH link. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. One really cool features about this amazing and free wp plugin is that the code it generates is completely portable. Hosted by Your Domain on Another Web Host - In this model, you first purchase multiple-domain webhosting, and then you can build free Wordpress websites on your own domains, taking advantage of the full power of Wordpress. If you are happy with your new look then click "Activate 'New Theme'" in the top right corner.

purcase and download - WPZOOM Tribune wordpress Theme, find and use the WPZOOM Discount Code. WPTouch is among the more well known Word - Press smartphone plugins which is currently in use by thousands of users. This plugin allows a blogger get more Facebook fans on the related fan page. E-commerce websites are meant to be buzzed with fresh contents, graphical enhancements, and functionalities. Moreover, many Word - Press themes need to be purchased and designing your own WP site can be boring.

Photography is an entire activity in itself, and a thorough discovery of it is beyond the opportunity of this content. Word - Press has ensured the users of this open source blogging platform do not have to troubleshoot on their own, or seek outside help. If you enjoyed this post and you would like to obtain additional information relating to wordpress backup plugin kindly visit the web page. I hope this short Plugin Dynamo Review will assist you to differentiate whether Plugin Dynamo is Scam or a Genuine. Enough automated blog posts plus a system keeps you and your clients happy. So, if you are looking online to hire dedicated Wordpress developers, India PHP Expert can give a hand you in each and every best possible way.

Additionally Word - Press add a default theme named Twenty Fourteen. In case you need to hire PHP developers or hire Offshore Code - Igniter development services or you are looking for Word - Press development experts then Mindfire Solutions would be the right choice for a Software Development partner. This allows for keeping the content editing toolbar in place at all times no matter how far down the page is scrolled. Word - Press is the most popular open source content management system (CMS) in the world today. Digital digital cameras now function gray-scale configurations which allow expert photographers to catch images only in black and white.

Every single module contains published data and guidelines, usually a lot more than 1 video, and when pertinent, incentive links and PDF files to assist you out. Automated deal feed integration option to populate your blog with relevant deals. It's not a secret that a lion share of activity on the internet is takes place on the Facebook. If this is not possible you still have the choice of the default theme that is Word - Press 3. I have never seen a plugin with such a massive array of features, this does everything that platinum SEO and All In One SEO, also throws in the functionality found within SEO Smart Links and a number of other plugins it is essentially the swiss army knife of Word - Press plugins.

Retrieved from "https://en.formulasearchengine.com/index.php?title=Papyrus_31&oldid=262469"