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I deleted The Friedrichs extension of ''T'' is ''T''<sub>max</sub>.<ref>A. Alfonso and B. Simon, The Birman-Krein-Vishik theory of self-adjoint extensions of semibounded operators. J. Operator Theory 4 (1980), 251-270.</ref> because it is not always true
 
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In [[geometry]], the '''semiperimeter''' of a [[polygon]] is half its [[perimeter]]. Although it has such a simple derivation from the perimeter, the semiperimeter appears frequently enough in formulas for [[triangles]] and other figures that it is given a separate name. When the semiperimeter occurs as part of a formula, it is typically denoted by the letter ''s''.
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==Triangles==
[[Image:Nagel point.svg|thumb|300px|In any triangle, the distance around the triangle from a vertex to the point on the opposite edge touched by an [[excircle]] equals the semiperimeter.]]
 
The semiperimeter is used most often for triangles; the formula for the semiperimeter of a triangle with side lengths ''a'', ''b'', and ''c'' is
:<math>s = \frac{a+b+c}{2}.</math>
 
===Properties===
 
In any triangle, any vertex and the point where the opposite [[excircle]] touches the triangle partition the triangle's perimeter into two equal lengths, thus creating two paths each of which has a length equal to the semiperimeter. If A, B, C, A', B', and C' are as shown in the figure, then the segments connecting a vertex with the opposite excircle tangency (AA', BB', and CC', shown in red in the diagram) are known as [[Splitter (geometry)|splitters]], and
 
<math>s = |AB|+|A'B|=|AB|+|AB'|=|AC|+|A'C|</math>
:<math>=|AC|+|AC'|=|BC|+|B'C|=|BC|+|BC'|.</math>
 
The three splitters [[Concurrent lines|concur]] at the [[Nagel point]] of the triangle.
 
A [[Cleaver (geometry)|cleaver]] of a triangle is a line segment that bisects the perimeter of the triangle and has one endpoint at the midpoint of one of the three sides. So any cleaver, like any splitter, divides the triangle into two paths each of whose length equals the semiperimeter. The three cleavers concur at the [[Spieker center|center of the Spieker circle]], which is the [[incircle]] of the [[medial triangle]]; the Spieker center is the [[center of mass]] of all the points on the triangle's edges.
 
A line through the triangle's [[incenter]] [[Bisection|bisects]] the perimeter if and only if it also bisects the area.
 
A triangle's semiperimeter equals the perimeter of its [[medial triangle]].
 
===Formulas invoking the semipermeter===
 
The area ''K'' of any triangle is the product of its [[inradius]] and its semiperimeter:
 
:<math> K = rs.</math> 
 
The area of a triangle can also be calculated from its semiperimeter and side lengths using [[Heron's formula]]:
 
:<math>K = \sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}.</math>
 
The [[circumradius]] ''R'' of a triangle can also be calculated from the semiperimeter and side lengths:
:<math>2R = \frac{abc} {2\sqrt{s(s-a)(s-b)(s-c)}}.</math>
This formula can be derived from the [[law of sines]].
 
The radius of the incircle (also known as the '''inradius''') is  
 
: <math>r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}}. </math>
 
The [[law of cotangents]] gives the [[cotangent]]s of the half-angles at the vertices of a triangle in terms of the semiperimeter, the sides, and the inradius.
 
In a [[right triangle]], the radius of the [[excircle]] on the [[hypotenuse]] equals the semiperimeter. The semiperimeter is the sum of the inradius and twice the circumradius. The area of the right triangle is <math>(s-a)(s-b)</math> where ''a'' and ''b'' are the legs.
 
==Quadrilaterals==
The formula for the semiperimeter of a quadrilateral with side lengths ''a'', ''b'', ''c'' and ''d'' is
:<math>s = \frac{a+b+c+d}{2}.</math>
 
One of the triangle area formulas involving the semiperimeter also applies to [[tangential quadrilateral]]s, which have an incircle and in which pairs of opposite sides have lengths summing to the semiperimeter&mdash;namely, the area is the product of the inradius and the semiperimeter:
 
:<math> K = rs.</math>
 
The simplest form of [[Brahmagupta's formula]] for the area of a [[cyclic quadrilateral]] has a form similar to that of Heron's formula for the triangle area:
 
:<math>K = \sqrt{\left(s-a\right)\left(s-b\right)\left(s-c\right)\left(s-d\right)}.</math>
 
[[Bretschneider's formula]] generalizes this to all [[quadrilateral]]s:
 
:<math> K = \sqrt {(s-a)(s-b)(s-c)(s-d) - abcd  \cdot \cos^2 \left(\frac{\alpha + \gamma}{2}\right)},</math>
 
in which <math>\alpha \,</math> and <math>\gamma \,</math> are two opposite angles.
 
The four sides of a [[bicentric quadrilateral]] are the four solutions of [[Bicentric quadrilateral#Inradius and circumradius|a quartic equation parametrized by the semiperimeter, the inradius, and the circumradius]].
 
==Regular polygons==
 
The area of a [[Convex polygon|convex]] [[regular polygon]] is the product of its semiperimeter and its [[apothem]].
 
== External links ==
*{{mathworld | title = Semiperimeter | urlname = Semiperimeter}}
 
[[Category:Triangle geometry]]

Latest revision as of 17:48, 7 February 2014

The ac1st16.dll error is annoying and rather well-known with all types of Windows computers. Not just does it make your computer run slower, but it will moreover avoid you from utilizing a range of programs, including AutoCAD. To fix this issue, you need to employ a simple method to remedy all the potential difficulties that cause it. Here's what you have to do...

Before really buying the software it is best to check found on the companies which create the software. If you will discover details on the kind of reputation each company has, maybe the risk of malicious programs is reduced. Software from reputed businesses have aided me, and other users, to create my PC run quicker.. If the product description refuses to look good to we, refuses to include details about the software, does not include the scan functions, you should go for another one which ensures you're paying for what you desire.

With the Internet, the risk to your registry is a bit more and windows XP error messages could appear frequently. Why? The malicious wares like viruses, Trojans, spy-wares, ad wares, and the like gets recorded too. Cookies are ideal examples. We receive to conserve passwords, plus stuff, proper? That is a simple example of the register working.

Windows mistakes can be caused by any amount of reasons, however, there's almost constantly 1 cause. There's a hidden part of your system that is responsible for making 90% of all Windows errors, and it's called the 'registry'. This really is the central database for a program and is where your computer stores all its program files and settings. It's a pretty important piece of Windows, that is must be able to function. However, it's equally 1 of the biggest causes of problems on a PC.

Another common cause of PC slow down is a corrupt registry. The registry is a important component of computers running on Windows platform. When this gets corrupted the PC will slowdown, or worse, not commence at all. Fixing the registry is easy with the use of the system plus tuneup utilities.

Files with the DOC extension are also susceptible to viruses, but this may be solved by advantageous antivirus programs. Another problem is that .doc files may be corrupted, unreadable or damaged due to spyware, adware, plus malware. These instances will avoid consumers from correctly opening DOC files. This is when efficient registry cleaners become practical.

When the registry is corrupt or full of errors, the signs could be felt by the computer owner. The slow performance, the frequent program crashes and the nightmare of all computer owners, the blue screen of death.

A registry cleaner is a system which cleans the registry. The Windows registry always gets flooded with junk data, info which has not been removed from uninstalled programs, erroneous file association plus alternative computer-misplaced entries. These neat small program software tools are quite common today plus you are able to find many wise ones found on the Internet. The superior ones provide you option to maintain, clean, update, backup, and scan the System Registry. When it finds supposedly unwelcome ingredients inside it, the registry cleaner lists them and recommends the user to delete or repair these orphaned entries plus corrupt keys.

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