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[[File:Perimiters.svg|thumb|250px|Perimeter is the distance around a two dimensional shape, or the measurement of the distance around something; the length of the boundary.]]
 
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A '''perimeter''' is a path that surrounds a [[two-dimensional]] [[shape]]. The word comes from the Greek ''peri'' (around) and ''meter'' (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a [[circle]] or [[ellipse]] is called its [[circumference]].


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Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.
 
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== Formulae ==
{| class="wikitable"
! shape !! formula || variables
|-
| [[circle]] || <math>2 \pi r = \pi d</math> || where <math>r</math> is the radius of the circle and <math>d</math> is the diameter.
|-
| [[triangle]] || <math>a + b + c\,</math> || where <math>a</math>, <math>b</math> and <math>c</math> are the lengths of the sides of the triangle.
|-
| [[square (geometry)|square]]/[[rhombus]] || <math>4a</math> || where <math>a</math> is the side length.
|-
| [[rectangle]] || <math>2(l+w)</math> || where <math>l</math> is the length and <math>w</math> is the width.
|-
| [[equilateral polygon]] || <math>n \times a\,</math> || where <math>n</math> is the number of sides and <math>a</math> is the length of one of the sides.
|-
| [[regular polygon]] || <math>2nb \sin\left(\frac{\pi}{n}\right)</math> || where <math>n</math> is the number of sides and <math>b</math> is the distance between center of the polygon and one of the [[Vertex (geometry)|vertices]] of the polygon.
|-
| general [[polygon]] || <math>a_1 + a_2 + a_3 + \cdots + a_n = \sum_{i=1}^n a_i</math> || where <math>a_{i}</math> is the length of the <math>i</math>-th (1st, 2nd, 3rd ... ''n''th) side of an ''n''-sided polygon.
|}


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The perimeter is the distance around all of a shape. Perimeters for more general shapes can be calculated as any path with <math>\int_0^L \mathrm{d}s</math> where <math>L</math> is the length of the path and <math>ds</math> is an infinitesimal line element. Both of these must be replaced with other algebraic forms in order to be solved: an advanced notion of perimeter, which includes [[hypersurface]]s bounding volumes in <math>n</math>-[[Dimension (mathematics)|dimensional]] [[Euclidean space]]s can be found in the theory of [[Caccioppoli set]]s.
 
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==Polygons==
[[File:PerimeterRectangle.svg|thumb|Perimeter of a rectangle.]]
[[Polygon]]s are fundamental to determining perimeters, not only because they are the simplest shapes but also because the perimeters of many shapes are calculated by [[Approximation#Mathematics|approximating]] them with [[limit of a sequence|sequences]] of polygons tending to these shapes. The first mathematician known to have used this kind of reasoning is [[Archimedes]], who approximated the perimeter of a circle by surrounding it with [[regular polygon]]s.


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The perimeter of a polygon equals the [[sum]] of the lengths of its [[Edge (geometry)|edges]]. In particular, the perimeter of a [[rectangle]] which width is <math>w</math> and length <math>\ell</math> is equal to <math>2w + 2\ell</math>.  
 
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An equilateral polygon is a polygon which has all sides of the same length (for example, a [[rhombus]] is a 4-sided equilateral polygon). To calculate the perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides.


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A [[regular polygon]] may be defined by the number of its sides and by its ''radius'', that is to say, the constant distance between its [[Centre (geometry)|centre]] and each of its [[Vertex (geometry)|vertices]]. One can calculate the length of its sides using [[trigonometry]]. If ''R'' is a regular polygon's radius and ''n'' is the number of its sides, then its perimeter is
 
:<math>2nR \sin\left(\frac{180^{\circ}}{n}\right).</math>
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==Circumference of a circle==
[[File:Pi-unrolled-720.gif|right|300px|thumb|If the diameter of a circle is 1, its circumference equals {{pi}}.]]
{{main|Circumference}}
The perimeter of a [[circle]], often called the circumference, is proportional to its [[diameter]] and its [[radius]]. That is to say, there exists a constant number [[pi]], {{pi}} (the [[ancient greek|greek]] ''p'' for perimeter), such that if ''P'' is the circle's perimeter and ''D'' its diameter then:
:<math>P = \pi\cdot{D}.\!</math>


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In terms of the radius ''r'' of the circle, this formula becomes:
 
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:<math>{P}={2}\pi\cdot{r}.\!</math>


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To calculate a circle's perimeter, knowledge of its radius or diameter and of the number {{pi}} is sufficient. The problem is that {{pi}} is not [[rational number|rational]] (it cannot be expressed as the [[quotient]] of two [[integer]]s), nor is it [[algebraic number|algebraic]] (it is not a root of a polynomial equation with rational coefficients). So, obtaining an accurate approximation of {{pi}} is important for the calculation. The search for the digits of {{pi}} is relevant to many fields, such as [[mathematical analysis]], [[algorithmics]] and [[computer science]].
 
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[[File:Hexaflake.gif|thumb|left|upright=0.6|The more one cuts this shape, the lesser the area and the greater the perimeter. The [[convex hull]] remains the same.]]
[[File:Neuf Brisach.jpg|thumb|The [[Neuf-Brisach]] fortification perimeter is complicated. The shortest path around it is along its [[convex hull]].]]
{{Main|Area (geometry)|convex hull}}
The perimeter and the [[area (geometry)|area]] are the main two measures of geometric figures. Confusing them is frequent, as well as believing that the greater one of them is, the greater is the other. Indeed, an enlargement (or a reduction) of a shape make its area grow (or decrease) as well as its perimeter. For example, if a field is drawn on a 1/{{formatnum:10000}} scale map, the actual field perimeter can be calculated multiplying the drawing perimeter by {{formatnum:10000}}. The real area is {{formatnum:10000}}{{sup|2}} times the area of the shape on the map.


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[[Proclus]] (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters.<ref>{{cite book|first1=T.|last1=Heath|title=A History of Greek Mathematics|volume=2|publisher=Dover Publications|year= 1981|page= 206|isbn=0-486-24074-6}}</ref> But a field's production is proportional to its area, not to its perimeter: many naive peasants may have got fields with long perimeters but low areas (thus, low crops).


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If one removes a piece from a figure, its area decreases but its perimeter may not. In the case of very irregular shapes, some people may confuse perimeter with [[convex hull]]. The convex hull of a figure may be visualized as the shape formed by a rubber band stretched around it. On the animated picture on the left, all the figures have the same convex hull: the big, first [[hexagon]].
 
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== Isoperimetry ==
{{Further|Isoperimetric inequality}}


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The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter. The solution is intuitive: it is the [[circle]]. In particular, that is why drops of fat on a [[broth]] surface are circular.
 
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This problem may seem simple, but its mathematical proof needs sophisticated theorems. The isoperimetric problem is sometimes simplified: to find the [[quadrilateral]], or the triangle or another particular figure, with the largest area amongst those having a given perimeter. The solution to the quadrilateral isoperimetric problem is the [[square]], and the solution to the triangle problem is the [[equilateral triangle]]. In general, the polygon with ''n'' sides having the largest area and a given perimeter is the [[regular polygon]], which is closer to being a circle than is an irregular polygon.


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== See also ==
 
* [[Arclength]]
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* [[Area]]
 
* [[Caccioppoli set]]
  <li>[http://453300.biz/thread-302271-1-1.html http://453300.biz/thread-302271-1-1.html]</li>
* [[Circumference]]
 
* [[Isoperimetric inequality]]
  <li>[http://general.assembly.codesria.org/spip.php?article87&lang=pt/ http://general.assembly.codesria.org/spip.php?article87&lang=pt/]</li>
* [[Pythagorean theorem]]
 
* [[Volume]]
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* [[Wetted perimeter]]
 
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{{wikibooks|Geometry|Chapter 8|Perimeters, areas and volumes}}
 
{{wikibooks|Geometry|Perimeter and Arclength}}
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* {{MathWorld |urlname=Perimeter |title=Perimeter}}
* {{MathWorld |urlname=Semiperimeter |title=Semiperimeter}}


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Perimeter is the distance around a two dimensional shape, or the measurement of the distance around something; the length of the boundary.

A perimeter is a path that surrounds a two-dimensional shape. The word comes from the Greek peri (around) and meter (measure). The term may be used either for the path or its length - it can be thought of as the length of the outline of a shape. The perimeter of a circle or ellipse is called its circumference.

Calculating the perimeter has considerable practical applications. The perimeter can be used to calculate the length of fence required to surround a yard or garden. The perimeter of a wheel (its circumference) describes how far it will roll in one revolution. Similarly, the amount of string wound around a spool is related to the spool's perimeter.

Formulae

shape formula variables
circle where is the radius of the circle and is the diameter.
triangle where , and are the lengths of the sides of the triangle.
square/rhombus where is the side length.
rectangle where is the length and is the width.
equilateral polygon where is the number of sides and is the length of one of the sides.
regular polygon where is the number of sides and is the distance between center of the polygon and one of the vertices of the polygon.
general polygon where is the length of the -th (1st, 2nd, 3rd ... nth) side of an n-sided polygon.

The perimeter is the distance around all of a shape. Perimeters for more general shapes can be calculated as any path with where is the length of the path and is an infinitesimal line element. Both of these must be replaced with other algebraic forms in order to be solved: an advanced notion of perimeter, which includes hypersurfaces bounding volumes in -dimensional Euclidean spaces can be found in the theory of Caccioppoli sets.

Polygons

Perimeter of a rectangle.

Polygons are fundamental to determining perimeters, not only because they are the simplest shapes but also because the perimeters of many shapes are calculated by approximating them with sequences of polygons tending to these shapes. The first mathematician known to have used this kind of reasoning is Archimedes, who approximated the perimeter of a circle by surrounding it with regular polygons.

The perimeter of a polygon equals the sum of the lengths of its edges. In particular, the perimeter of a rectangle which width is and length is equal to .

An equilateral polygon is a polygon which has all sides of the same length (for example, a rhombus is a 4-sided equilateral polygon). To calculate the perimeter of an equilateral polygon, one must multiply the common length of the sides by the number of sides.

A regular polygon may be defined by the number of its sides and by its radius, that is to say, the constant distance between its centre and each of its vertices. One can calculate the length of its sides using trigonometry. If R is a regular polygon's radius and n is the number of its sides, then its perimeter is

Circumference of a circle

If the diameter of a circle is 1, its circumference equals Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park..

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The perimeter of a circle, often called the circumference, is proportional to its diameter and its radius. That is to say, there exists a constant number pi, Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park. (the greek p for perimeter), such that if P is the circle's perimeter and D its diameter then:

In terms of the radius r of the circle, this formula becomes:

To calculate a circle's perimeter, knowledge of its radius or diameter and of the number Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park. is sufficient. The problem is that Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park. is not rational (it cannot be expressed as the quotient of two integers), nor is it algebraic (it is not a root of a polynomial equation with rational coefficients). So, obtaining an accurate approximation of Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park. is important for the calculation. The search for the digits of Potter or Ceramic Artist Harry Rave from Cobden, spends time with hobbies for instance magic, property developers house in singapore singapore and fitness. Finds inspiration through travel and just spent 7 months at Keoladeo National Park. is relevant to many fields, such as mathematical analysis, algorithmics and computer science.

Perception of perimeter

The more one cuts this shape, the lesser the area and the greater the perimeter. The convex hull remains the same.
The Neuf-Brisach fortification perimeter is complicated. The shortest path around it is along its convex hull.

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. The perimeter and the area are the main two measures of geometric figures. Confusing them is frequent, as well as believing that the greater one of them is, the greater is the other. Indeed, an enlargement (or a reduction) of a shape make its area grow (or decrease) as well as its perimeter. For example, if a field is drawn on a 1/10,000 scale map, the actual field perimeter can be calculated multiplying the drawing perimeter by 10,000. The real area is 10,000Showcasing you the finest up and coming new condo launches in Singapore where you can search and discover the perfect house. Now we have new condo that may even satisfy the discerning few, it doesn't matter what's your necessities or your lifestyle needs. You'll certain to search out the dream apartment right here.

MAS agrees that it is crucial for banks to make use of valuations that are reflective of actual property values. We anticipate banks to adopt sound valuation processes. These embody participating unbiased valuers from corporations that aren't involved within the property transaction as gross sales agents or consultants, allocating valuation assignments randomly or on a rotational basis, obtaining a number of valuations for each property, and checking that the valuations are affordable.

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While every effort has been made to make sure that all information displayed herein are accurate and complete, the data are indicative relatively than definitive. Thus its accuracy, whether express or implicit, isn't assured and to the fullest extent permitted by relevant laws. The Writer/Developer/Huttons Real Property Group does not accept accountability for any errors, inaccuracies, omissions or for any loss which could end result directly or indirectly from reliance on the content material herein. The Writer also reserves the best to correct or update the content material at any time without prior notification. Users are advised to contact the advertiser for any clarifications or latest updates.

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Freedman would probably level out that my marinara sauce is not notably healthy (wine and bacon, after all, are simply foodie types of salt, sugar and fats) and, serving for serving, must be dearer than $2-per-jar Ragu. He may argue that top property developers in singapore a couple of years, Ragu or General Foods or Kraft will supply a pasta sauce that is nutritionally identical to mine, and that I might be a snob not to buy it. And he is perhaps right. But for now, neither of us can escape the reality that food, like the whole lot else we buy, is designed to be cheap to make, to last forever and to style better than the following product down the shelf. And in addition like all the pieces else, after you purchase it, you're on your own. World Entrepreneurship and Improvement Index (GEDI). times the area of the shape on the map.

Nevertheless there is no relation between the area and the perimeter of an ordinary shape. For example, the perimeter of a rectangle of width 0.001 and length 1000 is slightly above 2000, while the perimeter of a rectangle of width 0.5 and length 2 is 5. Both areas equal to 1.

Proclus (5th century) reported that Greek peasants "fairly" parted fields relying on their perimeters.[1] But a field's production is proportional to its area, not to its perimeter: many naive peasants may have got fields with long perimeters but low areas (thus, low crops).

If one removes a piece from a figure, its area decreases but its perimeter may not. In the case of very irregular shapes, some people may confuse perimeter with convex hull. The convex hull of a figure may be visualized as the shape formed by a rubber band stretched around it. On the animated picture on the left, all the figures have the same convex hull: the big, first hexagon.

Isoperimetry

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The isoperimetric problem is to determine a figure with the largest area, amongst those having a given perimeter. The solution is intuitive: it is the circle. In particular, that is why drops of fat on a broth surface are circular.

This problem may seem simple, but its mathematical proof needs sophisticated theorems. The isoperimetric problem is sometimes simplified: to find the quadrilateral, or the triangle or another particular figure, with the largest area amongst those having a given perimeter. The solution to the quadrilateral isoperimetric problem is the square, and the solution to the triangle problem is the equilateral triangle. In general, the polygon with n sides having the largest area and a given perimeter is the regular polygon, which is closer to being a circle than is an irregular polygon.

See also

References

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Sales transaction volumes have been expected to hit four,000 units for 2012, close to the mixed EC gross sales volume in 2010 and 2011, in accordance with Savills Singapore. Nevertheless the last quarter was weak. In Q4 2012, sales transactions were 22.8% down q-q to 7,931 units, in line with the URA. The quarterly sales discount was felt throughout the board. When the sale just starts, I am not in a hurry to buy. It's completely different from a private sale open for privileged clients for one day solely. Orchard / Holland (D09-10) House For Sale The Tembusu is a singular large freehold land outdoors the central area. Designed by multiple award-profitable architects Arc Studio Architecture + Urbanism, the event is targeted for launch in mid 2013. Post your Property Condos Close to MRT DTZ's auction group in Singapore auctions all types of residential, workplace and retail properties, retailers, homes, accommodations, boarding houses, industrial buildings and development websites. Auctions are at the moment held as soon as a month.

Whitehaven @ Pasir Panjang – A boutique improvement nicely nestled peacefully in serene Pasir Panjang personal estate presenting a hundred and twenty rare freehold private apartments tastefully designed by the famend Ong & Ong Architect. Only a short drive away from Science Park and NUS Campus, Jade Residences, a recent Freehold condominium which offers high quality lifestyle with wonderful facilities and conveniences proper at its door steps. Its fashionable linear architectural fashion promotes peace and tranquility living nestled within the D19 personal housing enclave. Rising workplace sector leads real estate market efficiency, while prime retail and enterprise park segments moderate and residential sector continues in decline International Market Perspectives - 1st Quarter 2014

There are a lot of websites out there stating to be one of the best seek for propertycondominiumhouse, and likewise some ways to discover a low cost propertycondominiumhouse. Owning a propertycondominiumhouse in Singapore is the dream of virtually all individuals in Singapore, It is likely one of the large choice we make in a lifetime. Even if you happen to're new to Property listing singapore funding, we are right here that will help you in making the best resolution to purchase a propertycondominiumhouse at the least expensive value.

Jun 18 ROCHESTER in MIXED USE IMPROVEMENT $1338000 / 1br - 861ft² - (THE ROCHESTER CLOSE TO NORTH BUONA VISTA RD) pic real property - by broker Jun 18 MIXED USE IMPROVEMENT @ ROCHESTER @ ROCHESTER PK $1880000 / 1br - 1281ft² - (ROCHESTER CLOSE TO NORTH BUONA VISTA) pic real estate - by broker Tue 17 Jun Jun 17 Sunny Artwork Deco Gem Near Seashore-Super Deal!!! $103600 / 2br - 980ft² - (Ventnor) pic actual estate - by owner Jun 17 Freehold semi-d for rent (Jalan Rebana ) $7000000 / 5909ft² - (Jalan Rebana ) actual property - by dealer Jun sixteen Ascent @ 456 in D12 (456 Balestier Highway,Singapore) pic real property - by proprietor Jun 16 RETAIL SHOP AT SIM LIM SQUARE FOR SALE, IT MALL, ROCHOR, BUGIS MRT $2000000 / 506ft² - (ROCHOR, BUGIS MRT) pic real estate - by dealer HDB Scheme Any DBSS BTO

In case you are eligible to purchase landed houses (open solely to Singapore residents) it is without doubt one of the best property investment choices. Landed housing varieties solely a small fraction of available residential property in Singapore, due to shortage of land right here. In the long term it should hold its worth and appreciate as the supply is small. In truth, landed housing costs have risen the most, having doubled within the last eight years or so. However he got here back the following day with two suitcases full of money. Typically we've got to clarify to such folks that there are rules and paperwork in Singapore and you can't just buy a home like that,' she said. For conveyancing matters there shall be a recommendedLondon Regulation agency familiar with Singapore London propertyinvestors to symbolize you

Sales transaction volumes have been expected to hit four,000 units for 2012, close to the mixed EC gross sales volume in 2010 and 2011, in accordance with Savills Singapore. Nevertheless the last quarter was weak. In Q4 2012, sales transactions were 22.8% down q-q to 7,931 units, in line with the URA. The quarterly sales discount was felt throughout the board. When the sale just starts, I am not in a hurry to buy. It's completely different from a private sale open for privileged clients for one day solely. Orchard / Holland (D09-10) House For Sale The Tembusu is a singular large freehold land outdoors the central area. Designed by multiple award-profitable architects Arc Studio Architecture + Urbanism, the event is targeted for launch in mid 2013. Post your Property Condos Close to MRT Template:Translation/Ref



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