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{{Infobox Unit
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| name      = Steradian
| image    = [[File:Steradian.svg|150px]]
| caption  = A graphical representation of 1 steradian.{{br}}The sphere has radius ''r'', and in this case the area ''A'' of the highlighted surface patch is ''r''{{sup|2}}. The solid angle Ω equals {{nowrap|''A''/''r''<sup>2</sup>}} which equals 1 in this example. The entire sphere has a solid angle of {{gaps|4π|sr}}.
| standard  = [[SI derived unit]]
| quantity  = [[Solid angle]]
| symbol    = {{unicode|㏛}}
}}
The '''steradian''' (symbol: '''sr''') or '''squared radian''' is the [[International System of Units|SI unit]] of [[solid angle]]. It is used in three-[[dimension]]al space, and functions analogously to the manner in which the [[radian]] quantifies [[planar angles]]. The name is derived from the [[Greek language|Greek]] ''stereos'' for "solid" and the [[Latin language|Latin]] ''radius'' for "ray, beam".
 
The steradian, like the radian, is [[Dimensionless quantity|dimensionless]], essentially because a solid angle is the ratio between the area subtended and the square of its distance from the vertex: both the numerator and denominator of this ratio have dimension length squared. It is useful, however, to distinguish between dimensionless quantities of different nature, so in practice the symbol "sr" is used to indicate a solid angle. For example, [[radiant intensity]] can be measured in watts per steradian (W·sr<sup>−1</sup>). The steradian was formerly an [[SI supplementary unit]], but this category was abolished from the SI in 1995 and the steradian is now considered an [[SI derived unit]].
 
==Definition==
[[File:Steradian cone and cap.svg|thumb|right|Section of cone (1) and spherical cap (2) that subtend a solid angle of one steradian inside a sphere]]
 
A steradian can be defined as the solid angle [[subtended angle|subtended]] at the center of a [[unit sphere]] by a unit [[area]] on its surface. For a general sphere of [[radius]] ''r'', any portion of its surface with area ''A'' = r<sup>2</sup> subtends one steradian.<ref>"Steradian", ''McGraw-Hill Dictionary of Scientific and Technical Terms'', fifth edition, Sybil P. Parker, editor in chief. McGraw-Hill, 1997. ISBN 0-07-052433-5.</ref>
 
The solid angle in steradians is related to the area it cuts out of a sphere:
::<math>\Omega = \frac{A}{r^2} \,</math>
:where
::''A'' is the surface area of the [[spherical cap]], 2π''rh'', and
::''r'' is the radius of the sphere.
 
Because the surface area ''A'' of a sphere is 4π''r''<sup>2</sup>, the definition implies that a sphere measures 4π&nbsp;≈&nbsp;12.56637 steradians. By the same argument, the maximum solid angle that can be subtended at any point is 4π&nbsp;sr.
 
==Other properties==
Since ''A'' = ''r''<sup>2</sup>, it corresponds to the area of a [[spherical cap]] (''A'' = 2π''rh'') (wherein ''h'' stands for the "height" of the cap), and the relationship ''h''/''r'' = 1/(2π) holds. Therefore one steradian corresponds to the plane (i.e. radian) angle of the cross-section of a simple cone subtending the plane angle ''2θ'', with ''θ'' given by:
 
:<math>
\begin{align}
\theta & = \arccos \left( \frac{r-h}{r} \right)\\
      & = \arccos \left( 1 - \frac{h}{r} \right)\\
      & = \arccos \left( 1 - \frac{1}{2\pi} \right) \approx 0.572 \,\text{ rad,} \mbox{ or } 32.77^\circ.
\end{align}
</math>
 
This angle corresponds to the plane aperture angle of 2''θ'' ≈ 1.144 rad or 65.54°.
 
A steradian is also equal to the spherical area of a [[polygon]] having an [[angle excess]] of 1 radian, to 1/(4π) of a complete [[sphere]], or to (180/π)<sup>2</sup> ≈ 3282.80635 [[square degree]]s.
 
The solid angle in steradians of a cone whose cross-section subtends the angle ''θ'' is:
 
:<math>\Omega = 2\pi\left(1 - \cos\theta\right)</math>.
 
==Analogue to radians==
In two dimensions, the angle in radians is related to the [[arc length]] it cuts out:
::<math>\theta = \frac{l}{r} \,</math>
:where
::''l'' is arc length, and
::''r'' is the radius of the circle.
 
Now in three dimensions, the solid angle in steradians is related to the area it cuts out:
::<math>\Omega = \frac{A}{r^2} \,</math>
:where
::''A'' is the surface area of the [[spherical cap]], 2π''rh'', and
::''r'' is the radius of the sphere.
 
==SI multiples==
Steradians only go up to 4π ≈ 12.56637, so the large multiples are not usable for the base unit, but could show up in such things as rate of coverage of solid angle, for example.
[[File:BlankMap-World6 steradian.svg|thumb|none|400px|Solid angle of various areas relative to Earth]]
{|class="wikitable"
! Multiple
! Name
! Symbol
! May be visualized as...
|-
|10<sup>1</sup>
| decasteradian 
|dasr
|Surface area of the [[Americas]] plus [[sea|liquid water]] on Earth, relative to [[Earth]] <span style="color:#000000;background:#ccffff;padding:0 0.2em;">(cyan on map)</span><ref>10.0 sr (404 million km&sup2; out of 510 million km&sup2;)</ref>
All constellations ''except'' those of the [[zodiac]] together subtend 0.992 dasr.
|-
|10<sup>0</sup>
| '''steradian'''
|sr
|Area of [[Oceania]] plus [[Asia]] excluding [[Russia]], relative to Earth <span style="color:#000000;background:#ffff00;padding:0 0.2em;">(yellow on map)</span><ref>1.01 sr (40.8 million km&sup2; out of 510 million km&sup2;)</ref>
The [[Heavenly_Waters_(astronomy)#Heavenly_Waters|Heavenly Waters]] [[constellation family]] subtends 1.16 sr.
|-
|10<sup>−1</sup>
| decisteradian 
|dsr
|Area of [[Algeria]] plus [[Libya]], relative to Earth <span style="color:#000000;background:#00ff00;padding:0 0.2em;">(green on map)</span><ref>0.102 sr (4.14 million km&sup2; out of 510 million km&sup2;)</ref>
The constellation [[Lupus (constellation)|Lupus]] subtends 1.02 dsr.
|-
|10<sup>−2</sup>
| centisteradian
| csr
|Area of [[Zimbabwe]], relative to Earth <span style="color:white;background:#0000ff;padding:0 0.2em;">(blue on map)</span><ref>0.00963 sr (391 000 km&sup2; out of 510 million km&sup2;); [[Paraguay]], at 0.0100 sr (407 000 km&sup2;) is closer to 1 csr, but has been shaded for the 10 sr region as part of the Americas</ref>
The smallest constellation, [[Crux]] subtends 2.09 csr.
|-
|10<sup>−3</sup>
| millisteradian
| msr
|Area of [[Switzerland]], relative to Earth <span style="color:white;background:#ff0000;padding:0 0.2em;">(red on map)</span><ref>0.00102 sr (41 300 km&sup2; out of 510 million km&sup2;)</ref>
The Earth, viewed from the Moon, subtends 1.2 msr.<ref>[http://lunarscience.nasa.gov/?question=3318 Near-side/far-side impact crater counts | NASA Lunar Science Institute]</ref>
|-
|10<sup>−6</sup>
| microsteradian
| µsr
|Area of [[Costa Mesa, California]], relative to Earth<ref>0.00000100 sr (40.7 km&sup2; out of 510 million km&sup2;)</ref>
The Sun and the Moon, viewed from Earth, each subtends 60 µsr.
|-
|10<sup>−9</sup>
| nanosteradian 
|nsr
|About 8 [[American football]] fields, relative to Earth
[[Mars]], viewed from Earth at its closest approach, subtends 11 nsr.<ref>π &times; (25.113 / 60 / 60 / 2)<sup>2</sup> / 3282.80635 &times; 1000000000</ref>
|-
|10<sup>−12</sup>
| picosteradian 
|psr
|Area of a small apartment, relative to Earth
[[Pluto]], viewed from Earth at its closest approach, subtends 0.24 psr.<ref>π &times; (0.115 / 60 / 60 / 2)<sup>2</sup> / 3282.80635 &times; 1000000000</ref>
|-
|10<sup>−15</sup>
| femtosteradian 
|fsr
|Area of a sheet of [[A5 paper]], relative to Earth
[[Alpha Centauri]] A, viewed from Earth, subtends 0.9 fsr.<ref>π &times; (0.007 / 60 / 60 / 2)<sup>2</sup> / 3282.80635 &times; 1000000000</ref>
|-
|10<sup>−18</sup>
| attosteradian 
|asr
|Area of a quarter-inch square, relative to Earth
[[Proxima Centauri]], viewed from Earth, subtends 20 asr.<ref>π &times; (0.001 / 60 / 60 / 2)<sup>2</sup> / 3282.80635 &times; 1000000000</ref>
|-
|10<sup>−21</sup>
| zeptosteradian
| zsr
|Cross-sectional area of 32 [[American wire gauge|gauge]] wire, relative to Earth
|-
|10<sup>−24</sup>
| yoctosteradian
| ysr
|Surface area of a [[red blood cell]], relative to Earth
|-
|}
 
==See also==
* [[Square degree]]
* [[List of constellations by area]]
 
== Notes and references ==
{{Reflist|2}}
 
 
{{SI units}}
 
[[Category:Natural units]]
[[Category:SI derived units]]
[[Category:Units of angle]]

Latest revision as of 23:05, 23 December 2014

Understandably, numerous anxiousness victims acquire clinical depression as properly, and others are prone to produce alcohol and drug dependencies. Sesame oil is great, but sunflower, coconut, or corn oil will work, too. In other words if you are looking for a quick fix (aren't we all), you may be in for a disappointment unless your next move is just right for you. Keep an eye out for my article, Panic Attacks and Anxiety: Adios. To some, these new regulations may seem intrusive, but they were instilled with the best of intentions.

WHY DO YOU IGNORE WARNING SIGNS & HINTS WHICH YOU MUST KNOW BY HEART ALREADY. Therefore, it may be beneficial to increase your intake of this vital mineral. If, for example, a child lives in a home where they are exposed to math, they will grow up and most likely acquire good math skills. At the hospital said they had had symptoms of panic attacks and that over time could have been the re symptoms from anticipatory anxiety, or that events similar to that triggered the panic attack could have the ability to make him wake anxiety disorder symptoms. Herbs for Anxiety are very useful in treating acute symptoms of stress and anxiety, but you need to supplement them with other types of coping mechanisms.

The reminder of the scene can again cause the attack. Notice these things, allow yourself to feel and embrace them. Are your worries logically justified or are you blowing things out of proportion. There are chemical messengers called neuro transmitters which transmit signals from one brain cell to another cell. But, yes, hypertension is on the rise in our society, but this is largely due to diet issues.

This is the largest step you will have to take when dealing with your anxiety. If you have a lot of stress in your life, learning coping strategies for anxiety can help you manage that stress. As you can see anxiety problems are not uncommon in children and when identified and treated, they can be short-lived. Having adequate rest and sleep always helps to relieve feelings of anxiety symptoms. Anxiety is a common emotion consisting of uncertainty and worry faced by many, whilst anxiety disorders are when such fears are experienced irrationally.

It is one of nature's best natural tranquilizers and has been used for centuries as a reliable remedy for nervous, menopausal and premenstrual tension, irritability, and fatigue and tension headaches. This is because at some time in the past we have come to associate specific situations or sensations with feelings of anxiety, and this has become what is known as a 'conditioned response', something that can be automatically triggered without or conscious mind even being aware of it. Repeat this exercise every time you feel an anxiety attack is about to strike, and gradually you would observe that the number of your worries and their intensity decrease. High grain intake and low fat intake is exactly the wrong combination to follow when trying to avoid high blood pressure. It could include sweating armpits, sweaty palms, even body sweat running down your back.

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