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[[Image:Cube diagonals.svg|thumb|right|250px|AC' (shown in blue) is a space diagonal while AC (shown in red) is a [[face diagonal]]]]
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In a [[cuboid|rectangular box]] or a [[magic cube]], the four '''space diagonals''' are the lines that go from a corner of the box or cube, through the center of the box or cube, to the opposite corner. These lines are also called ''triagonals'' or ''volume diagonals''.
 
[[File:Spacediagonal(equation-graphic).jpg|thumb|the pic demonstrates how to graphically build a spacediagonal and mathematically calculate it with Pythagoras Theorem]]
 
For the cube to be considered magic, these four lines must sum correctly.
 
The word triagonal is derived from the fact that as a variable point travels down the line, three coordinates change. The equivalent in a [[square (geometry)|square]] is [[diagonal]], because two coordinates change. In a [[tesseract]] it is [[quadragonal]] because 4 coordinates change, etc.
 
The '''space diagonal''' of a [[cube]] with side length <math>a</math> is <math>a\sqrt {3}</math>.
 
== ''r''-agonals ==
This section applies particularly to [[Magic hypercubes]].
 
The magic hypercube community has started to recognize an abbreviated expression for these ''space diagonals''. By using ''r'' as a variable to describe the various
''agonals'', a concise notation is possible.
 
If ''r'' =
* 2 then we have a diagonal. 2 coordinates change.  
* 3 = a ''triagonal''. 3 coordinates change
* 4 = a ''quadragonal''. 4 coordinates change
* ''n'' = the dimension of the hypercube, the ''2<sup>n-1</sup>'' agonals are required to sum correctly for the hypercube to be considered magic.
...
By extension, if ''r'' =
* 1, the line is parallel to a face. Only 1 coordinate changes. A 1-agonal may be called a monagonal, in keeping with a diagonal, a triagonal, etc. Lines parallel to the faces of the hypercube have, in the past, also been referred to as i-rows.
 
Because the prefix ''pan'' indicates ''all'', we can concisely state the characteristics or a magic hypercube.
 
For example;
* If pan-''r''-agonals sum correctly for ''r'' = 1 and 2, we know the square is pandiagonal magic.
* If pan-''r''-agonals sum correctly for ''r'' = 1 and 3, we have a pantriagonal magic cube (the equivalent of a pandiagonal magic square).
* If the ''r''-agonals sum correctly for ''r'' = 1 and ''n'', then the magic hypercube is simple magic regardless of what dimension it is.
 
The length of an ''r''-agonal of a [[hypercube]] with side length ''a'' is <math>a\sqrt {r}</math>.
 
==See also==
* [[Magic cube]]
* [[Magic hypercube]]
* [[Magic cube classes]]
* [[Hypotenuse]]
 
==References==
* John R. Hendricks, ''The Pan-3-Agonal Magic Cube'', Journal of Recreational Mathematics 5:1:1972, pp 51–54. First published mention of pan-3-agonals
* Hendricks, J. R., ''Magic Squares to Tesseracts by Computer'', 1998, 0-9684700-0-9, page 49
* Heinz & Hendricks, ''Magic Square Lexicon: Illustrated'', 2000, 0-9687985-0-0, pages 99,165
 
== External links ==
* {{MathWorld |urlname=SpaceDiagonal |title=Space Diagonals}}
* [http://www.magichypercubes.com/Encyclopedia/index.html  de Winkel Magic Encyclopedia]
* [http://members.shaw.ca/hdhcubes/cube_basics.htm Heinz - Basic cube parts]
* [http://members.shaw.ca/johnhendricksmath/ John Hendricks Hypercubes]
 
[[Category:Magic squares]]
[[Category:Elementary geometry]]

Revision as of 15:03, 8 February 2014

With your current mindset, you'll require some form of motivation for you to succeed with your fitness program. Most of the time your dog acts out in destructive ways not because you are gone but because he is bored. Involuntary facial tension is also one of the most emotionally debilitating symptoms because it severely restricts a person’s ability to convey even simple facial gestures, such as smiling, that are critical to forming trust with other people. Perimenopause worsen existing anxiety disorders and bring it to the surface. For some adults, this kind of psychological trauma goes even further and results in the disorder.

This creates a void that the victim of separation anxiety doesn. Once you feel the anxiety starting to take hold, play your favorite tunes. If you are considering quitting, have a frank discussion with a physician. Be able to connect with others also allows you to live a more fulfilled life. Many people think that when they are anxious they would get heat attack, but it is not true.

Phobias can be two major types: social phobia and specific phobia. Considering medication can make adverse reactions, various most people with anxiety disorder are afraid to take them owing to anxieties about brief and long phrase facet outcomes. Once the tests are done and things are clarified it can be seen as a reaction to stress. Since anxiety is the main culprit for having unstable emotional and mental state after losing a child custody case, people who are experiencing this are advised to various techniques that would help them relax such as meditation and deep breathing as well as muscle relaxation. And don’t forget to watch what you eat, quit smoking, and quit drinking so much coffee.

I can't tell you how frightening that sensation was. These are also the signs as well as signs and symptoms of a heart attack. You should definitely learn the way long you'll have to take the drug. It is likely the case that your attention is less drawn to your emotional wellbeing and spiritual needs. It is a reality that children are extremely receptive to the feelings of the people who are around them.

With the right approach, you'll be amazed at how good you can feel in a very short time. We have reviewed e - Books, video programs, audio programs, music relaxation and natural herbal remedies and have found none come close to the same effictiveness of Panic Away. thousands people feel far preferable about heading to a real person but for thousands of us this is simply not an alternative irrespective of whether it be from the money standpoint or perhaps a standpoint from the distress of one more human knowing our deficiencies. Before you hit the sheets at night, you should think about all of the great stuff that is occurring in your life right now. The need for you to recognize how to prevent and deal with anxiety attack cannot be exaggerated.

If you liked this article therefore you would like to be given more info concerning health anxiety kindly visit our own website.