Failure rate

AC' (shown in blue) is a space diagonal while AC (shown in red) is a face diagonal

In a 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.

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 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 $a$ is $a{\sqrt {3}}$.

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^n-1 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 $a{\sqrt {r}}$.

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

• 
  
  I had like 17 domains hosted on single account, and never had any special troubles. If you are not happy with the service you will get your money back with in 45 days, that's guaranteed. But the Search Engine utility inside the Hostgator account furnished an instant score for my launched website. Fantastico is unable to install WordPress in a directory which already have any file i.e to install WordPress using Fantastico the destination directory must be empty and it should not have any previous installation files. When you share great information, others will take note. Once your hosting is purchased, you will need to setup your domain name to point to your hosting. Money Back: All accounts of Hostgator come with a 45 day money back guarantee. If you have any queries relating to where by and how to use Hostgator Discount Coupon, you can make contact with us at our site. If you are starting up a website or don't have too much website traffic coming your way, a shared plan is more than enough. Condition you want to take advantage of the worldwide web you prerequisite a HostGator web page, -1 of the most trusted and unfailing web suppliers on the world wide web today. Since, single server is shared by 700 to 800 websites, you cannot expect much speed.
  
  
  
  Hostgator tutorials on how to install Wordpress need not be complicated, especially when you will be dealing with a web hosting service that is friendly for novice webmasters and a blogging platform that is as intuitive as riding a bike. After that you can get Hostgator to host your domain and use the wordpress to do the blogging. Once you start site flipping, trust me you will not be able to stop. I cut my webmaster teeth on Control Panel many years ago, but since had left for other hosting companies with more commercial (cough, cough) interfaces. If you don't like it, you can chalk it up to experience and go on. First, find a good starter template design. When I signed up, I did a search for current "HostGator codes" on the web, which enabled me to receive a one-word entry for a discount. Your posts, comments, and pictures will all be imported into your new WordPress blog.
• de Winkel Magic Encyclopedia
• Heinz - Basic cube parts
• John Hendricks Hypercubes