Jump to content
Main menu
Main menu
move to sidebar
hide
Navigation
Main page
Recent changes
Random page
Help about MediaWiki
Special pages
Niidae Wiki
Search
Search
Appearance
Create account
Log in
Personal tools
Create account
Log in
Pages for logged out editors
learn more
Contributions
Talk
Editing
Magic square
(section)
Page
Discussion
English
Read
Edit
View history
Tools
Tools
move to sidebar
hide
Actions
Read
Edit
View history
General
What links here
Related changes
Page information
Appearance
move to sidebar
hide
Warning:
You are not logged in. Your IP address will be publicly visible if you make any edits. If you
log in
or
create an account
, your edits will be attributed to your username, along with other benefits.
Anti-spam check. Do
not
fill this in!
===Magic constant=== {{main|Magic constant}} The constant that is the sum of any row, or column, or diagonal is called the [[magic constant]] or magic sum, ''M.'' Every normal magic square has a constant dependent on the order {{mvar|n}}, calculated by the formula <math>M = n(n^2 + 1)/2</math>. This can be demonstrated by noting that the sum of <math>1,2,...,n^2</math> is <math>n^2(n^2 + 1)/2</math>. Since the sum of each row is <math>M</math>, the sum of <math>n</math> rows is <math>n M = n^2(n^2 + 1)/2</math>, which when divided by the order {{mvar|n}} yields the magic constant as <math>M = n(n^2 + 1)/2</math>. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence [[OEIS:A006003|A006003]] in the [[On-Line Encyclopedia of Integer Sequences|OEIS]]).
Summary:
Please note that all contributions to Niidae Wiki may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see
Encyclopedia:Copyrights
for details).
Do not submit copyrighted work without permission!
Cancel
Editing help
(opens in new window)
Search
Search
Editing
Magic square
(section)
Add topic