What is the equation for finding the magic constant of a magic square?

In summary, the conversation is about finding the magic constant for a magic square, which is the sum of all numbers in a row, column, or diagonal. The formula for the magic constant is M_{2}\left( n \right)\; =\; \frac{n\left( n^{2}+1 \right)}{2}, which was derived from the series \mbox{S}=\left[ \frac{n+1}{2}+\left( n-1 \right)n \right]. The conversation also touches on using Gauss' formula for the sum of consecutive numbers and dividing by the number of rows/columns to find the magic constant.
  • #1
BobFijiwinkle
5
0
Hey all. I'm trying to convert a series which gives me the magic constant for a magic square into an equation. How would I go about doing this?

The series is:
[tex] \mbox{S}=\left[ \frac{n+1}{2}+\left( n-1 \right)n \right] [/tex]
 
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  • #2
What do you mean by the magic constant? The sum - so for a 3 x 3 from 1-9 you want 15?

Simply sum 1 to n2, then divide by n?
 
  • #3
Yes, that's what I mean by the magic constant.

Yes, I know that, but I'm trying to derive the formula from the series to prove that that is correct.

BF
 
  • #4
I'm not sure that it is. Plugging 3 into your formula gives 10, to say nothing of what happens if n is even.

What is the sum of 1 + 2 + 3 + ... a, where a is an integer?
 
  • #5
Let me get something clear.

I'm trying to prove that the magic constant is

[tex]M_{2}\left( n \right)\; =\; \frac{n\left( n^{2}+1 \right)}{2}[/tex]
 
  • #6
Ahh, that looks a lot more like the formula I've got.

To explain where I'm coming from with my request for the sum of 1 + 2 + 3 + ... a (hint Gauss), if you sum these, then divide by the number of rows / colums you ought to get somewhere. I didn't want to say the sum of 1 to n2, in case it got confused as 1 + 4 + 9 etc.
 

1. What is a magic constant equation?

A magic constant equation is a mathematical formula that produces a constant number when certain rules are applied. This constant number is often known as a "magic number" and is considered to have special properties or significance.

2. How is a magic constant equation used?

Magic constant equations are often used in recreational mathematics and puzzles. They can also be found in other fields such as computer science and physics, where they can be used to solve complex problems or to model certain phenomena.

3. Can anyone create a magic constant equation?

Yes, anyone with a knowledge of mathematics can create a magic constant equation. However, creating a truly unique and interesting one may require a lot of creativity and problem-solving skills.

4. Are there different types of magic constant equations?

Yes, there are several different types of magic constant equations, including magic squares, magic cubes, and magic stars. Each type has its own set of rules and properties that make it unique.

5. What is the significance of magic constant equations?

The significance of magic constant equations lies in their ability to produce constant numbers using simple mathematical operations. They also offer a fun and challenging way to explore mathematical concepts and can be used in various fields to solve problems and make discoveries.

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