Can this be done in a simplier way? Magic Squares

  • Context: Undergrad 
  • Thread starter Thread starter Dustinsfl
  • Start date Start date
  • Tags Tags
    Magic Squares
Click For Summary

Discussion Overview

The discussion revolves around the proof of Axiom 1 related to 3x3 magic squares, with participants exploring whether a simpler and more concise method exists for this proof. The conversation includes technical details, mathematical reasoning, and references to previous work in the forum.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses that their proof using summation notation is lengthy and cumbersome, seeking a simpler approach.
  • Another participant questions the specifics of Axiom 1 and finds the provided PDF difficult to understand.
  • A different participant provides a link to a previous discussion for context and indicates a need to form a basis for S but is uncertain about how to start.
  • Another participant suggests considering specific equations related to the magic square and provides a series of equations that could help in forming the basis matrices.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the simplicity of the proof or the clarity of the provided materials. Multiple approaches and uncertainties remain in the discussion.

Contextual Notes

There are limitations regarding the clarity of the PDF and the assumptions underlying the equations proposed for forming the basis. The discussion does not resolve these issues.

Dustinsfl
Messages
2,217
Reaction score
5
Proving Axiom 1 of all 3 x 3 magic squares.

I used summation notation to do so but it is extremely long and cumbersome.

I attached the pdf file with the work.

Is there a way to do this in a simpler more concise manner?
 

Attachments

Last edited:
Physics news on Phys.org
I just added the pdf file I forgot to add.
 
What is this axiom 1 that you're trying to prove? That PDF is impenetrable.
 
To form the basis, consider the equations you have regarding some [tex]A[/tex] a magic square, denote [tex]x_i = a_{1i} \in A \quad 1 \le i \le 3[/tex] and [tex]x_i = a_{2i} \in A \quad 4 \le i \le 6[/tex] and so on, then:

[tex]x_1 + x_2 + x_3 = x_4 + x_5 + x_6[/tex]
[tex]x_1 + x_2 + x_3 = x_7 + x_8 + x_9[/tex]
[tex]x_1 + x_4 + x_7 = x_2 + x_5 + x_8[/tex]
[tex]x_1 + x_4 + x_7 = x_3 + x_6 + x_9[/tex]
[tex]x_1 + x_2 + x_3 = x_1 + x_4 + x_7[/tex]

If you play with these equations for a bit you can get the basis matrices.
 

Similar threads

Undergrad Can New Theorems Predict Incomplete 5x5 Magic Square Solutions?
  • · Replies 68 ·
3
Replies
68
Views
13K
Undergrad Notation questions about kernel, cokernel, image and coimage
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Linear least squares regression for model matrix identification
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Optimizing Drumstick Bounce: Finding the Magic Fulcrum Point
  • · Replies 31 ·
2
Replies
31
Views
3K
High School A Simpler Way to Find the Shaded Area?
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Confusion about the Direct Sum of Subspaces
  • · Replies 3 ·
Replies
3
Views
5K
Python Python "ImportError: bad magic number ...."
  • · Replies 1 ·
Replies
1
Views
5K
MHB Number of ways to divide a square grid in half
  • · Replies 3 ·
Replies
3
Views
4K
How Can You Generalize 3 x 3 Magic Squares?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Two Ways of Calculating the Solution to the Infinite Square Well?
  • · Replies 28 ·
Replies
28
Views
4K