Area Magic Squares |
Geometrical Interpretation of matrices |
Area Matrix Definition (PDF) An Area Matrix (A,M) is a combination of a positive matrix A and a set M of continuous graphs. An Area Magic Square (AMS) is an area matrix (A,M) where the matrix A is a magic square. Less mathematical definitions (PDF) |
Linear Area Magic Squares of order 3 |
Third-Order Linear Area Magic Squares - Algorithm (PDF) |
1 to 9 | 2 to 10 | 3 to 11 | 4 to 12 | 5 to 13 | 6 to 14 | 7 to 15 | 8 to 16 | |
Solution 1 | ||||||||
Solution 2 |
2017-01-06: First Third-Order Linear Area Magic Square (PDF) |
Theory of area magic squares (PDF) |
Third-Order Integer Area Square (PDF) |
Curved Area Magic Square (PDF) |
Linear Area Magic Squares of order 4 |
2017-01-14: First Order-4 Linear Area Magic Square |
Article: Semi-orthogonal linear area magic squares of order 4 - part 1 (PDF) |
Article: Semi-orthogonal linear area magic squares of order 4 - part 2 (PDF) |
Data: All 720 order-4 linear area magic squares up to S=200 (TXT) |
equivalent type 1 |
equivalent type 2 |
magic sum 144 |
Other Area Magic Squares of order 4 |
Classical Magic Square 2017-02-26 (PDF) |
Consecutive Numbers 2017-02-02 (PDF) |
Area Magic Squares of order 5 |
Semi-orthogonal linear area magic squares of order 5 do not exist. (Equal areas would occur) If linear area magic squares of order 5 exist, they would consist of large entries. |
Semi-orthogonal convex AMS 2017-02-09 |
Rounded linear AMS 2017-02-15 (PDF) |
Links | |
Hans-Bernhard Meyer: | Observations on 4x4 Area Magic Squares with vertical Lines |
William Walkington: |
Area Magic Squares and Tori of order 3 Area Magic Squares of order 6 Area Magic Squares of order 4 |
Carlos Rivera: | Area Magic Squares with prime numbers (solutions by Jan van Delden) |
Home: Notes on Magic Squares | Walter Trump, Nürnberg, Germany, (c) 2017-01-28, last update 2018-06-19 |