Geometric Magic Squares: A Challenging New Twist Using Colored Shapes Instead of Numbers

Lee Sallows

Dover Publications Inc. | 2013 | 160 páginas | epub | 15 Mb

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Traditional magic squares employ a chessboard-like arrangement of numbers in which the total of all rows, columns, and diagonals add up to the same number. This innovative approach by a Dutch engineer challenges puzzlists to think two dimensionally by replacing numbers with colorful geometric shapes. Dozens of creative puzzles, suitable for ages 12 and up.

Contents
Part I: Geomagic Squares of 3×3 
1. Introduction
2. Geometric Magic Squares
3. The Five Types of 3×3 Area Square
4. Construction by Formula
5. Construction by Computer
6. 3×3 Squares
7. 3×3 Nasiks and Semi-Nasiks
8. Special Examples of 3×3 Squares
Part II: Geomagic Squares of 4×4 
9. Geo-Latin Squares
10. 4×4 Nasiks
11. Graeco-Latin Templates
12. Uniform Square Substrates
13. Dudeney’s 12 Graphic Types
14. The 12 Formulae
15. A Type I Geomagic Square
16. Self-Interlocking Geomagics
17. Form and Emptiness
18. Further Variations
Part III: Special Categories 
19. 2×2 Squares
20. Picture-Preserving Geomagics
21. 3-Dimensional Geomagics
22. Alpha-Geomagic Squares
23. Normal Squares of Order-4
24. Eccentric Squares
25. Collinear Collations
26. Concluding Remarks
Appendix I. A Formal Definition of Geomagic Squares
Appendix II. Magic Formulae
Appendix III. New Advances with 4×4 Magic Squares
Appendix IV. The Dual of the Lo shu
Appendix V. The Lost Theorem
Glossary 
References