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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 twist by a Dutch engineer utilizes colorful geometric shapes instead of numbers, challenging puzzlists to think two dimensionally. Includes dozens of creative puzzles for ages 12 and up.
Table of Contents
I Geometric Squares of 3x3
2. Geomagic Squares
3. The Five Types of 3x3 Area Square
4. Construction by Formula
5. Construction by Computer
6. 3x3 Squares
7. 3x3 Nasiks and Semi-Nasils
8. Special Examples of 3x3 Squares
II Geometric Magic Squares of 4x4
9. Geo-latin Squares
10. 4x4 Nasiks
11. Graeco-latin Templates
12. Uniform Square Substrates
13. Dudeney's 12 Graphic Types
14. The 12 Formulae
15. A Type 1 Geomagic Square
16. Self-interlocking Geomagics
17. Form and Emptiness
18. Further Variations
III Special Categories
19. 2x2 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 1. Formal Definition of Geomagic Squares
Appendix 2. Magic Formulae
Appendix 3. New Advances with 4x4 Magic Squares
Appendix 4. The Dual of Lo shu
Appendix 5. The Lost Theorem