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

by Sallows, Lee C.F.

• ISBN13: 9780486489094
• ISBN10: 0486489094
• Format: Paperback
• Copyright: 2013-04-17
• Publisher: Dover Publications

Summary

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.

Author Biography

London-born Lee Sallows has lived in Nijmegen in the Netherlands for the past 41 years and until recently worked as an electronics engineer for Radboud University. His longtime hobbies of computational wordplay and recreational mathematics have led to related articles as well as this collection of geometric magic squares.

Table of Contents

Foreword

I Geometric Squares of 3x3

1. Introduction

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

Glossary

References