Synopses & Reviews
Traditional magic squares are squares of numbers in which the rows, columns, and diagonals all add up to the same total. With a voluminous literature going back some 2,500 years, the universal assumption has ever been that magic squares are inherently arithmetical objects. In this innovative work by a British engineer, the author initiates a Copernican revolution in our understanding by replacing numbers with two-dimensional forms. The result is not merely a novel kind of geometrical magic square but a revelation that traditional magic squares are now better seen as the one-dimensional instance of this self-same
geometrical activity.
Review
The magic squares Sallows constructs do not add to the same number ineach straight line, but contain the same assembly of shapes or symbols in each line. Among his topics are the five types of 3X3 areasquare, construction by formula, special examples of 3X3 squares, Graeco-Latin templates, uniform square substrates, Dudeney's 12graphic types, a type I geomagic square, self-interlocking geomagics, form and emptiness, picture-preserving geomagics,three-dimensional geomagics, alpha-geomagic squares, normal squares of order-4, and collinear collations. No particular mathematical skill is required to play.Annotation ©2014 Ringgold, Inc., Portland, OR (protoview.com)
Synopsis
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.
Synopsis
This innovative approach to magic squares challenges puzzlists to think two dimensionally by employing colorful geometric shapes instead of numbers. Dozens of creative puzzles, suitable for ages 12 and up.
Synopsis
This innovative work replaces magic square numbers with two-dimensional forms. The result is a revelation that traditional magic squares are now better seen as the one-dimensional instance of this self-same
geometrical activity.
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