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The concept of a magic square is of ancient origin; the simple 3 by 3 square called “Lo Shu” being the first to appear. The cells of a magic square are populated with consecutive positive integers in such a way that all rows and columns have the same sum. “Magic Polygons” presents a natural generalization which involves polygons with more than 4 sides. A polygon is first tiled with parallelograms with the result that sequences of parallelograms with mutually parallel sides form streams which extend from one boundary edge to an opposite boundary edge. These streams form the analog of rows and columns in a magic square: the tiles are labeled with integers so that all streams have the same sum. Instead of using the positive integers 1, 2, 3, ... to label the tiles, various abelian groups are used, thus adding a further new dimension to the constructions. Related topics such as “Latin Polygons”, “Magic Cylinders” and “Magic Circle Systems” are also introduced.
Make More Immersive and Engaging Magic Systems in GamesGame Magic: A Designer's Guide to Magic Systems in Theory and Practice explains how to construct magic systems and presents a compendium of arcane lore, encompassing the theory, history, and structure of magic systems in games and human belief. The author combines rigorous scholarly analysis wi
This book presents the state-of-the-art in successfully engineered self-organizing systems. It goes further, too, to examine ways to balance design and self-organization in the context of applications. As demonstrated throughout, finding this balance helps to deal with diverse practical challenges. The case studies described illustrate the richness of the topic and provide guidance on its more intricate areas.
Jumpstart your students' minds with daily warm-ups that get them thinking mathematically and ready for instruction. Daily Math Stretches offers practice in algebraic thinking, geometry, measurement, and data for grades 6-8 to provide an early foundation for mastering mathematical learning. Written by Guided Math author Laney Sammons and with well-known, research-based approaches, this product provides step-by-step lessons, assessment information, and a snapshot of how to facilitate these math discussions in your classroom. Digital resources are also included for teacher guidance with management tips, classroom set-up tips, and interactive whiteboard files for each stretch.