Magic Polygons
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Magic Polygons
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.
Advances in Applied Self-organizing Systems
Author: Mikhail Prokopenko
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-11-24
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.
Golden Dawn Magic
An easy-to-follow, step-by-step guide to the Golden Dawn system of magic The Golden Dawn system of magic is known throughout the world as one of the most effective and comprehensive approaches to working with occult powers. But for beginners or intermediate practitioners, it can be difficult to know where to start and where to go for expert guidance. Golden Dawn Magic shares bite-sized exercises and meditations to help you build the skills that are needed for the more advanced rituals, guiding beginner and intermediate practitioners on a powerful journey of magical work. Chic and Sandra Tabatha Cicero, senior adepts of the Golden Dawn, provide a firm foundation in practical Golden Dawn theory and methods, without the complex lessons and grades of more traditional approaches. This collection ofaccessible step-by-step instructions for visualization, meditation, energy projection, and working with willpower opens the doorways of magic. You will also discover hands-on exercises for learning the Golden Dawn's approach to esoteric arts like tarot and the Qabalah. Once you've mastered the fundamental skills, this book guides you through dozens of more advanced rites, rituals, and techniques, including: Greater and Lesser Banishing Rituals • Expanded Visualizations • Opening by Watchtower • Ritual of the Rose Cross • Prayer of Osiris • Exordiums of Thoth • Godform Assumption • Achieving Invisibility • Creating Your Own Talisman •Telesmatic Images • And Many More Whether you are just becoming interested in the Golden Dawn or you have already gained some experience in these methods, Golden Dawn Magic will be an extraordinary aid to you as you move forward on your journey in this powerful system of magic.