Octagon Magic

Octagon Magic

An orphan girl meets the inhabitants of the mysterious Octagon House—and discovers a portal to America’s past—from the Gandalf Grand Master of Fantasy. Lorrie happens upon a strange and fascinating secret! Did a witch live in the eight-sided house? Was it haunted? There were lots of scary stories about the strange house—but none could match the secret Lorrie uncovered. One day, she climbed the high iron gate and escaped into the garden to save a kitten from some cruel boys—and met the mysterious lady of the house. The woman let Lorrie explore all the odd-shaped rooms. In one of them was a rocking horse and a large, eight-sided dollhouse—an exact miniature of the big house. The dollhouse was beautifully furnished—as if someone lived there! It drew Lorrie back into exciting adventures that she had to face with courage and daring!

Big Magic Number Puzzles

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.