Geometric Puzzle Design by Stewart Coffin

By Stewart Coffin

This ebook discusses easy methods to layout «good» geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs.
It outlines significant different types of geometric puzzles and offers examples, occasionally going into the heritage and philosophy of these examples.
The writer offers demanding situations and considerate questions, in addition to useful layout and woodworking how to inspire the reader to construct his personal puzzles and scan together with his personal designs.
Aesthetics, phychology, and mathematical concerns all issue into the definition of the standard of a puzzle.

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Example text

The Sam Loyd dissection puzzle described in the previous section was most likely developed by dissecting the square into the cross, after which the other interesting problem shapes were probably discovered. Creative Puzzles of the World by van Delft and Botermans contains an excellent chapter on geometric dissections as practical puzzles. Further investigation might uncover a dissection by which several polygons could be constructed from a neat set of pieces. For example, what are the fewest pieces required to construct three different regular polygons?

Practically all puzzles described in this book are inherently of the symmetrical order symmetry—dissymmetry—symmetry. The intriguing symmetries of the polyhedral shapes are often what attract the attention of the viewing public, much to the chagrin of the designer, for all of the creative work lies hidden within and is so often overlooked. Traditionally, artistic endeavors from music to poetry to oil paintings have nearly always been framed in symmetry of some sort, or at least were until the twentieth century.

The most obvious problem shapes to construct with such pieces are hexagonal clusters. These are shown in Figure 45 in increasing size. Thus, a set of the three size-three pieces plus the seven size-four pieces just happens to construct the 37-block hexagonal cluster (Figure 46a). It also constructs a snowflake-shaped figure (Figure 46b) plus many other geometric and animated shapes. Beeler found by computer analysis that the hexagonal cluster has 12,290 solutions, and the snowflake pattern (from which a commercial version of this puzzle derived its name) has 167 solutions.

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