By Stewart Coffin
This ebook discusses the way 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 background and philosophy of these examples.
The writer offers demanding situations and considerate questions, in addition to useful layout and woodworking the way to motivate the reader to construct his personal puzzles and test along with his personal designs.
Aesthetics, phychology, and mathematical concerns all issue into the definition of the standard of a puzzle.
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This e-book discusses how you can layout «good» geometric puzzles: two-dimensional dissection puzzles, polyhedral dissections, and burrs. It outlines significant different types of geometric puzzles and gives examples, occasionally going into the heritage and philosophy of these examples. the writer offers demanding situations and considerate questions, in addition to functional layout and woodworking easy methods to inspire the reader to construct his personal puzzles and scan together with his personal designs.
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Extra info for Geometric Puzzle Design
If complete sets are being considered, then Table 2 suggests that only the size-four and size-five sets look interesting. First, we will dispose of the size-four set. If the reader will mark and cut the five size-four pieces out of cardboard, it should be easy to convince oneself that it is impossible to assemble them into a 4 × 5 rectangle. But how can you be sure? This problem will be used as a simple example to illustrate two common analytical approaches to puzzles of this type. Mark a 4 × 5 board on paper.
Chapter 2. Two-Dimensional Combinatorial Puzzles 29 A subset of ten Cornucopia pieces can also be assembled to form a solid 6 × 10, 5 × 12, or 4 × 15 rectangle. (Note: the 3 × 20 rectangle is impossible. Can the reader discover a neat and simple proof of this? Hint: place pieces no. ) Combinatorial theory shows that a subset of ten pieces can be chosen from a set of 17 pieces 19,448 different ways. Which of these subsets will fit any of the boards shown in Figure 38, and in how many different ways?
Most attention has been given to the regular polygons. Choose any two regular polygons, and cut one of them into as many pieces as you wish to form the other. It may sound easy until you actually try it! The classic problem in geometric dissections is to find the minimum number of pieces required to perform a dissection between various pairs of common polygons. An excellent book on the subject is Recreational Problems in Geometrical Dissections and How to Solve Them, by Harry Lindgren. Famous puzzle inventor Henry Dudeney was a pioneer in geometric dissections.
Geometric Puzzle Design by Stewart Coffin