© 1994 by Dr. Karl Scherer
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Most of us might have solved puzzles with several hundred or even several thousand pieces. These dissected pictures can keep you occupied for hours and days on end, and it is very satisfying when the full picture finally appears in front of you for the first time.
On the other end of the spectrum there are very complicated tilings
and tessellations like those of the meanwhile famous non repetitive Penrose
tilings of the plane.
They have a complex mathematical structure, but are still often very beautiful to look at.
Between these extremes there is a vast middle ground of puzzles and related problems that are based on elementary shapes, which can give us some mathematical insight, but are still easy enough for the general public to understand, to experiment with and to investigate into new areas.
The author's first book "A Puzzling Journey To The Reptiles And Related Animals" tried to cover some of this hardly investigated middle ground by describing the adventurous journey of three scientists into the land of self similar shapes.
The book "NUTTS And Other Crackers" ventures into some other and hitherto undetected areas of geometrical puzzles.
The first chapter describes the tangram-like game NUTTS. Unlike the tiles of tangram, the tiles
of NUTTS are a mathematically connected set of simple shapes, similar to
the set of polyominoes or polyamonds.
Of the thousands of interesting shapes that can be tiled with the NUTTS tiles, only about one hundred are presented here. That gives you lots of problems to solve and still leaves you a lot to invent...
Note that there is a free NUTTS game with every book!
The second chapter presents some new problem areas connected with Pythagorean
triangles (i.e., right triangles with integral sides). Among other topics,
we will look at how we can dissect certain shapes into Pythagorean triangles.
Here again the book contains many problems which you may solve and many areas for further investigations...
The third chapter is similar to the second, but it relates to dissections of shapes into triangles with integral areas. Can the plane be dissected into triangles, each having a different integral area? See for yourself...
The fourth chapter tries to classify tilings. We introduce the three new characteristics "pure", "neat" and "alternating" tiling. These classifications will lead to new and fascinating tilings of the plane, of squares and of many other shapes.
The final chapter 5 delivers some surprising results connected with those integral triangles (i.e., triangles with integral sides) which can be placed on the lattice grid.
Over and over the reader will be astonished how simple shapes can have such curious implications.
The book shows that even in today's complex world many new and joyful insights can be gained by everybody and that mathematics and the field of puzzles can still advance just by looking at a simple idea in a new way.
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