...................................................................................................

...................................................................................................

© 1994 by Dr. Karl Scherer

Click here for the list of contents

Click here to download the book

**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...
**

**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. **

**Joyful reading!
The author**

Pages : 300 (!)

Price : NZ$ 50 including packaging and postage in New Zealand

US$ 40 including packaging and airmail postage world-wide

Please add NZ$ 5 (US$2) if you want a three-coloured NUTTS game with the book

instead of a monochrome one; colours are subject to availability.

Please ask for rebates if you want to buy larger quantities.

Please send cheques to the address below:

Backup-zip

Atlantis Puzzles & Games

11 Utting Street, Birkdale, Auckland, New Zealand