P. Brass, W. Moser, J. Pach:
Research Problems in Discrete Geometry
Springer, New York, 2005
Facsimile edition: China Science Press, Beijing, 2006
Japanese translation: Springer, Tokyo, 2009
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Although Discrete Geometry has a rich history extending more than 150 years, it abounds in open problems that
even a high-school student can understand and appreciate. Some of these problems are notoriously difficult and
are intimately related to deep questions in other fields of mathematics. But many problems, even old ones, can
be solved by a clever undergraduate or a high-school student equipped with an ingenious idea and the kinds of
skills used in a mathematical olympiad. "Research Problems in Discrete Geometry" is the result of a twenty-five year old project initiated by the late Leo Moser. It is a collection of more than 500 attractive open problems in the field, many of which can be understood without extensive preparation. The largely self-contained chapters provide a broad overview of discrete geometry, along with historical details and the most important partial results related to these problems. This book is intended as a source book for both professional mathematicians and graduate students who love beautiful mathematical questions, are willing to spend sleepless nights thinking about them, and who would like to get involved in mathematical research. Important features include:
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