Like the intriguing Fibonacci and Lucas numbers, Catalan numbers
are also ubiquitous. "They have the same delightful propensity for
popping up unexpectedly, particularly in combinatorial problems,"
Martin Gardner wrote in Scientific American. "Indeed, the Catalan
sequence is probably the most frequently encountered sequence that
is still obscure enough to cause mathematicians lacking access to
Sloane's Handbook of Integer Sequences to expend inordinate amounts
of energy re-discovering formulas that were worked out long ago,"
he continued. As Gardner noted, many mathematicians may know the
abc's of Catalan sequence, but not many are familiar with the
myriad of their unexpected occurrences, applications, and
properties; they crop up in chess boards, computer programming, and
even train tracks. This book presents a clear and comprehensive
introduction to one of the truly fascinating topics in mathematics.
Catalan numbers are named after the Belgian mathematician Eugene
Charles Catalan (1814-1894), who "discovered" them in 1838, though
he was not the first person to discover them. The great Swiss
mathematician Leonhard Euler (1707-1763) "discovered" them around
1756, but even before then and though his work was not known to the
outside world, Chinese mathematician Antu Ming (1692?-1763) first
discovered Catalan numbers about 1730. A great source of fun for
both amateurs and mathematicians, they can be used by teachers and
professors to generate excitement among students for exploration
and intellectual curiosity and to sharpen a variety of mathematical
skills and tools, such as pattern recognition, conjecturing,
proof-techniques, and problem-solving techniques. This book is not
intended for mathematicians only but for a much larger audience,
including high school students, math and science teachers, computer
scientists, and those amateurs with a modicum of mathematical
curiosity. An invaluable resource book, it contains an intriguing
array of applications to computer science, abstract algebra,
combinatorics, geometry, graph theory, chess, and world series.
General
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