Elementary Approaches to the Teaching of the Combinatorial Problem of Rectangular Islands
The Topic of Islands
In this snapshot we consider the combinatorial problem of rectangular islands by elementary means. Although some of the corresponding results are quite new, the topic of islands and the methods for its investigation is suitable also for high school students. We offer a bunch of exercises, representations and methods usable by a math teacher who wants to consider some of the problems from the field with students. The questions which arise need no advanced mathematical knowledge. Because most of the problems are of finitary type, experimental mathematics with computer support proves to be useful for the formulations of general conjectures related to the bounds of the number of islands in a particular configuration.
Intuitively the combinatorial problem can be described as follows: Our world is a rectangular grid with cells. Each cell has a height and an island consisting of cells rises up from its neighbourhood, i.e., all of its cells are higher than the...
KeywordsComputer Algebra System Rectangular Grid Height Function Island System General Conjecture
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