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Expanding the problems or fruitful results of simple questions in mathematics

Pietraszkiewicz P.

Zeszyty Naukowe / Wyższa Szkoła Oficerska Wojsk Lądowych im. gen. T. Kościuszki

2015

Nr 1

92--96

In this article, three famous, ancient geometric problems (angle trisection, squaring the circle, and the Delian problem) are described as expanding mathematical problems, i.e., a transition from the problems already solved to new problems of a higher level. The author recalled centuries of work by mathematicians trying to solve the above mentioned problems of geometry. It was emphasized that only the use of algebra in the nineteenth century made it possible to give (unfortunately negative) answer to the question about the feasibility of these geometry structures. The article highlights the need for putting simple questions (e.g. in the category of “expanding problems”). Asking such questions may lead to new, not always easy, but often interesting problems.