The article concerns the following problem: Given square $ABCD$ with the side of 1. Find points $E,F$ so that the sum $l=\left|AE\right|+\left|DE\right|+\left|EF\right|+\left|BF\right|+\left|CF\right|$ is the smallest possible. Four solutions are given which are examples of the connection between several mathematical disciplines (geometry, algebra and calculus). The article concludes with a note on the history of the presented problem (leading to P. Fermat and others).

The paper presents demonstrations of activity-oriented mathematics teaching methods focused on using construction sets of geometric solids Polydron in the teaching of mathematics. The text contains mathematical tasks and methodic notes to the use of Polydron building sets in the teaching of mathematics.