Volume XX , issue 2 ( 2017 ) | back |

70 years of the Mathematical Society of Serbia | 47$-$63 |

**Abstract**

The Mathematical Society of Serbia was founded in January 1948. During these 70 years of existence, the Society had a broad spectrum of activities: organization of scientific work, concerns for education, popularization of mathematics, etc. In the range of its activities we can quote the editing of five journals as well as a large number of various publications mostly assigned to young mathematician and programmers. The Society is the organizer of all competitions in mathematics and informatics in Serbia and its care is also preparation of Serbian teams for the participation at international competitions. Finally, through the Society, Serbian mathematicians realize their contacts with international associations. Our aim in this paper is to give a brief survey of activities the Society had in the time of its existence.

**Keywords:** Mathematical society; Mathematical congress; Mathematical olympiad; Olympiad in informatics.

**MSC Subject Classification:** A30

**MathEduc Subject Classification:** 01A74

Borromean rings and mathematical storytelling | 64$-$73 |

**Abstract**

Diverse mathematical concepts like Gray codes, linking number, Borromean and Brunnian rings, mapping degree (and others), are incorporated in mathematical stories which should make the subject more attractive and mathematics more accessible and easier to comprehend.

**Keywords:** Mathematical storytelling; Borromean rings; Brunnian rings; Gray codes; linking number.

**MSC Subject Classification:** 97G90

**MathEduc Subject Classification:** G94

Transforming the disk model of hyperbolic geometry to the upper half-plane model | 74$-$80 |

**Abstract**

The isomorphism between the two Poincaré models of Hyperbolic Geometry is usually proved through a formula using the Möbius transformation. In this article, we present a geometrical procedure which transforms one model onto the other and leads to these transformations. This can be utilized in the educational process.

**Keywords:** Hyperbolic geometry; transformations; disk model; upper half-plane model.

**MSC Subject Classification:** 97G50

**MathEduc Subject Classification:** G55

Lagrange's formula for vector-valued functions | 81$-$88 |

**Abstract**

In this paper we derive a variant of the Lagrange's formula for the vector-valued functions of severable variables, which has the form of equality. Then, we apply this formula to some subtle places in the proof of the inverse function theorem. Namely, for a continuously differentiable function $f$, when $f'(a)$ is invertible, the points $a$ and $b = f(a)$ have open neighborhoods in the form of balls of fixed radii such that $f$, when restricted to these neighborhoods, is a bijection whose inverse is also continuously differentiable. To know the radii of these balls seems to be something hidden and tricky, but in the proof that we suggest the existence of such neighborhoods is ensured by the continuity of the involved correspondences.

**Keywords:** Mean value theorem; inverse mapping theorem.

**MSC Subject Classification:** 97I60

**MathEduc Subject Classification:** I65