MATHEMATICS–PHYSICS–INFORMATICS

On the occasion of the unreached doc. Stanislav Trávníček's birthday

Editor MFI — 2025-06-01

The national round of the 74th year of the Mathematics Olympiad (category A)

Pavel Calábek — 2025-06-01

The national round of the 74th year of the Mathematics Olympiad (category P)

Pavel Töpfer — 2025-06-01

The national round of the 66th year of the Physics Olympiad (category A)

Lukáš Richterek — 2025-06-01

Kinship triangles

Pavel Leischner — 2025-06-01

Two triangles are said to be kinship if their two corresponding sides are equal and the sum of the angles between the sides is a straight angle. The article describes the characteristics of such triangles and presents examples of their use.

Numerical Attributes of the Logical Connectives

Miloslav Závodný — 2025-06-01

The present paper deals with the numerical attributes of the logical connectives. We put the truth functions representing the connectives as formulas using arithmetic operations to truth values of logical variables: a'=1–a, (a∧b)=ab, (a∨b)=a+b-ab= 1–a'b'= a+a'b = b+b'a, (a ⇒ b) = 1–a+ab = 1–ab' = a'+ab = b+a'b' and (a ⇔ b) = 1–(a–b)²=ab+a'b'=1–ab'–a'b. In this way, we solve formulas of a propositional calculus just as arithmetic expressions. Several illustrative examples are supplied here.

Three special points lying on one line VI

Jaroslav Zhouf — 2025-06-01

This article is the sixth continuation of the theme of an interesting trio of points that lie on the same line. The main roles presented here are those that can be used in school teaching. In addition, there is, for example, a statement about the Simson line.

Interesting math problems

Editor MFI — 2025-06-01

We continue to publish other problems of our traditional section.

The possibility of using programming in solving selected MO mathematics problems by students

Ladislav Perk — 2025-06-01

The article deals with the possibility of using programming to solve selected tasks from the Mathematical Olympiad (MO) by primary and secondary school students. It presents a systematic approach to experimentation and searching as a tool that can facilitate the solution of tasks that would otherwise be difficult or practically unsolvable for students using conventional mathematical methods. The text provides seven specific examples of MO tasks, for which the solution is achieved using simple algorithms in the Python language. The article does not emphasize code optimization, but rather its comprehensibility for readers with basic programming experience. The emphasis is on the connection between mathematics and computer science, the development of digital competencies, and interdisciplinary relationships. The article shows that even basic programming knowledge can expand students' possibilities in solving non-trivial mathematical problems and supports the idea of incorporating programming approaches into mathematics education.

Visualization using stars and the pitfalls of nonlinear relationships

Ondřej Vencálek — 2025-06-01

The article focuses on the issue of data visualization using stars, which are commonly used to evaluate the quality of various services, products, or phenomena. The author points out that converting numerical data into stars is not a trivial task and can easily lead to misleading interpretations. Using a specific example of visualising the effectiveness of COVID-19 vaccines, he demonstrates how the choice of transformation function (e.g., linear, logarithmic, or based on order) significantly impacts the resulting impression of the data. The text emphasizes that none of the presented visualizations is unambiguously correct or ideal—each has its advantages and pitfalls. The author warns that visualization using stars (and other simplified displays) is easily misused for manipulative purposes and recommends caution when interpreting such graphs. The article concludes with a discussion of the nature of the relationship between antibody levels and the degree of protection against infection and encourages deeper reflection on such simplifications.

New textbook Mathematics for Secondary Schools – Stereometry

Petr Emanovský — 2025-06-01

Reviews of two other translations of important books

Zdeněk Půlpán — 2025-06-01

We measure the holding force of magnetic foils

Markéta Mysíková — 2025-06-01

The holding force of magnetic foils is measured using the Vernier school system by tearing the foil off the base. The original magnetic polarization of the foil is then changed to a Halbach array structure with different periods, and the effect on the holding force of the foil is monitored. The measurements show that the original Halbach array structure used in magnetic foils is optimal in terms of holding force compared to the magnetic pole structures we have created.