| Author | Redakce |
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Vol. 27 (2019), No. 1, February 2020
Content
Proof of Equivalence of Two Ellipse Definitions [CZ]
| Author | J. Blažek |
| Abstract | Dynamic geometry software opened completely new approach to processing and solving geometrical problems. Due to its features it is possible to experiment and attain facts, significantly facilitating solution processes. This article presents a case study, in which author uses the means of dynamic geometry to prove the equivalence of two ellipse definitions – as a locus of points having constant sum of distances from two fixed points, and as a locus of points having constant ratio of distances from a fixed point and directrix line. |
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Mechanical Transmissions in Mathematical Teaching [CZ]
| Author | J. Fiala |
| Abstract | The contribution deals with the Mathematics teaching in the secondary school, concretely with solving applied tasks coming from technical practice. It generally deals then with modern teaching methods. In the contribution we solve two concrete mathematical tasks on the topic of the generally known mechanical transmissions. We comment the tasks on the didactic-methodological field, we make mention of benefits and difficulties of their using in Mathematics teaching at the secondary school and we complement our own experience from teaching at the secondary school for teachers' use. |
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Ancient Problems vs. Modern Technology
| Author | Š. Gergelitsová, T. Holan |
| Abstract | Geometric constructions using a ruler and a compass have been known for more than two thousand years. It has also been known for a long time that some problems cannot be solved using the ruler-and-compass method (squaring the circle, angle trisection); on the other hand, there are other problems that are yet to be solved. Nowadays, the focus of researchers' interest is different: the search for new geometric constructions has shifted to the field of recreational mathematics. In this article, we present the solutions of several construction problems which were discovered with the help of a computer. The aim of this article is to point out that computer availability and performance have increased to such an extent that, today, anyone can solve problems that have remained unsolved for centuries. |
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Arithmetic and Boxes [CZ]
| Author | Š. Gergelitsová, T. Holan |
| Abstract | The paper is based on the presentation of the ATest system that was given by the authors at the 9th conference “The use of computers in mathematics education”. The ATest system is focused on supporting arithmetic skills of pupils. It not only helps pupils to automate performing of arithmetic operations but, moreover, it utilizes their abilities to look for possible constructions of a given result. ATest application helps to gamify a classroom. It brings elements of constructivist teaching. |
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Propedeutic of Fractions in Mathematics Using Music and Computers [SK]
| Author | J. Hnatová, A. Prídavková |
| Abstract | The concept of fraction is introduced in the Slovak context only at the propedeutic level in the primary stage of education. The paper presents proposal of an auditory model of the term which uses mathematics, music education and set of interactive equipment. The set is supported by SmartNotebook software. Creating activities in this program is a part of the undergraduate teacher training at Faculty of Education, University of Preshov, in the subject Mathematics and Computer. |
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About Factorization of Polynomials with Integer Coefficients [CZ]
| Author | J. Hora |
| Abstract | The article contains an example of using classical algorithm for factorization of polynomial with integer coefficients, discovered by Theodor von Schubert. This algorithm was rediscovered by L. Kronecker. However, algorithm is suitable only for small degree polynomials of one indeterminate. Finally, the algorithm for factorization of a polynomial with coefficients in the body Z_p, p - prime number is briefly described. Two Czech, respectively Slovak mathematicians contributed to its elaboration. This algorithm is the basis of modern factorization algorithms. |
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Mathematical Way to Technology – the Self-Locking Pliers [CZ]
| Author | H. Mahnelová |
| Abstract | The self-locking pliers are an example of a mechanical linkage with one degree of freedom. Two of its four joints move along circular trajectories, one of them, the so-called driving point, affects the distribution and transmission of force. Using a dynamic computer model, it is possible to demonstrate the rate of change of length with which the size of the lever, transmission and the gripping of the pliers change. The example can conveniently be used to demonstrate the practical application of mathematical concepts such as locus of points, power function properties, square root function, cosine function at a given interval, properties of a right and general triangle. In the paper, the kinematic equation of the pliers will be derived. |
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Learning Solids with GeoGebra [CZ]
| Author | Š. Voráčová |
| Abstract | In the paper, we highlighted some opportunities and examples on how GeoGebra can be used in classrooms to explore some basic concepts in spatial geometry. We present our interactive education materials designed specifically for teaching spatial geometry. We focus on volumes of solids, which are the most critical problems in geometry education. Interactive spatial representation enables the student to see and explore relations and concepts that were difficult to show in past prior to technology. |
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