Кафедра математики, фізики та методик їх навчання

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3D-моделювання у навчанні фізики
(ФОП Цьома С. П., 2021) Каленик Михайло Вікторович; Kalenyk Mykhailo Viktorovych
У статті обговорюються аспекти використання 3D-моделювання у навчанні фізики з метою попереднього відпрацювання низки експериментальних дій та операцій, формування загальних підходів до планування та проведення окремих етапів експериментального дослідження, а також збільшення рівня сформованості умінь та навичок у виконанні фізичного експерименту.
4-вимірні вектори в СТВ
(2011) Мороз Іван Олексійович; Moroz Ivan Oleksiiovych; Іваній Володимир Степанович; Ivanii Volodymyr Stepanovych; Холодов Роман Іванович; Kholodov Roman Ivanovych
Вивчення явищ, які протікають з великими швидкостями, вимагає врахування скінченності швидкості передачі взаємодії. Це, спільно з вимогою інваріантності законів всіх явищ по відношенню до зміни системи відліку, приводить до необхідності нерозривного розгляду простору і часу та введення єдиного об’єкту, у якому протікають всі процеси в природі – чотиривимірного простору-часу.
Application of Mind Mapping Technique in Teaching Physics in General Secondary Education Institutions
(International Science Group, Boston : Primedia eLaunch, 2024) Kalenyk Mykhailo Viktorovych; Каленик Михайло Вікторович
The monograph explores the methodology of using mind mapping technique in teaching physics in general secondary education. The basics of creating mind maps, their effectiveness in visualizing and structuring complex information, including physical phenomena and laws, are described. The advantages of the methodology are considered: the development of critical thinking, increasing motivation to learn, facilitating the memorization of material. The key stages of implementing mind mapping in physics lessons and the role of this technique in shaping students' creativity and analytical skills are outlined. The work focuses on the psychological and pedagogical aspects of the technique, its impact on the quality of the educational process and individualization of learning.
Cloud-based Service GeoGebra and its Use in the Educational Process: the BYOD-approach
(2019) Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Бондаренко Юлія Анатоліївна; Кондратюк Світлана Миколаївна; Дегтярьова Неля Валентинівна; Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Bondarenko Yuliia Anatoliivna; Kondratiuk Svitlana Mykolaivna; Dehtiarova Nelia Valentynivna
The authors propose one of the possible ways to solve the problem of insufficient number of computers in public educational institutions and limited access to computer classes in Ukraine. Such a way is the introduction of the BYOD-approach (Bring Your Own Device) in the learning process. The authors specify the content and correlation of the concepts of "information technologies", "computer technologies", "cloud technologies" to determine the type of service GeoGebra. The authors propose different ways of using the GeoGebra service. They are studied to prepare future math teachers for the use of modern information (digital) technologies in professional activities.
Computer Mathematical Tools: Practical Experience of Learning to Use Them
(2014) Semenikhina Olena Volodymyrivna; Семеніхіна Олена Володимирівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article contains general information about the use of specialized mathematics software in the preparation of math teachers. The authors indicate the reasons to study the mathematics software. In particular, they analyze the possibility of presenting basic mathematical courses using mathematical computer tools from both a teacher and a student, argue in favour of using software instead of traditional paper-and-board style. The special course of the study of mathematics software (main tasks of the course are disclosed; knowledge and skills that students should possess on completion of their studies are dedicated; content of computer workshop is detailed) is briefly described. Also the authors give a detailed solution and its methodic basis of typical problem with the use of the SCM Maple. The typical errors which made by students in the use of specialized mathematics packages are characterized. Author’s own experience of teaching computer workshop of the study of mathematical computer tools by the students of Sumy State Pedagogical Makarenko University is presented and analyzed.
Computer Tools “Trace” and “Locus” in Dynamic Mathematics Software
(2014) Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article describes the results of use of tools "Trace" and "Locus" in dynamic mathematics software. Examples of solutions of stereometric locus problems to construct static traces in software GeoGebra5.0, Cabri3D and plane geometry problems to construct both static traces and traces that are perceived as independent dynamic objects in software MathKit and GeoGebra are given. Attention is focuses on the differences of the actions of these tools. Author notes the possibility of forming a logical and constructive thinking with their use.
Computer Visualization of Logic Elements of the Information System Based on PROTEUS
(2019) Shamonia Volodymyr Hryhorovych; Semenikhina Olena Volodymyrivna; Drushliak Maryna Hryhorivna; Lynnyk Serhii Ivanovych; Шамоня Володимир Григорович; Семеніхіна Олена Володимирівна; Друшляк Марина Григорівна; Линник Сергій Іванович
The article considers the possibility of a computer visualization of the code decoder work in Proteus, which is used in a laboratory workshop when studying the topic "Digital logic" of the discipline "Architecture of Information Systems" (the field of study “12 Information technologies” and “01 Education, 014 Secondary education. Computer science”). Modelling and simulation dur-ing the laboratory work contribute to the awareness of the importance of visual-ization as a means of positive impact on the level of future IT-specialists’ edu-cational achievements. This was confirmed by the analysis of the obtained re-sults at the significance level of 0.05 according to Student’s test.
Conditions of Dedekindness of Generalized Norms in Non-periodic Groups
(2019) Lukashova Tetiana Dmytrivna; Drushliak Maryna Hryhorivna; Lyman Fedir Mykolaiovych; Лукашова Тетяна Дмитрівна; Друшляк Марина Григорівна; Лиман Федір Миколайович
The authors consider generalized norms for different systems of infinite and noncyclic subgroups in nonperiodic groups. Relations between these norms are established. The conditions under which the given norms are Dedekind, in particular, central, are studied.
Constructing a Model of the Axis Form in a S-Shaped Riser of a Cultivator Paw
(Eastern-European Journal of Enterprise Technologies, 2024) Pylypaka S.; Hropost V.; Volina T.; Kalenyk Mykhailo Viktorovych; Ruzhilo Z.; Dieniezhnikov Serhii Serhiiovych; Tarelnyk N.; Tatsenko O.; Semirnenko S.; Motsak Svitlana Ivanivna; Пилипака С.; Хропост В.; Воліна Т.; Каленик Михайло Вікторович; Ружило З.; Дєнєжніков Сергій Сергійович; Тарельник Н.; Таценко О.; Семірненко С.; Моцак Світлана Іванівна
When cultivating the soil, a force of resistance to the movement of cultivator paw acts on it. It has a variable value and causes a moment of force applied to the riser of the paw. Under the action of the moment, the elastic axis of the riser changes its shape. This affects the position of the paw in the soil. The form of an S-shaped riser whose elastic axis consists of two circle arcs has been considered in this study. During cultivator operation, one part of the riser bends, increasing the curvature of the elastic axis, and the other, on the contrary, unbends, that is, its curvature decreases. The modeling of the shape of the elastic axis of the paw riser is based on the theory of resistance of materials, according to which the curvature of the elastic axis of the cantilevered band is directly proportional to the applied moment and inversely proportional to its stiffness. If the shape of the cross-section of the riser along its entire length is unchanged and the properties of the metal are also the same, then the stiffness is constant. In the case of small deflections of the band, the linear theory of bending is used, but the deflections in the riser are significant, so the nonlinear theory has been used for this case. At the same time, it is taken into account that the elastic axis of the riser already has an initial curvature, the sign of which changes after passing through the point of connection of the component arcs. To model the shape of the elastic axis of the S-shaped paw riser, the deformation of the arcs of the circles that form this paw was calculated separately. Numerical integration methods were used to find the shape of the deformed elastic axes of both parts of the riser. They were connected into a whole and a deformed elastic axis of the S-shaped riser was obtained. Two variants of the riser with different lengths of their elastic axis, but the same height and the same angle of entry into the soil, were considered. The combination of the component arcs of the riser shows that, under the action of the same force, the deviation from the specified movement depth for one riser is 2 cm, and for the other – 4 cm
Constructing Geometrical Models of Spherical Analogs of the Involute of a Circle and Cycloid
(Eastern-European Journal of Enterprise Technologies, 2023) Nesvidomin A.; Pylypaka S.; Volina T.; Kalenyk Mykhailo Viktorovych; Shuliak I.; Semirnenko Y.; Tarelnyk N.; Hryshchenko I.; Kholodniak Y.; Sierykh L.; Несвідомін А.; Пилипака С.; Воліна Т.; Каленик Михайло Вікторович; Шуляк І.; Семірненко Ю.; Тарельник Н.; Грищенко І.; Холодняк Ю.; Сєрих Л.
The common properties of images on a plane and a sphere are considered in the scientific works by scientists-designers of spherical mechanisms. This is due to the fact that the plane and the sphere share common geometric parameters. They include constancy at all points of the Gaussian curve, which has a zero value for a plane and a positive value for a sphere. Figures belonging to them can slide freely on both surfaces. With unlimited growth of the radius of the sphere, its limited section approaches the plane, and the spherical shape transforms into a plane. Thus, a loxodrome that crosses all meridians at a constant angle is transformed into a logarithmic spiral that intersects at a constant angle the radius vectors that come from the pole. The tooth profile of cylindrical gears is outlined by the involute of a circle. A spherical involute is used for the corresponding bevel gears. Other spherical curves are also known, which are analogs of flat ones. The formation of a cycloid and an involute of a circle are associated with the mutual rolling of a line segment with each of these figures. If the segment is fixed and the circle rolls along it, then the point of the circle describes the cycloid. In the case of a stationary circle along which a segment is rolled, the point of the segment will execute the involute. To move to the spherical analogs of these curves, it is necessary to replace the circle with a cone, and the straight line with a plane. The spherical prototype of the cycloid will be the trajectory of the point of the base of the cone, which rolls along the plane, that is, along the sweep of the cone. The sweep of a cone is a sector, the radius of the limiting circle of which is equal to the generating cone. If this sweep, like a section of a plane, is rolled around a fixed cone, when its top coincides with the center of the sector, then the point of the limiting radius of the sector will execute a spherical involute. This paper analytically implements these two motions and reports the parametric equations of the spherical analogs of the circle involute and the cycloid
Construction of Mathematical Model of Particle Movement by an Inclined Screw Rotating in a Fixed Casing
(Eastern-European Journal of Enterprise Technologies, 2023) Volina T.; Pylypaka S.; Kalenyk Mykhailo Viktorovych; Dieniezhnikov Serhii Serhiiovych; Nesvidomin V.; Hryshchenko I.; Lytvynenko Ya.; Borodai A.; Borodai D.; Borodai Ya.; Воліна Т.; Пилипака С.; Каленик Михайло Вікторович; Дєнєжніков Сергій Сергійович; Несвідомін В.; Грищенко І.; Литвиненко Я.; Бородай А.; Бородай Д.; Бородай Я.
Screw conveyors are used to move bulk materials vertically upwards, horizontally, and at an angle to the horizon. The processes that take place when particles are moved by a screw conveyor in vertical and horizontal directions have been studied. There is a significant difference between them: for transportation in the vertical direction, the necessary conditions must be ensured (sufficient angular speed of rotation of the screw), and for horizontal transportation, the movement of the particle occurs at any angular speed of rotation of the screw. Therefore, when changing the inclination of the axis of the screw, there comes a moment when transportation becomes possible, while it was impossible in the vertical direction. This paper considers the movement of a particle under the condition that it simultaneously contacts two surfaces: the moving surface of the screw and the stationary surface of the cylindrical casing in which the screw rotates. Their common line along which the particle slides is a helical line – the periphery of the screw. The particle slides along the helical line of the rotating screw, i.e., it is in relative motion with respect to it. At the same time, it slides along the surface of the casing, relative to which it is in absolute motion. The trajectory of the particle’s absolute motion is its sliding track on the casing surface. When constructing differential equations of the relative motion of particles, the forces applied to the particle were taken into account. The initial position was taken to be the vertical direction of the screw to transport the particle upwards. If an auger in a cylindrical casing is tilted from the vertical direction to a certain angle, then all applied forces (except the force of weight) will also tilt to this angle. On the basis of this, generalized differential equations of the relative motion of a particle during its transportation by an inclined screw were built. They made it possible to derive a generalized mathematical model of the movement of a particle by an inclined screw that rotates inside a fixed casing.
Cтруктура и свойства полимерных композитов и нанокомпозитов, подвергнутых термомагнитной обработке
(2015) Стадник Олександр Дмитрович; Stadnyk Oleksandr Dmytrovych; Мороз Іван Олексійович; Moroz Ivan Oleksiiovych; Медведовська Оксана Геннадіївна; Medvedovska Oksana Hennadiivna; Білик Володимир Миколайович; Bilyk Volodymyr Mykolaiovych
В работе исследовано воздействие термомагнитной обработки на структуру и свойства полимерных композиционных материалов, на основе эпоксидно-диановой смолы, поливинилиденфторида, полиэтилена, поли-4-метилпентена-1. В качестве наполнителей использовали порошки: электролитическое железо, карбонильный никель и нанокобальт. Определено значение температуры плавления и кристаллизации, а также диапазон температур плавления (кристаллизации). Установлена зависимость степени кристалличности, коэрцитивной силы и остаточной намагниченности полимерных композиционных материалов от концентрации наполнителя и условий обработки.
Designing a Helical Knife for a Shredding Drum Using a Sweep Surface
(Eastern-European Journal of Enterprise Technologies, 2024) Pylypaka S.; Hropost V.; Nesvidomin V.; Volina T.; Kalenyk M.; Volokha M.; Zalevska O.; Shuliak I.; Dieniezhnikov Serhii Serhiiovych; Motsak Svitlana Ivanivna; Пилипака С.; Хропост В.; Несвідомін В.; Воліна Т.; Каленик Михайло Вікторович; Волоха М.; Залевська О.; Шуляк І.; Дєнєжніков Сергій Сергійович; Моцак Світлана Іванівна
The object of this paper is a helical blade in a shredding drum from a sweep surface. Such drums are used in harvesters for crushing plant mass. If the flat blades are installed on the drum, cutting of the plant mass occurs simultaneously along the entire length of the blade. This could cause a pulsating dynamic load. If a flat knife with a straight blade is installed at an angle to the axis of the drum, then the distances from it to the points of the blade will be different, as well as the cutting conditions along the blade. The elliptical shape enables the same distance from the axis of rotation to the points of the blade, but this does not solve the problem. Many short flat knives with a straight blade can be mounted on the drum, placing them in such a way that the time between the individual knives is minimized. However, all these disadvantages can be eliminated by a helical knife with a blade in the form of a helical line. The design of a helical knife from an unfolding helicoid has been considered. In differential geometry, the bending of unfolded surfaces of zero thickness is considered. Bending of the workpiece into a finished product occurs with minimal plastic deformations, the magnitude of which depends on the thickness of the workpiece sheet. The methods of differential geometry of unfolding surfaces were applied to the analytical description of the surface of the helical knife. The parametric equations of the unfolding helicoid were derived according to the given structural parameters of the knife in space and on the plane. That has made it possible to mathematically describe the contour lines that cut the knife from the surface and on its sweep. Formulae for calculating a flat workpiece through the structural parameters of the knife have been derived. Thus, with the specified structural parameters of the knife R=0.25 m, τ=20°, j=65°, according to the resulting formula, we find the radius of the knife blade on a flat workpiece: R0=4.8 m
Determining the Shape of a Flexible Thread in the Field of Horizontal and Vertical Forces
(Eastern-European Journal of Enterprise Technologies, 2024) Volina T.; Pylypaka S.; Nesvidomin V.; Kalenyk Mykhailo Viktorovych; Spirintsev D.; Dieniezhnikov Serhii Serhiiovych; Hryshchenko I.; Rebrii A.; Herashchenko T.; Soloshchenko Viktoriia Mykolaivna; Воліна Т.; Пилипака С.; Несвідомін В.; Каленик Михайло Вікторович; Спірінцев Д.; Дєнєжніков Сергій Сергійович; Грищенко І.; Ребрій А.; Геращенко Т.; Солощенко Вікторія Миколаївна
In theoretical mechanics, the equilibrium of a flexible, inextensible thread is considered, to which the tension force of its ends and the distributed force of weight along the length of its arc are applied. An unsolved problem is finding the shape of the thread under the action of other distributed forces. This study has considered the equilibrium of a completely flexible thread, to which, in addition to this force, a transverse distributed force is applied. A sail serves as an example. Wind of equal intensity in the plane of the orthogonal section of the sail can be considered a distributed force. The sail can be cut into narrow strips with the same shape of the curves of the cross-section, which are equal to the cross-section of the sail as a whole. The theory of flexible thread is applied in the current study. The task is reduced to finding the curve of the cross-section of the sail. The object of research is the formation of a cylindrical surface from a flexible thread under the action of distributed forces applied to it. An important characteristic of the shape of a flexible thread is its curvature. Its dependence on the length of the arc was found and it was established that the found curve is a chain line (catenary). This is the feature of the current research and its distinguishing characteristics. The significance of the results stems from the derived analytical dependences, according to which the change in the ratio between the distributed forces acting on the flexible thread deforms it, but it retains the shape of the catenary. At the same time, the angle of deviation of its axis of symmetry from the vertical changes. In the absence of a horizontal distributed force and the presence of only a distributed force of weight, the axis of symmetry of the chain line is directed vertically – at an angle of 90° to the horizontal. If they are equal, this angle is 45°. Scope of application includes structures with stretched supporting wires, conveyor belts, flexible suspended ceilings, the shape of which can be calculated by using our results.
Dynamic Mathematics Software as a Necessary Component of Modern-Math-Teachers Preparation in Ukraine
(2016) Semenikhina Olena Volodymyrivna; Семеніхіна Олена Володимирівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The article discusses the relevance of the study of dynamic Mathematics software by future math teachers in Ukraine. The focus is on the requirement, not only to know about specialized dynamic software, but also to be able to organize an effective learning process with its usage. The arguments for the organization of special courses in the study of dynamic Mathematics software are based on the need to demonstrate the skills of usage of modern Mathematics software. The authors describe their own experience of teaching the course at A. S. Makarenko Sumy State Pedagogical University (Ukraine), which is included in the curricula as variable course of math-teacher preparation, in particular, the successive changes of the content of the course, due to constant and rapid development of Information Technology, during all periods of learning.
Finite 2-Groups with a Non-Dedekind Non-Metacyclic Norm of Abelian Non-Cyclic Subgroups
(2019) Lyman Fedir Mykolaiovych; Лиман Федір Миколайович; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна; Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна
The authors study ﬁnite 2-groups with non-Dedekind non-metacyclic norm of Abelian non-cyclic subgroups depending on the cyclicness or the noncyclicness of the center of a group G. The norm is deﬁned as the intersection of the normalizers of Abelian non-cyclic subgroups of G. It is found out that such 2-groups are cyclic extensions of their norms of Abelian non-cyclic subgroups. Their structure is described.
Gamification in Developing Readiness for Self-Fulfillment in Students of Higher Educational Institutions
(2023) Tsurkan Liudmyla; Dubinka Mykola; Savchenko Nataliia; Slipchyshyn Lidiia; Kalenyk Mykhailo Viktorovych; Цуркан Людмила; Дубинка Микола; Савченко Наталія; Сліпчишин Лідія; Каленик Михайло Вікторович
The aim of the article is to study the peculiarities of the issue of gamification when developing readiness for self-fulfillment in students of higher educational institutions (HEIs) in the course of education. Methods. The research involved testing, factor analysis, and statistical data processing. The following research methods were used: the Ryff Scales of Psychological Well-Being (RPWB); the Personal Orientation Inventory (POI). Reliability of tools and methods was determined using Cronbach’s α. Statistical data were processed using Spearman’s correlation coefficient and Fisher’s test. Results. The following results were obtained during the research. The Self-acceptance Scale has the lowest arithmetic mean, which is also within the lower manifestation limit. There are no high indicators on this scale. The largest share of the sample — 61.25% — has a medium self-acceptance level, of which 32.5% are students of the experimental group (EG), and 28.75% are students of the control group (CG). Conclusions. Based on the obtained data, it is possible to unequivocally assert the effectiveness of gamification in developing students’ readiness for self-fulfillment. Prospects. It is necessary to continue the search for effective means of developing readiness for self-fulfillment in order to take into account the individual characteristics of each student. innovative education.
Generalized Norms of Groups
(2016) Drushliak Maryna Hryhorivna; Друшляк Марина Григорівна; Lukashova Tetiana Dmytrivna; Лукашова Тетяна Дмитрівна; Lyman Fedir Mykolaiovych; Лиман Федір Миколайович
In this survey paper the authors have tried to specify all the known results concerning the norms of the group and its generalizations. Special attention is paid to the analysis of their own research of different generalized norms, particularly the norm of non-cyclic subgroups, the norm of Abelian non-cyclic subgroups, the norm of infinite subgroups, the norm of infinite Abelian subgroups and the norm of other systems of Abelian subgroups.
Implementation of the Principle of Continuation of Physical Education in Primary and Primary Schools
(2021) Каленик Михайло Вікторович; Kalenyk Mykhailo Viktorovych
The curricula of the new Ukrainian school for grades 1-4, grades 5-6, physics programs for grades 7-11 and the content classification between subjects are analyzed. Appropriate methodological improvements are proposed to close the gap between primary and secondary education, in the context of studying certain physical concepts, by improving the adaptation of students in the transition from primary to primary school, in particular, in the transition from certain issues of mathematics, science and others to physics, where the implementation of subject competence. In view of this, it is suggested that primary and secondary school teachers, when studying the components of the content of the school course of physics, follow the generalized plans for their study, as in the school course of physics.
Incorporating the Basics of Nanoscale Science and Technology in the Cycle of Natural and Mathematical Sciences of Secondary School
(2015) Пасько Ольга Олександрівна; Pasko Olha Oleksandrivna
The fundamental aspect of research problem is teaching reorientation to the needs of society in nanotechnology. The author substantiated expediency of development of elective courses in nanotechnology and their implementation in the educational process of secondary school. It is directly related to the achieved level of informatization and computerization of education. Author propose to use of certain computer software for modeling and visualization of nano-objects.

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