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1
Kompetencje geometryczne nauczycieli matematyki
100%
PL
Practice proves that students tend to face difficulties in learninggeometry. This observation is partially confirmed by the results of educationalresearch as well as external exams. It happens repeatedly that studentsget lower marks in arithmetic or algebra tasks. The causes of such situationare complex. One of the reasons is that teaching geometry requires specialteaching skills characteristic for this specific teaching branch as well as theneed for “specific vision”. Therefore, I decided to study the geometric skillsof mathematics teachers more carefully. For this purpose, I made use of tworesearch results: international research TEDS-M 2008 as well as nationwideresearch The research of needs the elementary education teachers as well asmathematics teachers have in the scope of their professional development.This article presents the results of the analysis together with my personalthoughts on education and improvement of teachers’ skills in the area of geometry.
2
A Renaissance mathematician’s art
85%
EN
Piero della Francesca is best known as a painter but he was also a mathematician. His treatise De prospectiva pingendi is a superb example of a union between the fne arts and mathemati‑ cal sciences of arithmetic and geometry. In this paper, I explain some reasons why his paint‑ ing is considered as a part of perspective and, therefore, can be identifed with a branch of geometry.
3
Fracture network modelling for shale rocks – a case study from the Baltic Basin
80%
EN
The discrete fracture network (DFN) approach offers many key advantages over conventional dual porosity approaches when the geometry and properties of discrete fractures play a significant role in geomechanics, and resource assessment (Dershowitz & Doe 1988). A comparison of the simulated data to real fractures observed on core samples increases confidence in the DFN approach. A DFN model typically combines deterministic and stochastic discrete fractures. The deterministic fractures are those directly imaged through seismic or intersected by wells. Other, usually smaller-scale fractures may not have been detected through seismic, yet may be very important for reservoir performance. These fractures are generated stochastically (Parney et al. 2000). The aim of this study is prediction of fracture properties for the Lower Palaeozoic shale rocks. The input data included seismic survey data, and well logs with FMI interpretation that were calibrated with measurements and observations on the cores to ensure accuracy in the estimates of fractures properties. This study was performed using Petrel software from Schlumberger. Typical workflows for modelling of oil and gas reservoirs were applied (e.g. Zakrevsky 2011). The result was a 3D fracture distribution model consisting of four zones. In each zone two generations of fractures were modelled based on well log data. Several seismic attributes were additionally considered as fracture density drivers for the spatial modelling. Finally, the ant tracking structural attribute was chosen as the best indicator of faults and fractures in a seismic cube. To improve the quality of the DFN model, should define the local stress distributions.
EN
Geometry has always contributed to a great extent and played a significant role in the development of many of the principles of the factor models. While factor-analytic principles and procedures have been generally developed by the heavy emphasis on matrix algebra, there is still a grave importance and need towards a geometrical approach and its application in the factor analysis. In this article the author provides, on selected issues, a description in reference to factor models from a geometric viewpoint with a discussion running through its advantages and disadvantages. Finally, at the end of the paper, conclusions in reference to good conditions of factors rotation are given. This article explains to what extent a geometrical approach brings specific value and offers an extra insight into factor analysis. As proved, geometry still provides an alternative framework which may be helpful for better understanding and data structure diagnosis.
EN
An important issue in construction of combustion chamber in compression-ignition engines is proper selection of its shape and size. Both features are dependent on several factors such as fuel injector location and angle, spray atomizer selection (amount of holes, their diameter and angular position), location of inlet valve and air turbulence. By doing research on prototype engine T370, an analysis of influence of combustion chamber size and its modifications going towards lip construction on flue gas toxicity was done. The diameter and depth of combustion chamber was being changed while maintaining the same compression ratio. After that, a modification of tested combustion chambers was made by creating so called “lip”, which aim was to create a swirl of injected fuel in the vertical plane. To visualize the changes in swirl, a numerical analysis of fuel injection into combustion chamber was made. In discussed study, emission tests were performed according to ECE-R49. During the research six combustion chambers with diameters 60, 63 and 66 mm (and their modification) were investigated. Tests were performed for several types of injectors and different injection timing. However, for analysis of combustion chamber size the results are presented for the same injectors but with optimized injection timing.
6
80%
EN
Although metamaterials and so-called left-handed media have originated from theoretical considerations, it is only by their practical fabrication and the measurement of their properties that they have gained credibility and can fulfil the potential of their predicted properties. In this review we consider some of the more generally applicable fabrication methods and changes in geometry as they have progressed, exhibiting resonant frequencies ranging from radio waves to the visible optical region.
EN
One of the main goals of mathematical education is to develop the skills for problem solving as well as skills that help carry out mathematical reasoning and argumentation.Geometric problems play here a special role. These require the person solving them to act with an inquiry attitude and a ‘specific vision’. The ‘specific vision’ is the ability one can manipulate with geometric objects in ones’ mind and perceive, separate and focus on the important information only. However, it is not enough to “see” it is also necessary to know how to interpret what is being seen. Although many researchers have dealt with the problem and many establishments have been made in this scope, the question of how to develop the skills of the “specific vision” stays still open.Herein article presents the research results which aimed at, among others, verification to what degree the combination of geometry problems formed into a bundle helps the secondary school students ‘notice’ and understand the presented situation and as a consequence to find the answer to few questions about this situation. We wanted to establish whether such an organised educational environment entails students natural thinking over the subsequent bundle of problems solved, or maybe makes them return to questions already solved, or by the usage of knowledge acquired helps students to find the problem solution for the next question or a correction for the committed mistakes. The analysis was based on some results coming from the survey School of Independent Thinking conducted by the Institute for Educational Research in 2011.
8
Dürer polyhedra: the dark side of melancholia
80%
EN
Dürer's engraving Melencolia I famously includes a perspective view of a solid polyhedral block of which the visible portion is an 8-circuit bounding a pentagon-triple+triangle patch. The polyhedron is usually taken to be a cube truncated on antipodal corners, but an infinity of others are compatible with the visible patch. Construction of all cubic polyhedra compatible with the visible portion (i.e., Dürer Polyhedra) is discussed, explicit graphs and symmetries are listed for small cases ( ≤ 18 vertices) and total counts are given for 10 ≤ vertices ≤ 26.
9
On the cohomology and geometry of principal sheeaves
80%
EN
We study the cohomological classification of principal sheaves, the latter being defined in a slightly different way than in [6], a fact allowing to consider on them geometrical objects like connections. The classification of vector sheaves (studied in [10]) is now a corollary of the classification of their principal sheaves of frames. In particular, principal sheaves with an abelian structural sheaf, equipped (the former) with a connection, admit a hypercohomological classification generalizing that of Maxwell fields given in [10].
10
Numerical comparison of two runners for gravitational vortex turbine
70%
EN
The main purpose of this study is to compare numerically the torque generated by two runners for a gravitational vortex turbine. One of the runners was an H-Darrieus turbine with the rotational flow into the chamber that helped to decrease its negative torque. The other runner was a standard (straight blade) turbine, which determined the performance in both cases. The study was conducted in ANSYSrCFX, where the model was configured at constant operating conditions in both cases. The standard runner performance was higher (75%) than that of the H-Darrieus runner. The highest torque for the standard and the H-Darrieus runners was 0.76 and 0.16 N m, respectively. The standard runner had a larger fluid contact area than the H-Darrieus runner, which extracted more energy.
EN
The paper analyzes, from the geometrical aspect, the quality of the new flux cored wire intended for cladding process in function of changes in cladding parameters such as welding speed, coefficient of thermal conductivity, power source setting, the length of projecting portion of the electrode. The results of bead geometry analysis allows to illustrate the nature of the impact of the examined input variables on parameters of generated surface. The most important parameters here are the depth of penetration and the height of clad. The experimental data were processed using the Plackett-Burman experiment, which describes the impact of technological parameters on the main parameters used during production of resisting panels. It shows mathematical relations describing correlations between the input parameters and the value of depth of penetration and hight of bead made by Flux Cored Arc Welding (FCAW).
EN
In the present study, plastic geoboards and accessories were created as geometry teaching tools for visually-impaired students, using 3D printing. Lines, shapes, and angles were illustrated by stretching rubber bands around rivet heads on a geoboard with square edge of 10 x 10 grid array and circular edge of 4-quadrant graph. The coordinate points of 2D geometry were explored by blind touch on braille scales and raised grid lines, while z-axis pillars were used for 3D geometry by connecting rubber bands to the plane. The experimental group revealed significantly more learning achievement than did the control group, and all participants agreed that the new geoboards enhanced the mental imagery and understanding of geometry.
13
On infinite partitions of lines and space
70%
Fundamenta Mathematicae
|
1997
|
tom 152
|
nr 1
75-95
EN
Given a partition P:L → ω of the lines in $ℝ^n$, n ≥ 2, into countably many pieces, we ask if it is possible to find a partition of the points, $Q:ℝ^n → ω$, so that each line meets at most m points of its color. Assuming Martin's Axiom, we show this is the case for m ≥ 3. We reduce the problem for m = 2 to a purely finitary geometry problem. Although we have established a very similar, but somewhat simpler, version of the geometry conjecture, we leave the general problem open. We consider also various generalizations of these results, including to higher dimension spaces and planes.
14
Anaximandrova geometrie
70%
EN
According to tradition Thales brought geometry to Greece from Miletus. Although discussion of the nature of Thales’ geometry has not arrived at a consensus, it seems that the theorems formulated were retrospectively applied in his concrete measurements. So far, however, we have no information about the geometry of Thales’ pupil and successor, Anaximander of Miletus. An exception is presented in the lexicon Suda which claims that Anaximander “in general showed the basics of geometry”. This lexicon at the same time states the points at which the employment of the geometry can be discerned. Most importantly, we have the question of the gnomon, with the help of which an order of measurement is realisable. Clear signs of the application of geometry are likewise shown by Anaximander’s whole conception of cosmology: the shape of the earth and its position at the centre of the universe, and the very description of the heavenly bodies. In addition one can discern geometry involved in the map of the world and the sphere. Thus, although Anaximander is not explicitly connected with geometry, extant texts demonstrate that he significantly exploited geometrical knowledge when he connected concrete observation with the geometrical organisation of the universe as a whole.
CS
Podle tradice přenesl geometrii do Řecka Thalés z Mílétu. Ačkoli v diskusích o povaze Thalétovy geometrie nepanuje konsensus, zdá se, že zformulované teorémy byly až dodatečně uplatněny na jeho konkrétní měření. Již o Thalétově „žákovi a nástupci“, Anaximandrovi z Mílétu, však nemáme žádné zprávy, které by se týkaly geometrie. Výjimku představuje lexikon Súda, který uvádí, že Anaximandros „vůbec ukázal základy geometrie“. Lexikon zároveň vyjmenovává momenty, v nichž může být užití geometrie spatřeno. V prvé řadě se jedná o gnómón, s jehož pomocí mohla být realizována řada měření. Zřejmé znaky uplatnění geometrie vykazuje též celá Anaximandrova koncepce kosmologie: tvar Země a její umístění ve středu univerza, i samotný popis nebeských těles. Podobně lze uplatnění geometrie spatřovat za mapou světa a sférou. Ačkoli tedy Anaximandros není explicitně s geometrií spojován, dochované texty ukazují, že její poznatky významně využil, když propojil konkrétní pozorování s geometrickým uspořádáním celého univerza.
EN
This study was designed to evaluate the effect of propellant formulation and geometry on the solid propellant grains internal ballistic performance using core, bates, rod and tubular and end-burn geometries. Response Surface Methodology (RSM) was used to analyze and optimize the effect of sucrose, potassium nitrate and carbon on the chamber pressure, temperature, thrust and specific impulse of the solid propellant grains through Central Composite Design (CCD) of the experiment. An increase in potassium nitrate increased the specific impulse while an increase in sucrose and carbon decreased specific impulse. The coefficient of determination (R2) for models of chamber pressure, temperature, thrust and specific impulse in terms of composition and geometry were 0.9737, 0.9984, 0.9745 and 0.9589, respectively. The optimum specific impulse of 127.89 s, pressure (462201 Pa), temperature (1618.3 K) and thrust (834.83 N) were obtained using 0.584 kg of sucrose, 1.364 kg of potassium nitrate and 0.052 kg of carbon as well as bate geometry. There was no significant difference between the calculated and experimented ballistic properties at p < 0.05. The bate grain geometry is more efficient for minimizing the oscillatory pressure in the combustion chamber.
EN
There are so many possibilities to the metric continuum from the Geometry to the Mathematical Analysis, with by the way the historical formulation from Pythagoras to Cantor or Dedekind to make up a new continuum’s theory. On this article I refer the possibilities to carry out where is a philosophical foundation to continuum that is a metric property of number, and the geometric space. Meanwhile, finally I propose to determine the philosophical foundations, gnoseological, and ontological to the continuum.
17
Kopuły i ich geometria
70%
EN
This article is focused on design of traditional historical domes. Outstanding works of architecture such as: the dome of Hagia Sophia, dome of the dome of the rock mosque, the dome of Florence Cathedral, the dome of Basil's Cathedral in Moscow, as well as less famous – Greek-Catholic Church of St. Michael the Archangel in Krowica Sama have been analyzed. According to the criterion of geometrical complexity we created the table in which the individual structures were systematized. The table also includes information on historical period, building materials, technology and dimensions for all examples. The paper aims to summarize the changes that took place in terms of how to construct and demonstrate the appropriateness of use of this type of solution, which led to the conclusion that each of new solutions is based on already existing one.
EN
This article present selected issued of the analysis of the computer modelling of the tiller’s sprocket with the Solid Edge ST software. The geometry presented in the article was prepared so that they may be used to perform simulation presenting the influence of the loads generated by the ground work on the distribution and values of the stress forces within the tiller’s sprocket - Finished Element Method. The analysis covered the sprockets subjected to the forces of: 200N, 400N, 600N, 800N and 1000N. Geometric models were developed based on the available catalogue materials and the Polish Standard PN+92/R-58051-1. The FEM analyses performed allowed suggesting solutions to optimise the whole geometry in terms of the strengths.
19
Geometry and inertia of the human body - review of research
70%
EN
The paper is devoted to such morphological quantities of the human body as (1) geometric, i.e., linear, planar, and spatial;(2) inertial, especially - mass, density, radius of center of mass, moment of inertia and its radius. Description of quantities was given, material used (live subjects, cadavers, models), and methods utilized: mechanical and electromechanical, optical, geometric (for inertia quantities), penetrating, calculation, modelling. The most important results were given, especially for inertial quantities.
20
70%
EN
The aim of this research was to show superiority of using real geometries in simulations of blood fl ow through cardiovascular system. Our model compared blood fl ow through an abdominal part of aorta reconstructed with a use of data from an AngioTK research with the 3DDoctor software to geometries with the same diameters at inlet and outlet as mention before but created only with the Gambit 2.2.30 software without data from AngioTK. Blood fl ow simulations were prepared with the Fluent 6.2.16 software. Calculations of fl ow through a real geometry allows to obtain realistic results of values connected with process of blood fl ow. Results showed that calculations blood fl ow through a virtual geometry lasted two times longer than for a real geometry. Mesh for a real geometry consist about 600.000 elements and for a virtual geometry about 900.000 elements. Wall shear stress and blood velocity was higher for a real geometry and closer to that in human organism. It was shown that calculating a virtual geometry vessel was to big simplifi cation when investigating blood fl ow through a vessel. Application of mathematical models based on real geometries gives more realistic results than artifi cial geometries. Virtual models have lots of simplifi cations which results are far away from expectations. Simplifi cations depend on the model that is used.
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