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The paper considers a pencil of conics, which basis is formed in such a way that three fundamental points coincide. By means of projective connections the following theorem has been proved: “if the basis of a pencil of conics includes three coinciding, fundamental points, e. g., A=B=C, and a different from them point D, then the range of points with a basis q passing through A=B=C has such a property,...
The two-semester division of an academic year was reintroduced in the academic year 1997/98 at all faculties of Politechnika Świętokrzyska (Holy Cross Polytechnic) after a four-year-long experiment consisting in a trimestrial system of the first-year student education. This was the reason why the author taught the first-semester students at the Faculty of Civil Engineering basics of descriptive geometry...
The paper contains author's reflections on introduclng new subjea "Elements of applied computer graphic", taught with an aid of the Corel program. The problems tackled in the paper include selecting a topic, establishing asyllabus of the course, and doing exercises. The works made by students are included as example
In this work the topology of networks is presented of chosen polyhedrons generated by transformations from icosahedron. Thę ideas of the polyhedron and spherical network are introduced interchangeably because of the identity of polyhedron vertices and truss joints of the spherical network. Each of obtained networks is treated as a full one-layer structure. Then two one-layer networks are placed and...
This paper quotes author's definitions [1] and illustrates them with some drawings. Variability intervals for radii and centres of generalised foci and variability intervals for generalis.d di.".trices are given for two sets F and G of these concepts introduced for an łtp,. and a hyperbola and for its set F for a parabola The sets are divided into five and four subsets, respectively, according...
The aim of this paper is to prove, by means ofa computer demonstration, the possibility ofusing AutoCad in lectures on topographic projection' namely in the pań related to topographic surface (PT). In order to illustrate a proposed adaptation the following examples of operations on PT have been selected: a profile, characteristic points, lines and shapes ofPT, lines and surfaces resulting from operations...
The paper contains a short review of Internet pages devoted to descriptive geometry and pays attention to Internet’s innate educational possibilities. Addresses relevant to pages concerning descriptive geometry courses, sets of exercises, virtual models of geometrical objects written in VRML, and geometrical Java applets have been listed and shortly characterised
In the article the possibility of 3D modelling in AutoCAD has been used to present plane sections and intersections of some polyhedra and surfaces. Several computer demonstrations in which slides are used have been described. The demonstrations have been divided into three parts: plane sections of surfaces, intersections of two surfaces and intersection of a polyhedron and a surface. Altogether seven...
The computer program OBIEKT 1.4 (Object 1.4) is a new version of this program. The previous version (l 2) was presented in the paper [5]. In the actual version, the program was modernized specially in modeling of surfaces. There are three individual types of basic surfaces defined in the program: the surface type A, type.B, type C (fig. 2). On the base of these basic surfaces is possible to prepare...
The teaching process of the geometrical bases of descriptive representations conducted (within the studying courses) in high technical schools in very many cases has been strongly restrained nowadays. People specifying the contents of the teaching syllabuses claim that in the age of a wide application of computer graphic programs conscious following of geometrical rules, which control the engineering...
Using the classic construction of a parabola’s tangent some properties of a conics streak and pencil are proved. These properties as a theorem in a more general case were published in the paper [1].The possibility of utilizing the theorem to construct the tangents and points of tangency to ellipse defined by the conjugated diameters and to hyperbola defined by its asymptotes is shown.
The subject of this work is determining optional number of points, the center and missing asymptote of hyperbola defined by three optional points and one asymptote. Presented problem is solved by two methods: the first one – based on using parallel chords determined according to Pascal theorem, and the second one issued from known construction of points of hyperbola defined by asymptotes and one point.
The paper introduces selected problems connected with creating and applying virtual models in teaching geometry. Advantages of VRNL language as a basic tool for constru
The authors present the needfull contents of the informatic education in the engineering departments. There are four subject groups considered: 1. operation and net systems; 2. application programmes; 3. computer graphics; 4. computer design and simulation systems.
One of many constructions of the tangent and point of tangents to ellipse is considered. The correctness of the presented constructions is proved by means Pascal’s theor
One of the important theorems concerning a bundle of conics is the one recognized as Weyer's theorem, or a generalized second Desargues' theorem [ 1 ]. The theorem may be expressed as follows. Weyer's Theorem. If a bundle of conics p2~,~, N (a2 , b2 , c 2 , .....) with four base points I, II, III and IV will be intersected with a conic k2 which does not belong to the given bundle, but which passes...
The author provides an overview of different methods applied by engineers to solve certain design problems. Manual and CAM methods have been introduced based on a problem of mutually tangent spheres. Pro/Engineering tool and its features have been described in the paper. Visual science theory introduced by G. Bertoline 12) has been investigated in context of both linguistics problems of the term translation...
The authors present, in the general way, their opinion about description graphical pages by using HTML and Yava languages and creating integrated.graphical date base
The name of Amadée François Frezier, French engineer, soldier and sailor, undoubtedly has been forgotten throughout passing centuries. If only he is mentioned today it is due to his sea expeditions. He was active in the decades of Luis XIV and Luis XV reign. He was a typical Renaissance individual gifted with lots of talents and abilities. His credits for development of descriptive geometry and its...
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