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Bridge across the I/11 road
Macák, Jan ; Šrubař, Jiří (referee) ; Panáček, Josef (advisor)
This diploma thesis deals with a project of a road bridge. The bridge is located on a second class road S 7.5/50 and goes over a I/11 road and a local road crossing in Bystřice. Three options of the road bridge are conceived out of which the connected beam girder is chosen for further development. A calculation of the structural stability of the load-bearing construction, that includes time analysis of the construction work (i.e. particular phases of the construction), is added to the project. The structural stability calculation is assessed in accordance with valid European standards. Drawing documentation, a time schedule and 3D visualization of the road bridge is also attached to the diploma thesis.
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Spatial generalizations of the properties of the triangle
Šrubař, Jiří ; Karger, Adolf (advisor) ; Boček, Leo (referee) ; Lávička, Miroslav (referee)
TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...
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Spatial generalizations of the properties of the triangle
Šrubař, Jiří
TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...
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Computer Representation of Surfaces
Chudáčková, Eliška ; Surynková, Petra (advisor) ; Šrubař, Jiří (referee)
In this work we first introduce the basics of surface study and than we get acquainted with three basic types of surfaces of computer graphics, Bézier, rational Bézier and B-spline surfaces. This is to prepare the reader for the study of the fourth type of surfaces - NURBS. All types of introduced surfaces are accompanied by examples and algorithms with programs implemented in MatLab environment. When studying the NURBS surfaces properties we also introduce the associated important geometric tools. With this base of knowledge we concentrate on examples of common surfaces represented as NURBS, that are again accompanied with representation in programs. i
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Spatial generalizations of the properties of the triangle
Šrubař, Jiří ; Karger, Adolf (advisor) ; Boček, Leo (referee) ; Lávička, Miroslav (referee)
TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...
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Spatial generalizations of the properties of the triangle
Šrubař, Jiří
TITLE Spatial generalizations of the properties of the triangle AUTHOR Jirˇı' Sřubarˇ SUPERVISOR Prof. RNDr. Adolf Karger, DrSc. DEPARTMENT Department of mathematics education ABSTRACT The present thesis describes various interesting properties of a triangle. The aim is to find and prove similar properties of its spatial generalization - a tetrahedron. Even though both synthetic and computational methods are used for proving spatial relations, synthetic approach is preferred whenever possible. The thesis is divided into two parts. In the first part, the properties of the tetrahedron analogous to the centroid and the orthocenter of the triangle are described. Also, conditions on the existence of the orthocenter of the tetrahedron are derived. Moreover, for tetrahedrons without an orthocenter, the so-called Monge point is introduced as its generalization. In the second part of the thesis, some further properties of the triangle are studied - - the Simson line, the de Longchamps point, the nine-point circle, the Euler line, the Lemoine point, the isodynamic points, the Lemoine axis and the Brocard axis. As the main contribution of the present thesis we define and prove the existence of spatial analogues of the above mentioned properties for the tetrahedron - the de Longchamps point, the twelve-point and...
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Bridge across the I/11 road
Macák, Jan ; Šrubař, Jiří (referee) ; Panáček, Josef (advisor)
This diploma thesis deals with a project of a road bridge. The bridge is located on a second class road S 7.5/50 and goes over a I/11 road and a local road crossing in Bystřice. Three options of the road bridge are conceived out of which the connected beam girder is chosen for further development. A calculation of the structural stability of the load-bearing construction, that includes time analysis of the construction work (i.e. particular phases of the construction), is added to the project. The structural stability calculation is assessed in accordance with valid European standards. Drawing documentation, a time schedule and 3D visualization of the road bridge is also attached to the diploma thesis.
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