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Platonic Solids
Polcarová, Markéta ; Kochánková, Jana (referee) ; Klodová, Lenka (advisor)
The work explores the possibilities of making monolithic shape of the objects and their transformation. The central theme is the geometry of the Platonic solids and the reproductive use of hot melt adhesive, which allows subsequent theme formation of objects due to its flexibility. In the process of creation occurs the transformation of geometric elements which looks like it has a visibly different shape but has same shape as the ideal spatial geometry of Platonic solids. Essential in this work is the action of gravity, which affects the possibilities of shaping the final objects.
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Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools
Dohnalová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.
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Secondary school polyhedrons with internet
Helm, Jan ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
The thesis is destined mainly for high school teachers and students of descriptive geometry. Above all it deals with the intersection and the construction of pyramids and prisms in projections. Students can meet with these phenomena at high schools during lessons of descriptive geometry. The constructions of the intersections of figures are demonstrated on solved tasks. The tasks are processed in graphic programmes GeoGebra and Cabri 3D prospering from the following advantages and facilities of these programmes: a stepping of the construction, a contour accentuation or a secretion of auxiliary lines etc. Besides these solved tasks, there are also some unsolved tasks for practice at the ends of chapters. The introductory chapter contains definitions and characters of common polyhedrons and regular (Platonic) figures. The thesis consists of web sites, a printed version and an enclosed printed version in .pdf format.
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Regular polyhedra and their properties
Pavlovičová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
This work is intended for all people from the general public especially for all people interested in regular polyhedra geometry. The work can be also used as didactic aid by education of regular polyhedra. It is an comprehensive text which summarizes description, history, classification of this five regular polyhedra. We will also focus on their properties and occurence. Basic calculations of surfaces, volumes and radii of the circles circumscribed and inscribed are in the work too. The text is supplemented with illustrative pictures made in GeoGebra and Cabri3D. Some chapters are supplemented with photos.
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Regular and semi-regular solids in higher dimensions
Pekař, Vojtěch ; Surynková, Petra (advisor) ; Hromadová, Jana (referee)
This thesis deals with multidimensional objects, which are known as Platonic and Archimedean solids in common euclidean space. Although we describe especially four-dimensional figures and their relations with lesser grade, this text is formulated in such a way, that includes even different dimensions, if it is possible in particular instances. There exist a few works about this and similar topics in foreign, but usually they require a little basics of algebra teaching at university. Our approach uses methods similar to these, which are normally teaching in descriptive geometry and therefore includes a large number of pictures. The matter is therefore available to secondary school students, who want to increase their space imagination.
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Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools
Dohnalová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
Title: Platonic and Archimedean solids and their properties in teaching of mathematics at secondary schools Author: Eva Dohnalová Department: Department of Didactics of Mathematics Supervisor: doc. RNDr. Jarmila Robová, CSc. Abstract: This work is an extension of my bachelor work and it is intended for all people interested in regular and semiregular polyhedra geometry. It is a comprehensive text which summarizes brief history, description and classification of regular and semiregular polyhedra. The work contains proofs of Descartes' and Euler's theorems and proofs about number of regular and semiregular polyhedra. It can be also used as a didactic aid in the instruction of regular and semiregular solids at secondary schools. This text is supplemented by illustrative pictures made in GeoGebra and Cabri3D. Keywords: Regular polyhedra, platonic solids, Platon, semiregular polyhedra, Archimedean solids, Archimedes, dulaism, Descartes' theorem, Euler's theorem.
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Regular polyhedra and their properties
Pavlovičová, Eva ; Robová, Jarmila (advisor) ; Halas, Zdeněk (referee)
This work is intended for all people from the general public especially for all people interested in regular polyhedra geometry. The work can be also used as didactic aid by education of regular polyhedra. It is an comprehensive text which summarizes description, history, classification of this five regular polyhedra. We will also focus on their properties and occurence. Basic calculations of surfaces, volumes and radii of the circles circumscribed and inscribed are in the work too. The text is supplemented with illustrative pictures made in GeoGebra and Cabri3D. Some chapters are supplemented with photos.
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Regular and semi-regular solids in higher dimensions
Pekař, Vojtěch ; Surynková, Petra (advisor) ; Hromadová, Jana (referee)
This thesis deals with multidimensional objects, which are known as Platonic and Archimedean solids in common euclidean space. Although we describe especially four-dimensional figures and their relations with lesser grade, this text is formulated in such a way, that includes even different dimensions, if it is possible in particular instances. There exist a few works about this and similar topics in foreign, but usually they require a little basics of algebra teaching at university. Our approach uses methods similar to these, which are normally teaching in descriptive geometry and therefore includes a large number of pictures. The matter is therefore available to secondary school students, who want to increase their space imagination.
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Secondary school polyhedrons with internet
Helm, Jan ; Hromadová, Jana (advisor) ; Šarounová, Alena (referee)
The thesis is destined mainly for high school teachers and students of descriptive geometry. Above all it deals with the intersection and the construction of pyramids and prisms in projections. Students can meet with these phenomena at high schools during lessons of descriptive geometry. The constructions of the intersections of figures are demonstrated on solved tasks. The tasks are processed in graphic programmes GeoGebra and Cabri 3D prospering from the following advantages and facilities of these programmes: a stepping of the construction, a contour accentuation or a secretion of auxiliary lines etc. Besides these solved tasks, there are also some unsolved tasks for practice at the ends of chapters. The introductory chapter contains definitions and characters of common polyhedrons and regular (Platonic) figures. The thesis consists of web sites, a printed version and an enclosed printed version in .pdf format.
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Geometry of Life-Supporting Forms in an Architectural Design
Volnohradský, Radan
Process of visual perception described in the first article is elaborately explored by neuroesthetic. It is a link to understand incoming images and reactions in brain. In this context it points out significance and beauty of fractal structures. Fractals and their use in urban design are content of next chapter. Than the focus is on explaining harmonic proportions (primarily Golden mean) and geometric forms which are mostly found in fractals. It is mentioned basic Pythagorean geometry with its metaphysical aspects. Same aspects are hidden in mysterious picture Flower of life and its geometrical transformation to Platonic solids - the matrix of universe. At the end the relation between geometry and architectural design is revealed and substantiated.
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