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Descriptive Geometry Teaching in the Czech Lands
Moravcová, Vlasta ; Bečvář, Jindřich (advisor) ; Janyška, Josef (referee) ; Lávička, Miroslav (referee)
This thesis documents the history of descriptive geometry teaching in the Czech lands from its beginnings (i.e. from the 1830s) to the World War II. The center of the work is the description of development of descriptive geo- metry teaching at secondary schools, especially "Realschule�, supplemented with an analysis of Czech secondary school textbooks and a brief comparison between the situation in the Czech lands and foreign countries. Attention is also paid to the characterisation of descriptive geometry lectures at Czech and German polytechnics and universities in Prague, Brno and Příbram, inclusive of university textbooks. The work also mentions a brief global de- velopment of projection methods and a contribution of Czech geometers to the development of descriptive geometry. The thesis is supplemented with large factual and pictorial addenda.
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Synthetic projective geometry
Zamboj, Michal ; Krump, Lukáš (advisor) ; Janyška, Josef (referee) ; Velichová, Daniela (referee)
A synthetic approach to the construction of projective geometry, its methods and selected results are given in the proposed thesis. The main historical drawbacks of the original proof of Chasles's theorem for non-developable ruled surfaces and von Staudt's formalization of projective geometry are commented. The corre- sponding theoretical background is elaborated on visual demonstrations with the accent to interrelations of classical synthetic, axiomatic and analytic points of view. Synthetic methods of projective geometry and their mixture with analytic methods are described on examples including numerous alternative proofs and generalizations of some theorems. A method of four-dimensional visualization is introduced in details. Elementary constructions of images of points, lines, planes and 3-spaces are followed by models of polychora, their sections and shadows. Chasles's theorem is proven for non-developable ruled quadrics on synthetic vi- sualizations, then generalized and proven within the pure projective framework for algebraic surfaces. The synthetic classification of regular quadrics is derived from descriptive geometry constructions of sections of four-dimensional cones and analytically verified in the projective extension of the real space. An integral part of the thesis is a...
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Descriptive Geometry Teaching in the Czech Lands
Moravcová, Vlasta ; Bečvář, Jindřich (advisor) ; Janyška, Josef (referee) ; Lávička, Miroslav (referee)
This thesis documents the history of descriptive geometry teaching in the Czech lands from its beginnings (i.e. from the 1830s) to the World War II. The center of the work is the description of development of descriptive geo- metry teaching at secondary schools, especially "Realschule�, supplemented with an analysis of Czech secondary school textbooks and a brief comparison between the situation in the Czech lands and foreign countries. Attention is also paid to the characterisation of descriptive geometry lectures at Czech and German polytechnics and universities in Prague, Brno and Příbram, inclusive of university textbooks. The work also mentions a brief global de- velopment of projection methods and a contribution of Czech geometers to the development of descriptive geometry. The thesis is supplemented with large factual and pictorial addenda.
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