Problem-posing is recognized as an important component in the nature of mathematical thinking (Kilpatrick, 1987). More recently, there is an increased emphasis on giving students opportunities with problem posing in mathematics classroom (English& Grove, 1998). These research has shown that instructional activities as having students generate problems as a means of improving ability of problem solving and their attitude toward mathematics (Winograd, 1991). In this study, teaching Taxicab Geometry which is a non-Euclidean geometry is aimed to mathematics teacher candidates by means of computer game-Simcity- using real life problems posing. This studies’ participants are forty mathematics teacher candidates taking geometry course. Because of using Simcity computer game, this game is based on Taxicab Geometry. Firstly, students had been given Taxicab geometry theory for two weeks and then seperated six each of groups. Each of groups is wanted to posing problem and solving from real life problems at Taxicab geometry. In addition to, students applied to problem solving at Simcity computer game. Studens were model into Simcity game. They founded ideal city, healty village, university campus, holiday village, etc. interesting of each others.

We prove a strict positivstellensatz for Weyl algebra elements fulfilling an additional, asymptotic strict positivity condition. As a tool we develop a non-commutative analogue to the Newton polytope.

An aim of this diploma thesis is to create interactive descriptive geometry coursebook. As a basis for coursebook creation was used "Present State of Descriptive Geometry Education on High Schools Survey" which was proceeded via questionnaire. Before the creation of coursebook itself were made analyses of accessible textbooks, geometric softwares in use and possible environments for coursebook content presentation. A result is integrated part of subject matter taught on high schools complemented by solved examples and interactive applets created in software GeoGebra. The coursebook content is presented in a form of HTML sites on a public website http://www.sadsam.cz/dg/ and also as an off- line version on DVD disc enclosed.

The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.

We introduce the definition of 1-cotilting object in a Grothendieck category and investigate its relation to the analogue of the standard definition of 1-cotilting module. The 1-cotilting quasi-coherent sheaves on a Noetherian scheme are stud- ied in particular: using the classification of hereditary torsion pairs in the category of quasi-coherent sheaves on a Noetherian scheme X, to each hereditary torsion- free class F that is generating we assign a 1-cotilting quasi-coherent sheaf whose 1-cotilting class is F. This provides a family of pairwise non-equivalent 1-cotilting quasi-coherent sheaves which are parametrized by specialization closed subsets of X avoiding the set of associated points of a chosen generator of the category of quasi-coherent sheaves. In many cases (e.g. for separated schemes), this set of avoided points can be chosen as the set of associated points of the scheme. 1

Diplomová práce se zabývá využitím programu GeoGebra ve výuce ma- tematiky, konkrétně v tématu konstrukce trojúhelník·. Cílem práce bylo na- vrhnout přípravu na hodiny výuky konstrukce trojúhelník· s využitím pro- gramu GeoGebra a následně ověřit, zda využití softwaru dynamické geometrie mělo vliv na zvládnutí nového učiva. Teoretická část obsahuje použité pojmy z planimetrie. V dalších dvou kapitolách se čtenář seznámí s programem GeoGebra a GeoTest a některými výzkumy, které jsou zaměřené na použití program· dynamické geometrie ve výuce matematiky. Následuje kapitola se- znamující s úlohami, které jsou v experimentu využity, a popisuje přípravu jednotlivých hodin. Poslední část je věnovaná pr·běhu experimentu, srovnání výsledk· žák· pomocí test· s kontrolní třídou. Získaná data jsou zpracována na základě pozorování a test·. Výsledky pozorování a analýzy potvrzují, že GeoGebra je vhodným doplňkem výuky konstrukce trojúhelník·. 1

The aim of this work is to introduce and assess the potential of using GeoGebra software on multiple levels of mathematical education process and to analyze the expectation of pupils and students using this program. A reader is introduced to GeoGebra program itself and to various researches and articles sharing this common topic - usage of dynamic geometry educational programs and GeoGebra in mathematical education. This work is supported by two field researches that were carried out at the second stage of an elementary school and by another reseach made with students of mathematical education at the Charles University, the Faculty of Education. Next part of this work presents and covers more possibilities of using this program in the educational process of the second stage of elementary schools, and it also shows various options the program offers not just for teaching of mathematics, but also for other fields.

The following text attempts to rethink the challenge of Edmund Husserl in his text On the Origin of Geometry. Interpretation of fundamental ontology developed by Martin Heidegger in Being and Time provides field on which it is possible to try to answer the question of the origin of geometry. It is conceived as a completely unique ontological possibility that nature is able to vouch for an explanation of the geometry.

This work is a collection of solved problems in descriptive geometry, supplemented by elementary theory needed for their solution. The theory includes definitions and elementary properties of polygons and their constructions. Theory about solids, mostly prisms and pyramids, is also included. The second chapter introduces theory of projection, including definitions of projection methods (Monge, center, etc.) and corresponding terms. The second part contains a collection of problems, where each problem is solved in four projection methods (there are problems of construction of a point, line, plane, prism and pyramid). For each problem there is an animation for Lisa Viewer program attached, which makes an integral part of the work. These animations allow to look at figures of the problems interactively and even in three dimensions. There is also a PDF document with problem assignment and solution for each problem, suitable for print. Powered by TCPDF (www.tcpdf.org)

Most current algorithms typically lack in robustness to noise or do not handle T-shaped curve joining properly. There is a challenge to not only detect features in the noisy 3D-data obtained from the digital scanners. Moreover, most of the algorithms even when they are robust to noise, they lose the feature information near the T-shaped junctions as the triplet of lines ``confuses'' the algorithm so it treats it as a plane. Powered by TCPDF (www.tcpdf.org)