|
|
Circle inverse and its utilization
Vach, Petr ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
The objective of this paper is to make reader acquainted with the depiction known as ring inversion. A definition of the depiction set forth in the introduction and a subsequent description including proofs of all characteristics of this depiction in two planes, namely a synthetic and an analytic plane with a complex variable, shall enable a reader to solve problems and tasks which are contained in the second part of this paper. The aim of this work is to familiarize a reader with the ring inversion in such a degree so that he will understand all of the characteristics and will be able to make use of this knowledge not only to solve theoretical problems but also in practice.
|
|
|
Mappings in geometry
Trkovská, Dana ; Kubát, Václav (advisor)
This diploma dissertation is dedicated to applications of geometrical mappings. It is intended as a tuitional material specially for students of the third year of the mathematics teachers programm at Mathematical and Physical faculty of Charles University in Prague. The text can be used as a supplementary material for a seminar at secondary school as well. It is based on lectures of the course Geometry II. Students are familiar with the term mapping already during the lessons at elementary and secondary schools. Therefore in the diploma dissertation we at first give only a summary of basic knowledge about mappings in geometry, in the language of mathematics textbooks. Next part of this thesis includes theoretical knowledge about mappings in geometry in the form of definitions and propositions together with their proofs. A great part is dedicated to characterization of affine mappings, specially isometries and similarities. At the end circular inversion is explained as an example of a mapping that is not affine. For better imagination the whole text is complemented with a number of figures. Theoretical part is followed by a collection of exercises. Of course, solutions of all exercises are given.
|
|
|
Kruhová inverze a její aplikace v geometrii
LÁLOVÁ, Eva
This thesis deals with the study of the circular inversion. In the first chapter we introduce the circular inversion and examine it predominantly from the construction point of view. In the second and third chapters we discuss the circular inversion mainly from the point of view of the analytical description. In the fourth chapter we study the characteristics of the circular inversion and its relation to the delineations as portrayed in high schools. The fifth and the sixth chapters contain examples of the use of the circular inversion and other delineations in the plane. We solve some of the Apollonius' problems and problems in limited picture plane.
|
|
|
Mappings in geometry
Trkovská, Dana ; Kubát, Václav (advisor)
This diploma dissertation is dedicated to applications of geometrical mappings. It is intended as a tuitional material specially for students of the third year of the mathematics teachers programm at Mathematical and Physical faculty of Charles University in Prague. The text can be used as a supplementary material for a seminar at secondary school as well. It is based on lectures of the course Geometry II. Students are familiar with the term mapping already during the lessons at elementary and secondary schools. Therefore in the diploma dissertation we at first give only a summary of basic knowledge about mappings in geometry, in the language of mathematics textbooks. Next part of this thesis includes theoretical knowledge about mappings in geometry in the form of definitions and propositions together with their proofs. A great part is dedicated to characterization of affine mappings, specially isometries and similarities. At the end circular inversion is explained as an example of a mapping that is not affine. For better imagination the whole text is complemented with a number of figures. Theoretical part is followed by a collection of exercises. Of course, solutions of all exercises are given.
|
|
|
Circle inverse and its utilization
Vach, Petr ; Zhouf, Jaroslav (advisor) ; Dvořák, Petr (referee)
The objective of this paper is to make reader acquainted with the depiction known as ring inversion. A definition of the depiction set forth in the introduction and a subsequent description including proofs of all characteristics of this depiction in two planes, namely a synthetic and an analytic plane with a complex variable, shall enable a reader to solve problems and tasks which are contained in the second part of this paper. The aim of this work is to familiarize a reader with the ring inversion in such a degree so that he will understand all of the characteristics and will be able to make use of this knowledge not only to solve theoretical problems but also in practice.
|
guest ::
