Neste trabalho abordaremos alguns assuntos relacionados Ãs SeÃÃes CÃnicas: elipse, parÃbola e hipÃrbole. O trabalho està dividido em cinco capÃtulos: IntroduÃÃo; Origem das CÃnicas; EquaÃÃes das CÃnicas; Propriedades de ReflexÃo das CÃnicas; Construindo CÃnicas. No segundo capÃtulo, falaremos sobre o problema da duplicaÃÃo do cubo que, segundo a HistÃria da MatemÃtica, deu origem as cÃnicas e citaremos alguns matemÃticos cujos trabalhos contribuÃram para o desenvolvimento do estudo dessas curvas. No terceiro capÃtulo, estudaremos as equaÃÃes cartesianas das cÃnicas, bem como as suas representaÃÃes grÃficas e os principais elementos da cada cÃnica. No quarto capÃtulo, apresentaremos as propriedades de reflexÃo das cÃnicas e algumas aplicaÃÃes muito interessantes dessas propriedades. No Ãltimo capÃtulo, demonstraremos alguns mÃtodos para construir cÃnicas e em seguida faremos essas construÃÃes na prÃtica atravÃs de materiais concretos e por meio de um programa de Geometria DinÃmica, chamado Geogebra. / In this paper we discuss some issues related to Conic Sections: ellipse, parabola and hyperbole. The work is divided into five chapters: Introduction; Origin of Conic Sections; Equations of Conic Sections; Reflection Properties of Conic Sections; Building Conic Sections. In the second chapter, weâll talk about doubling the cube problem that, according to the History of Mathematics, originated the conic sections and talk about some mathematicians whose work contributed to the study of these curves. In the third chapter, we will study the Cartesian equations of conic sections, as well as their graphical representations and the main elements of each curve. In the fourth chapter, we presented the reflection properties of conic sections and some very interesting applications of these properties. In the last chapter, we will show some methods to construct conic sections and then we will make these constructs in practice through concrete materials and through a dynamic geometry program, called Geogebra.

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra

TITLE: Agebraic Curves in History and School AUTHOR: Bc. Tomáš Fabián DEPARTMENT: The Department of mathematics and teaching of mathematics SUPERVISOR: prof. RNDr. Ladislav Kvasz, Dr. ABSTRACT: The thesis includes a series of exercises for senior high school students and the first year of university students. In these exercises, students will increase their knowledge about conics, especially how to draw them. Furthermore, students can learn about two unfamiliar curves: Conchoid and Quadratrix. All these curves are afterwards used for solving other problems - some Apollonius's problems, Three impossible constructions etc. Most of the construction is done in GeoGebra software. All the tasks are designed for students to learn how to work with this software. The subject discussed is put into historical context, and therefore the exercises are provided with historical commentary. The thesis also includes didactic notes, important or interesting solutions of exercises, possible issues, mistakes and another relevant notes. KEYWORDS: conic, circle, ellipse, parabola, hyperbole, conchoid, quadratrix, trisecting an angle, squaring the circle, rectification of the circle, doubling a cube, Apollonius's problem, GeoGebra