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Conic sections as intersections of the cutting plane with the surface of a double cone
Košťáková, Sára ; Halas, Zdeněk (advisor) ; Moravcová, Vlasta (referee)
1 Abstract This bachelor thesis points out several blank spaces in the current tea- ching of conic sections. It concentrates mainly on the relation between the cutting of a conic surface and conic sections defined planimetrocally. Further on the thesis describes the origin of names for conic sections and adds many interesting details, like a cut of a cone by Dürer, relationship between an elliptical cut of a cylindrical surface and a sinusoid, and pointing out seve- ral chosen basic application of conic sections. A huge part of the thesis is dedicated to the characterization of specific uses of conic sections in archi- tecture and, mainly, in painting, and describing geometric reconstructions and analysis of specific art pieces with further commentary. 1
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Algebraic Curves in History and School
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Jančařík, Antonín (referee)
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
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Algebraic curves in history and school
Fabián, Tomáš ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
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
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System for support of conic sections teaching
Hejlová, Eliška ; Surynková, Petra (advisor) ; Karger, Adolf (referee)
The work presents own software for geometric drawing aimed to construction of conic sections. It's designed for high school students and their teachers, to use in lessons of descriptive geometry and mathematics. It contains a number of exercises with solutions which are prepared to solve in the program. Next part of this work is a theory about conic sections. We show various definitions, constructions and some basic properties. We also show a construction and properties of tangent in the point of conic section. Theory is supplemented by animations and pictures made in program GeoGebra. There are also proofs of equivalence of presented definitions. 1
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Geometry in architecture
BÁRTOVÁ, Michaela
The reader will understand the relationship between geometry and everyday life. Selected curves and bodyes are mathematically described. It is illustrated with photos of architectural elements. 3D models are made in GeoGebra and SketchUp. Blending theory and practice to help understand the geometry. It can be used for teaching math and geometry. This thesis discusses about the conic, selected technical curves and quardics.
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Collection of examples on the topic of conics
HRONOVÁ, Žaneta
Diploma thesis deals especially with practical examples on the topic of conics. It is divided into two parts. The first part includes chapters with examples on the topics discussed in the course Geometry I. In the second part affine properties of conics, which can be used in construction tasks, Pascal's theorem and Brianchon's theorem and their use are mentioned. The aim of this thesis is to ilustrate the conics on typical examples for those interested and then to show them the interesting properties, for which there is no space in the course Geometry I.
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The use of dynamic geometry software to determine conics and other curves around us.
TEN HAGEN, Libor
This bachelor thesis concerns conics and their occurrence in the world around us. The aim is to point out the connection between geometry and everyday live, between theory and practical use of conics. The first part deals with conics, their equations and constructions. Some pictures made in software GeoGebra are given as well. Second part deals with basic information of constructions of bridges and describes their properties. The third part contains photographs of conics. Most of photographs depict bridges, which are analyzed in the software GeoGebra. Every photographed object is shortly described.
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