|
|
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
|
|
|
Proofs of selected geometric constructions
Vaňková, Marie ; Zamboj, Michal (advisor) ; Jančařík, Antonín (referee)
This bachelor thesis is the summary of the chosen constructions used in descriptive and kinematic geometry. These constructions are always described in detail and proven. The first chapter is devoted to the very concept of curve and curvature. The second chapter is focused on conic sections, ie ellipses, hyperbolas and parabolas. These curves are defined, their main characteristics are described, and their equation is derived. Further o , the chapter contains of the various kinds of constructions of these curves. It is par- ticularly about point structures and structures using osculating circles. The third chapter deals with the cyclic curves, ie cycloid, epicycloid, hypocycloid, peri- cycloid and involute of a circle. For these curves, the motion by which they arise is defined, and the given curve's parametric expression is presented. The following is a description of the construction of this motion and proof that the points of this construction correspond to the parametric expression of the cyclic curve. Finally, the fourth chapter focuses on conchoids, which together with cyclic curves rank among the kinematic curves. Even here the motion by which conchoids are created is first introduced, the construction of this motion is described, and it is proved that the constructed points correspond to the...
|
|
|
Loci of given properties
DVOŘÁKOVÁ, Andrea
This bachelor thesis focuses on the description of the loci of given properties and its use in solving of the simple tasks in high schools. It is also focused on the analysis of more difficult problems related to the conic sections. These problems are solved in planimetric or analytic form. There is also a chapter dealing with the axial affinity. It extends the curriculum at high schools.
|
|
| |
|
|
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
|
guest ::
