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Lecturer(s)
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Jukl Marek, doc. RNDr. Ph.D.
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Chodorová Marie, RNDr. Ph.D.
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Course content
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1. Projective characteristics of conic sections: Projective definition of conic sections, regular and singular conic sections. Dividing ratio of tetra points and tangents on conic sections. Points of intersection of lines and conic sections. Tangents from a point to a conic section. The Pascal theorem and its application in problem solving. The Brianchon theorem and its application. Involution on conic sections. Axis of an involution, center of an involution. Application in problem solving. Polar characteristics of conic sections. Construction based on polarity. Bunch and series conic sections. The Desargues involution. Constructional usage of the Desargues theorem. 2. Affine characteristics of conic sections: Affine classification of regular conic sections. Centers and asymptotes of conic sections. Construction of asymptotes. Diameters of conic sections. Conjugate averages of median conic sections. Conjugate direction to the direction of parabola diameter. 3. Metric characteristics of conic sections: Axes of conic sections. Construction of axes of median conic sections. Construction of parabola axes. Apexes, vertical tangents. Focal characteristics of conic sections. Focus, directrix.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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To master solving the construction of conic section from elemnts on the base of projective and affine characteristic.
3. Application Students apply knowledge of projective, affine and metric characteristic of conic sections.
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Prerequisites
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unspecified
KAG/GPGE2
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Assessment methods and criteria
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Oral exam, Written exam
Credit: active participation in seminars. Exam: the student has to understand the subject and be able to solve assigned problems.
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Recommended literature
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Bureš, Burešová. (1983). Projektivní geometrie I. SPN Praha.
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Havlíček K. (1956). Úvod do projektivní geometrie kuželoseček. SNTL Praha.
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Chodorová M. (2013). Projektivní geometrie. VUP Olomouc.
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