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Last update: RNDr. Jakub Staněk, Ph.D. (10.07.2020)
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Last update: Mgr. Lukáš Krump, Ph.D. (16.10.2023)
The credit is for continuous activity in the exercises, with the fact that they are not strictly distinguished exercises and lectures - we have them as needed. Activity on exercises can be either on-site or based on home preparation. In case of insufficient activity or greater absence, homework will be given as compensation. |
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Last update: RNDr. Jakub Staněk, Ph.D. (10.07.2020)
Richter-Gebert, J.: Perspectives on projective geometry: a guided tour through real and complex geometry, Springer 2011
Hlavatý, V., Projektivní geometrie I. Praha, Melantrich, 1944.
Havlíček, K.: Úvod do projektivní geometrie kuželoseček. Praha, SNTL, 1956. |
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Last update: RNDr. Jakub Staněk, Ph.D. (10.07.2020)
Projective line and plane, geometric point, homogeneous coordinates, projective extension of the affine line, affine plane, proper and improper points. Cross ratio, harmonic quadruple. Projectivity on the line, in the plane. The duality principle.
Projectivity and perspectivity of linear systems. Constructions of projectivities, perspectivities, direction line, direction point, Pappos theorem. Fixed points of a projectivity on a line. Involution. Complete quadripoint, quadrilateral.
Projective construction of conics. Construction of a tangent line, of tangent points. Construction of a projetivity on a conic. Involution on a conic.
Affine classification of regular conics, special constructions for hyperbola, parabola, ellipse. Perpendicularity, circle, constructions with an auxiliary circle.
Pascal and Brianchon theorems.
Pole and polar, conjugated poles and polars. Conjugated diameteres, foci. |