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Last update: ZHOUF/PEDF.CUNI.CZ (21.02.2009)
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Last update: ZHOUF/PEDF.CUNI.CZ (21.02.2009)
The goal is to introduce the basic notions and problems of plane geometry. The course aims at systematization and development of secondary school knowledge. It helps the students understand the connection of geometry and real world more deeply. |
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Last update: Mgr. Marie Holíková, Ph.D. (03.10.2017)
BOČEK, L., ZHOUF, J.: Planimetrie. Praha : PedF UK 2009. ISBN 978-80-7290-594-2 POMYKALOVÁ, E.: Planimetrie. Matematika pro gymnázia. Praha : Prometheus 2005. ISBN 978-80-7196-358-5 KUŘINA, F. Umění vidět v matematice. SPN, 1990, ISBN 80-04-23753-3 KUŘINA, F.: 10 geometrických transformací. Praha : Prometheus 2002. ISBN 80-7196-231-7 KUŘINA, F. 10 pohledů na geometrii. Praha: Matematický ústav AV ČR, 1996, 249 s. ISBN 80-85823-21-7 SEKANINA, M., Geometrie. 1,2. Praha: SPN, 1988 |
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Last update: ZHOUF/PEDF.CUNI.CZ (21.02.2009)
Lecture and seminars. |
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Last update: Mgr. Marie Holíková, Ph.D. (03.10.2017)
Podmínky k udělení zápočtu: |
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Last update: ZHOUF/PEDF.CUNI.CZ (21.02.2009)
Triangles. Quadrilaterals. Cyclic and tangential quadrilaterals. Circle. Circle power. Radical line. Euclidan constructions. Constructions using other tools. Sets of points of given properties. Definition and basic properties of geometric congruences in plane. Composition of geometric congruences. Classification of geometric congruences in plane. Direct and indirect geometric congruences. Group of geometric congruences. Definition and basic properties of homothecy. Similitude ration and its properties. Composition of homothecies. Monge's theorem. Circle in homothecy. Group of homothecies. Definition and basic properties of similarity. Decomposition of direct and indirect similarity (processes of construction). Similarity invariants (processes of construction). Classification of similarities in plane. Menelaos' and Ceva's theorem. Pappus's theorem. Double similitude ratio and its properties. Circle inversion (basic properties Apollonius' problems). Principles of axiomatic system conception of geometry. |