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Kurzovní přednáška z geometrie pro navazující magisterské učitelské studium (konstruovatelnost pravítkem a kružítkem,
klasifikace geometrií). Propojení geometrických témat se školskou matematikou (hlubší pohled na skalární součin a na
základy školské geometrie).
Last update: Robová Jarmila, doc. RNDr., CSc. (04.06.2020)
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Basic literature:
Dlab V., Bečvář J.: Od aritmetiky k abstraktní algebře. Serifa, Praha, 2016.
Greenberg M. J.: Euclidean and Non-Euclidean Geometries: Development and History. 4rd ed. W. H. Freeman, 2007.
Stillwell J.: The Four Pillars of Geometry. Springer, 2010.
Additional literature:
Tignol J.-P.: Galois' Theory of Algebraic Equations. World Scientific Publishing, Singapore, 2001.
Wolfe H. E.: Introduction to Non-Euclidean Geometry. Dover Publications; Reprint 2012.
Stanovský D.: Základy algebry. Matfyzpress, Praha, 2010. Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (04.06.2020)
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Constructability with a ruler and compass
Constructible points and numbers. Duplication of a cube, trisection of an angle, quadrature of a circle. Constructability of regular polygons.
Classification of geometries
Fundamentals of Euclidean geometry, absolute geometry, pangeometry. Non-Euclidean geometries and their models.
Klein's Erlangen program, classification of geometries.
Riemannian classification of geometries, connection with differential geometry, significance of scalar product in geometry and in school mathematics. Last update: Halas Zdeněk, Mgr., DiS., Ph.D. (04.06.2020)
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