The idea of an angle has several meanings at school mathematics. We propose the survey of different understandings of this notion with respect to the age of pupils, the level of school. We discuss the difficulties in defining and understanding of the notion of an angle. Of course, we discuss the topic with respect to Polish programmes of school mathematics.
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It is shown that the identity component of the group of al compac tly suported C infinity -diffeomorphisms of a manifold with corners is perfect provided the manifold has no vertices. An analogous result for Cr -diffeomorphism still holds whenever r > n+1, wheren is the dimension of the manifold. These results constiute a generalization of a well-known theorem by Thurston and Mather on the simplicity of diffeomorphism groups of boundaryless manifolds.
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