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The article gives examples of construction tasks of first and second degree on a Euclidean plane, which can be solved with the use of a simple ruler. For this purpose, the theoretical backgrounds of projective geometry have been used. It has been proved that in the projective approach some constructions on a Euclidean plane become linear constructions. In particular, a linear construction of this type may be the typical operation of inversion in respect of a circle and an arbitrary conic as well...
In the article the errors in the solutions of geometry problems made by the candidates for the first year of the mathematical studies at the Pedagogical University of Cracow during the entrance examinations in 2003 and 2004 are analysed. Every geometry problem is provided with the examples of its solutions, and the detailed conclusions are drawn from the analysis. In the final part of the article a general didactic analysis of the errors is carried out as well as some aspects of teaching necessary...
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