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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 23, No. 1, pp. 55-63 (2007)
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On the fixed point of a collineation of the real projective plane

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István Krisztin Német

University of Szeged, Szeged

**Abstract:** Using the "extended Euclidean plane" model we prove the existence of the fixed point of a collineation of the real projective plane. At first we obtain the collineation as a product of a reflection in a line, a reflection in a point and a central-axial collineation. Then we prove the existence of the fixed point of the product of the second and the third mappings, and also that it is possible to choose the center of the second one so that this fixed point will lie on the axis of the first one. We examine the locus of the mentioned fixed point, too.

**Keywords:** Real projective plane-geometry, fixed point of a collineation.

**Classification (MSC2000):** 51M04; 51N20, 51A05

**Full text of the article:**

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