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A gallery of conics by five elements. (English) Zbl 1305.51015

This paper addresses the beginner in constructive geometry of conics in the projectively extended real affine plane; the author offers an extensive training in dealing with infinite elements and with duality. The main task says: A conic \(c\) is given by five points in general position; construct a further point of the conic (is done via Pascal’s theorem). The author discusses all further eleven (not necessarily unique) determinations of a conic by points and tangents using well-known theorems which are listed above as keywords.
Occasionally the author leaves the frame of plane geometry and employs descriptive geometry when a task is solved by spacial interpretation.
The reviewer considers the gallery to be incomplete because the determinations of conics by elements of osculation or hyperosculation are missing.

MSC:

51M15 Geometric constructions in real or complex geometry
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