A gallery of conics by five elements (Q2929580)
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scientific article; zbMATH DE number 6369206
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A gallery of conics by five elements |
scientific article; zbMATH DE number 6369206 |
Statements
13 November 2014
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geometry of conics
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involutory projectivity
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common harmonics of two pairs of collinear points
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pencil of conics
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range of conics
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quadratic transformation
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eleven point conic
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eleven tangent conic
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Desargues' theorem for pencils of conics
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Desargues' theorem for ranges of conics
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Plücker's theorem
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Pascal's theorem
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Brianchon's theorem
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A gallery of conics by five elements (English)
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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.NEWLINENEWLINEOccasionally the author leaves the frame of plane geometry and employs descriptive geometry when a task is solved by spacial interpretation.NEWLINENEWLINEThe reviewer considers the gallery to be incomplete because the determinations of conics by elements of osculation or hyperosculation are missing.
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