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- W2563514400 abstract "The circumcircles of the cyclic quadrilaterals in the family Q(Λ) of all quadrilaterals for which Λ is the median parallelogram osculate an octic curve, which is described. When Λ is a rhombus this curve reduces to a pair of double ellipses. In a previous paper [1] we showed that, given a parallelogram Λ = FGHI, there exists a doubly infinite family Q(Λ) of quadilaterals, namely all quadrilaterals having three (and therefore all four) of the vertices of Λ as the midpoints of its sides, taken in order; and within Q(Λ) there exists a singly infinite family of cyclic quadrilaterals, whose centres have as locus a rectangular hyperbola Cen(Λ) through the vertices of Λ (or an orthogonal line-pair, namely the diagonal lines, when Λ is a rhombus). We now wish to describe the curve Γ which these circumcircles osculate. Let C(Λ) denote the family of circumcircles." @default.
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- W2563514400 date "2008-01-01" @default.
- W2563514400 modified "2023-09-26" @default.
- W2563514400 title "Osculation by circumcircles of a pantograph" @default.
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