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Distance Product Cubics
2020
KoG
The locus of points that determine a constant product of their distances to the sides of a triangle is a cubic curve in the projectively closed Euclidean triangle plane. In this paper, algebraic and geometric properties of these distance product cubics shall be studied. These cubics span a pencil of cubics that contains only one rational and non-degenerate cubic curve which is known as the Bataille acnodal cubic determined by the product of the actual trilinear coordinates of the centroid of
doi:10.31896/k.24.3
fatcat:46akfkh6ijajza6nyxx5glorg4