Geometrical properties of some Euler and circular cubics. II (Q1581000)

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scientific article; zbMATH DE number 1507995
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Geometrical properties of some Euler and circular cubics. II
scientific article; zbMATH DE number 1507995

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    Geometrical properties of some Euler and circular cubics. II (English)
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    14 September 2000
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    This is a continuation of part I of this paper [the authors, ibid. 66, No.~1-2, 72-103 (1999; Zbl 0958.51022)] which has been separately reviewed. They obtain several results on the relations between triangles and cubic curves. A comparatively straightforward example: given any circular cubic, there is a triangle such that isogonal conjugates of points on the curve are again on the curve, and conversely, any triangle has this property for some circular cubic curves. Some of these theorems are extremely complex even to state, and as in the first half of this work, many of the figures must be seen to be believed!
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    triangle
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    Euler cubic
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    circular cubic
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    Neuberg cubic
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    isogonal conjugate
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