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- W1572003102 abstract "We consider the distances between a line and a set of points in the plane defined by the L^p-norms of the vector consisting of the euclidian distance between the single points and the line. We determine lines with minimal geometric L^p-distance to the vertices of an equilateral triangle for all 1<= p<=infty. The investigation of the L^p-distances for pne 1,2,infty establishes the passage between the well-known sets of optimal lines for p=1,2,infty. The set of optimal lines consists of three lines each parallel to one of the triangle sides for 1<= p < 4/3 and 2<p<=infty and of the three perpendicular bisectors of the sides for 4/3<p<2. For p=2 and p=4/3 there exist one-dimensional families of optimal lines." @default.
- W1572003102 created "2016-06-24" @default.
- W1572003102 creator A5060060343 @default.
- W1572003102 date "2011-09-21" @default.
- W1572003102 modified "2023-09-27" @default.
- W1572003102 title "Geometrically L^p-optimal lines of vertices of an equilateral triangle" @default.
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