On Isosceles Sets In Minkowski Plane

In 1998, P. Fisburn put forward the concept of planar κ;-isosceles sets and achieved a lot of important results in Euclidean plane. Let P be a finite planar point set, if every λ-point subset of this set contains a 3-point subset such that one of the three points is equidistant from the others, then P is called κ-isosceles set.Let C C R2 be a convex body. For arbitrary different points a, b ∈ R2, denote by|ab|the Euclidean length of the line-segment ab. Let a1b1 be a longest chord of C parallel to the line-segment ab. dC(a,b) represents relative distance between a and b, and dC(a,b)=2|ab|/|a1b1|.Two-dimensional normed linear space is called Minkowski planeThis paper extends planar κ-isosceles set to Minkowski plane, and get some results: there are three types of isosceles in Minkowski; obtains the configurations of 3-isosceles 4-point set containing T; there are four configurations of 3-isosceles 5-point set which contains the triangle T= abc; there are two configurations of 3-isosceles 6-point set which contains the triangle T= abc; there is only one configuration of 3-isosceles 7-point set which contains the triangle T= abc. No exist 3-isosceles 8-point set. Get configurations of 3-isosceles 4-point set which only one edge coincides with the triangle T= abc.