engleski

Heptagonal triangle as the extreme triangle of Dixmier-Kahane-Nicolas inequality

Let T be a triangle in the Euclidean plane. Let g(T) be the orthic triangle of the triangle T, and let g^{; ; n+1}; ; (T) be the orthic triangle of the triangle g^n(T). In [2] it is proved that for n->∞ the triangle g^n(T) tends to the point L. It has also been shown that |OL| <=4/3 R for all triangles T and that |OL| = 4/3 R if T is a heptagonal triangle, where (O, R) is the circumscribed circle of the triangle T. In this paper it will be geometrically proved that the equality in Dixmier–Kahane–Nicolas inequality |OL| <= 4/3 R is valid in the case of a heptagonal triangle. The relationship between the initial heptagonal triangle T and the obtained point L will also be investigated.

heptagonal triangle; indirect similarity

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