ABSTRACT. We show that for any convex body K ~ E 2 there exists a triangle T such that T c K ~ (3(x/i7-1)/4)T, where 2T is a suitable homothetic copy of T with ratio 2. As a corollary we show that if (Ki) are homothetic copies of a given convex body K c E 2 with area V(K) = 1, then the condition E V(K~) >~ 9(9-x/~)/4 is sufficient for the existence of a translative covering of K by (Ki).
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