The paper considers the problem of recognition of triangles by orientation-dependent chord length distribution. The following results are obtained: 1. The explicit form of the covariogram and orientation-dependent chord length distribution function for a triangle. 2. The explicit form for the chord length distribution function for a triangle. 3. The length of the maximal chord of a triangle is continuous function on direction. 4. If we have orientation-dependent chord length distribution function for an everywhere dense set, then we can uniquely recognize the triangle with respect to reflections and translations. 5. For any finite subset A, there are two non-congruent triangles with the same values of orientation dependent chord length distribution functions on A.

Ara Gasparyan, Victor Ohanyan

Journal of Contemporary Mathematical Analysis 48 (3), 110-122, 2013

Bounded convex domain, covariogram, chord length distribution

60D05, 52A22, 53C65

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