Recognition of triangles by covariogram
A. G. Gasparyan, Victor K. Ohanyan · Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) · 2013
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 u ∈ S 1 (S 1 is the space of all directions in the plane). 4. If we have orientation-dependent chord length distribution function for an everywhere dense set of S 1, then we can uniquely recognize the triangle with respect to reflections and translations. 5. For any finite subset A ⊂ S 1, there are two non-congruent triangles with the same values of orientationdependent chord length distribution functions on A.