On unit distances in a convex polygon

On unit distances in a convex polygon

For any convex quadrilateral, the sum of the lengths of the diagonals is greater than the corresponding sum of a pair of opposite sides, and all four of its interior angles cannot be simultaneously acute. In this article, we use these two properties to estimate the number of unit distance edges in convex n-gons and we: (i) exhibit three large groups of cycles formed by unit distance edges that ...

The Sum of Distances between Vertices of a Convex Polygon with Unit Perimeter

a study on corrosion reasons of heat exchanger in ammonia unit

چکیده ندارد.

The number of distinct distances from a vertex of a convex polygon

Erdős conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least bn/2c distinct distances to the other points of P . The best known lower bound due to Dumitrescu (2006) is 13n/36−O(1). In the present note, we slightly improve on this result to (13/36 + ε)n − O(1) for ε ≈ 1/23000. Our main ingredient is an improved bound on the maximum ...

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon