If a configuration of m triangles in the plane has only n points as vertices, then there must be a set of max { dm/(2n− 5)e Ω(m3/(n6 log n)) triangles having a common intersection. As a consequence the number of halving planes for a three-dimensional point set is O(n log n). For all m and n there exist configurations of triangles in which the largest common intersection involves max {dm/(2n− 5)...

In this paper, we analyze the results of triangles under discrete curve shortening flow, specifically isosceles triangles with top angles greater than π3 , and scalene triangles. By considering the location of the three vertices of the triangle after some small time , we use the definition of the derivative to calculate a system of differential equations involving parameters that can describe t...

We discuss a famous problem about right triangles with rational side lengths. This elementarysounding problem is still not completely solved; the last remaining step involves the Birch and Swinnerton-Dyer conjecture, which is one of the most important open problems in number theory (right up there with the Riemann hypothesis). 6.

We study the computational complexity of binary valued constraint satisfaction problems (VCSP) given by allowing only certain types of costs in every triangle of variable-value assignments to three distinct variables. We show that for several computational problems, including CSP, Max-CSP, finite-valued VCSP, and general-valued VCSP, the only non-trivial tractable classes are the well known max...