Understanding the natural geometry of crystals has long fascinated scientists, especially when studying how materials behave at different temperatures and pressures. One major question in this area is ...

Thus, for a quadrilateral, k is 4, and the number of points required will be 1 + 2 4-2 = 1 + 2 2 = 5. For a convex pentagon, k is 5, and the number of points required will be 9.

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Ф-function technique, a ...

This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns ...

A quadrilateral can be divided into two triangles so the same property also holds for a quadrilateral which is not convex (as shown above). 4. Examine the table.