Frieze patterns
We discuss here the geometry of frieze patterns, and add a few words about Greek vases, molecular symmetry, and 2D crystallography. The work is written primarily for school students.
math.HO↗
arXiv subjects
Peter Panov
Publications and source records attributed to Peter Panov.
On geometric medians of triangles
We obtain universal affine type estimates for the location of the geometric medians of triangle perimeters and for the location of the geometric medians of triangular domains. At the end, some alternative implementations of the triangle space are discussed.
math.OC↗
On the geometric median of triangular domains and other median type points
The geometric median of a domain is the point that minimises the average distance from itself to the points of the domain. We will give a gradient system of equations that defines the geometric median of a triangular domain and will prove a simple geometric property of the median. This property states that all three average distances from the median to the sides of the triangle are equal. Further we generalise these results to other types of domains and to other types of median like points.
math.OC↗