Author Archives: David Orden

<span property="name">David Orden</span>
PhD in Mathematics (Universidad de Cantabria, 2003), associate professor of applied mathematics at the Universidad de Alcalá. His main research interests are Discrete and Computational Geometry, Graph Theory, and their applications to other fields.

Questions on the digit expansion of mathematical constants, such as , , or have fascinated mathematicians for centuries. However, many of these questions remain elusive to the efforts of researchers.
For instance, it is not known for sure if the […]

Visual illusions, a perceptual behavior where what we “see” differs from the physical reality, are used in vision science to understand the nature of human perception. Most of the known visual illusions come from 2D pictures and their motions, but […]

Imagine you were a watchman, having to patrol some streets. Today you were assigned to straight, well-illuminated, and wide streets, that can be checked with a glance from the intersection.
Before starting the route, you want to determine the […]

Proportional symbol maps (also known as graduated symbol maps) are used in Cartography to visualize quantitative data associated with specific locations. For a given point on a geographic map, a symbol (usually a disk or a square) is scaled […]

We have already introduced the first half of a paper by Lowell Beineke and Robin Wilson, which traces the origins of the crossing number of a graph. After focusing on the brick factory problem, proposed by the Hungarian number-theoretist […]

A previous post presented the fascinating history of the brick factory problem, which wonders about the smallest possible number of rail crossings when connecting kilns and storage yards, which is mathematically modeled by the crossing number of the complete […]

The crossing number of a graph, defined as the minimum number of edge crossings arising when the graph is drawn in the plane, turns out to be a mathematical concept with a fascinating history.
Lowell Beineke and Robin Wilson […]

Choose your favorite convex polyhedron in the space. Make sure it is convex, since the current post is restricted to that kind of polyhedra
An unfolding of your convex polyhedron is a development of its surface to a single […]

Among his around 1525 papers, Paul Erdős considered On sets of distances of n points as his most important contribution to discrete geometry. There, he stated:
On the boundary of every convex body, there exists a point P […]

Consider a set of distinct points in the plane, no three of them on the same line. Draw straight-line segments joining pairs of those points. This is called a geometric graph and here we are going to focus on […]