# Category archives: Mathematics

## The complexity of drawing good proportional symbol maps

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 such that its area is proportional to the numerical value associated to the point. This scaled […]

## The history of the crossing number of the complete graph

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 Paul Turán, the second half of the paper is devoted to the crossing number of the […]

## Progress checking Zarankiewicz’s conjecture on the brick factory problem

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 bipartite graph . Proposed by Paul Turán after the Second World War, the first advances on […]

## The fascinating history of the brick factory problem

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 trace the origins of the crossing number, with particular emphasis in the war-time experiences of the […]

## Every convex polyhedron can be refolded to a different one

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 polygon in the plane (possibly overla pping). In order to obtain an unfolding, the surface of […]

## How much should we … produce?

Decision making in areas such as production planning, distribution and grid management, logistics or financial portfolio management is usually based on mathematical models, mathematical optimization themselves. Let us assume that we have to take a decision of how many units to produce of two products A and B. The production system is common and has […]

## Advances on an Erdős problem on convex boundaries

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 such that every circle with center P intersects that boundary in at most 2 points. (Note that […]

## Always look on the light side of graphs

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 the segments of such a graph. Every segment has two sides, defined by the line in […]

## Epistemology in the courts. Or, Sherlock Holmes is dead, long live to Thomas Bayes.

Strange as it may sound to many people, the fact is that some of the most interesting work on epistemology that is being currently done in Spain is carried out at the headquarters of the Spanish gendarmerie (the well known force called Guardia Civil), in particular, at the Area of Statistics within the corps’ Service […]

## The Holy Spirit game, or a sip of conclave economics

Imagine the following situation: about 100 people have to choose one of them for an important position; they have different preferences about who must be chosen, some may have a stronger or lighter interest in being elected, but, and this is essential, it is very likely that most of them will have to cast their […]