# Category Archives: Mathematics

## Where should you place a business if one of your customers keeps moving?

Imagine you are the owner of a hot dog stand and, after many stressful years in the streets of New York City, you are moving the business to the countryside.

Of course, you want all the potential users to have […]

## We can learn a lot from a walk with real numbers

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 […]

## How to create the illusion of antigravity motions

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 […]

## Finding a shortest route is not easy for a watchman patrolling streets

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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]

## 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 […]