# Category Archives: Mathematics

## How many mutually touching cylinders can be arranged in 3D?

An old problem, restated by Martin Gardner in 1959, asked if six cigarettes that can be placed so that each touches the other. Gardner was surprised by fifteen readers discovering that actually seven cigarettes can be arranged with that […]

## In how many ways can you fold a strip of stamps?

When was the last time you used a postage stamp? Even if it was a long time ago, you may have hold in your hands a strip of stamps. Maybe you have even tried to fold it into a stack, […]

## Game Theory explains professionals’ play

You play rock-paper-scissors against someone. What is the best strategy? Of course, it depends of what your opponent does. If he is someone who always plays “rock”, then you better play “paper”. But if your opponent is not that naïve […]

## 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 […]