# Category archives: Mathematics

## Flip me to the moon

This post is dedicated to the memory of Professor Ferran Hurtado , inspirational friend and colleague. Triangulations are extremely useful in computer graphics, with terrain modeling being an outstanding example: A mesh of points in 2D is triangulated and then the triangulation is lifted to obtain an -monotone polyhedral surface in 3D, called a 2.5D […]

## Triangulations are rigid. You can do better using pseudo-triangles

Triangles are, definitely, among the most used mathematical objects. One of the reasons is that they are simple (actually the smallest polygon). Another very important reason is that they are rigid, which is the property behind the many structures composed by triangles we can see in our daily life. But, surprisingly enough, triangulations are not […]

## The math of sex and hunger. A short history of population dynamics

The field of population dynamics lies between mathematics and biology. Its subject of study is the evolution of biological populations with time. The natural language for dynamical problems is that of differential equations, and population dynamics is not an exception to this rule. Such a powerful tool was well known since the times of Isaac […]

## Helping Spider-Man to plan his moves efficiently

We all know how Spider-Man moves through the city, shooting spider-webs from wall to wall. But, have you ever wondered if he is actually using the shortest route? And, if so, how does he compute it? Since walls introduce a third dimension into the problem, the algorithms in a usual GPS navigator are no longer […]

## 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 condition . Some years later, in 1968, Littlewood raised the question if it possible in 3-space […]

## 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, one stamp wide, so that the strip was easier to store. Have you ever wondered […]

## 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 and searches for his best play, what would you do? The first thing to notice […]

## 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 your stand as close as possible. After thinking on it for a while, you take […]

## 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 number 1 appears infinitely often in the decimal expansion of . Among the most remarkable […]

## 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 not so many make use of 3D solid objects. An example of the latter is […]