This post introduces a game we created a few years back for use in outreach. It takes about five minutes to learn to play, tops, but the game has interesting strategy — some of which can be discovered by just playing. In fact, the trick of blocking an opponent’s entry point is one several students discovered spontaneously and with some delight. Graph domination is also played on boards that are simple enough that the people participating in your outreach activity can make their own. In fact “make up your own board” is one of the possible activities. The materials needed are the board and some tokens in two colors or types. The game illustrates the concept of domination from graph theory. Readers familiar with war games will recognize “domination” as covering some of the same issues that are covered by zones of control.
Colorful vines in the sixth order Mandelbrot set.
This post is about a collection of related games that can be used for arithmetic practice. The three games are appropriate to different sorts of personalities and situations, but they all use the same basic move. The game requires both addition and multiplication, just hard enough to be good for practicing mental arithmetic. Near the bottom of the post is information from simulation studies that let you know which scores are likely, unlikely, or impossible. The fact that some score are impossible is, itself, an interesting piece of mathematics.
A flower spiral from the sixth order Mandelbrot set.
Occupy Math has talked about non-linearity before, but today’s post gets up close and personal with non-linearity in some matters that endanger your life. We begin with one of the most deadly things in North America: the car. Cars kill about 100 people per day — but this is not like having a tree fall on you. You have substantial control over your chances of dying in a car accident or killing someone else with a car. This post will look at this and other dangerous situations in which much of your ability to control your fate and the fate of others lies in the non-linear nature of the situation.
This is another view, a floral one, of the 7th degree Mandelbrot set.
The Fibonacci numbers are a famous sequence of numbers. The sequence starts with two 1s. After that, the next number in the sequence is obtained by adding the last two. This gives us 1,1,2,3,5,8,13,21,34,55,89,144,… Today’s post is about a collection of activities looking for patterns in the Fibonacci numbers and other similar sequences. It turns out that there are a whole lot of patterns to search for, some harder, some easier. The activities also look at what happens if you start with something besides 1,1, which turns out to be interesting.
This week, a view from the 7th order Mandelbrot set. Star centered fractal geode.
This Occupy Math is about how dangerous it is to be statistically illiterate. The idea was kicked off by a wonderful article in theGuardian with examples of the dangers of not knowing about statistics. The lead anecdote is about people leaving an employer because of a cluster of five instances of a rare, non-contagious disease. The problem is that the cluster could easily have happened by chance — and a check for a source of danger found nothing. People left their jobs to avoid something that was quite likely the result of random chance. As the Guardian notes, the price of statistical illiteracy goes up sharply during a pandemic. Worse, a number of groups are spreading misinformation about the pandemic and possible responses to it. This Occupy Math will try and illuminate the issues.
A view into the Quintic Mandelbrot set with lots of colors, on blue.