# The World Cup Group Stage, Math at First Sight, and Geokone

Welcome to this week’s Math Munch! We’ve got some World Cup math from a tremendous recreational mathematics blog and a new mathematical art tool. Get ready to dig in!

Brazuca: The 2014 World Cup Ball

I’ve been meaning to share the really fantastic Puzzle Zapper Blog, because it’s so full of cool ideas, but the timing is perfect, because IT’S WORLD CUP TIME!!! and the most recent post is about the math of the world cup group stage! It’s called “World Cup Group Scores, and “Birthday Paradox” Paradoxes,” and I hope you’ll give it a read. (For some background on the Birthday Paradox, watch this Numberphile video called 23 and Football Birthdays.)

The thing that got me interested in the article was actually just this chart. I think it’s really cool, probably because I always find myself two games through the group stage, thinking of all the possible outcomes. If you do nothing else with this article, come to understand this chart. I was kind of surprised how many possible outcomes there are.

All Possible World Cup Group Stage Results

Long story short (though you should read the long story), there’s about a 40% chance that all 8 world cup groups will finish with different scores.

Alexandre Owen Muñiz, Author of Puzzle Zapper.  (click for an interview video about Alexandre’s interactive fiction)

Puzzle Zapper is the recreational mathematics blog of Alexandre Owen Muñiz. You can also find much of his work on his Math at First Sight site. He has a lot of great stuff with polyominoes and other polyforms (see the nifty pics below). Alexandre is also a writer of interactive fiction, which is basically a sort of text-based video game. Click on Alexandre’s picture to learn more.

The complete set of “hinged tetrominoes”

A lovely, symmetric family portrait of the “hinged tetriamonds”

I hope you’ll poke around Alexandre’s site and find something interesting to learn about.

For our last item this week, I’ve decided to share a new mathematical art tool called Geokone. This app is a recursive, parametric drawing tool. It’s recursive, because it is based on a repeating structure, similar to those exhibited by fractals, and it’s parametric, because the tool bar on the right has a number of parameters that you can change to alter the image. The artistic creation is in playing with the parameter values and deciding what is pleasing. Below are some examples I created and exported.

I have to say, Geokone is not the easiest thing in the world to use, but if you spend some time playing AND thinking, you can almost certainly figure some things out! As always, if you make something cool, please email it to us!

##### Now go create something!  Click to go to Geokone.net.

I hope you find something tasty this week. Bon appetit!

### 6 responses »

1. were do you learn all this stuff? So is there a purpose of making the soccer balls for the world cup different color and design?

2. what do you learn reading about soccer game of 2014 ? is a idea for make new balls for the world cup different color , dising and types ?

3. That is so cool Ive played soccer for a really long time and I’ve seen all the different shapes that they are making now.its also cool how they began to cut off the corners and then how the ball vegans to form with all the shapes they began to put in it and the soccer ball that I like is the one that just came out on fifa 14 World Cup.

4. In the first geokrone with the triangles are they corner to corer or what ? Also are you taking one shape and making it something interesting ?

• To be honest, I dont exactky know. The best thing to donis keep playing. Keep it simple and try to ubderstand one piece at a time.

5. In the first geokrone with the triangles are they corner to corer or what ? Also are you taking one shape and making it something interesting ?