The World Cup is happening! It’s inspiring to watch excellent soccer players…inspiring us to write about some excellent math. We’ll venture out on the field with a few soccer and math tidbits.

- The soccer ball that I think of as typical – in other words, the one that I remember from Days of Yore – is an Archimedian solid, made from 20 regular hexagons and 12 regular pentagons. Specifically, it’s a truncated icosahedron because it can be built from lopping the corners off of a regular icosahedron. It’s also a buckminsterfullerene, although that’s only the formal name: friends can call it a buckyball. The buckyball was Red Hot News in 1985, because it was a new way of putting Carbon atoms together. Scientists Harold W. Kroto, Robert F. Curl, and Richard E. Smalley* named it after architect R. Buckminster Fuller*, whose geodesic domes had inspired them to try and create such a carbon cluster. But this soccerball-shaped soccerball doesn’t limit itself to Ancient Greeks and Modern Scientists, oh no. It also dabbles in the arts, as shown in this photo below from Labor Park in Dalien, China.
- Soccer balls aren’t the only thing math-related in soccer: there’s also the number of people on a team. Each team has 23 players, which means that on any team there is a 50% chance that two people on that team share a birthday. With 32 teams playing in the world cup, you’d expect about half of them to have birthday-sharing teammates, and in fact, as the BBC pointed out earlier this week, exactly 16 of the 32 teams do. For example, tomorrow (June 20) six people have birthdays, including two (Asmir Begovic and Sead Kolasinac) on the team from Bosnia and Herzegovina. Now oddly enough, even though you’d expect half the teams to have teammates sharing a birthday, the fact that it’s exactly half is actually rather strange: with a 50% chance of two teammates getting to share cake, the probability that exactly 16 of the 32 teams satisfy that is only 14% – it’s just that at that point it’s equally likely to be more or fewer days. Ironically, it’s rather unexpected to actually hit the expected value.
- One final math fact about the World Cup: one of the referees for yesterday’s match between Chile and Spain is actually a former high school math teacher! Not all that former, either: Mark Geiger taught in New Jersey alongside his brother, winning the Presidential Award for Excellence in Math and Science Teaching, but eighteen months ago he left teaching in order to referee full-time, hoping for a shot at the World Cup. Not a bad gig, and he always has those math skills to fall back on if he finds he misses teaching.

*Whenever I type “[Occupation] [Person’s Name]” I get the urge to add “renowned” and then go read *Da Vinci Code* again.

*The photo of the sculpture is by Uwe Aranas, Creative Commons License. And if you didn’t follow the link to the BBC article, “The Birthday Paradox ath the World Cup” by James Fletcher, it’s worth a read – it has a lot more detail about the birthday paradox and sports.
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