The Olympic Games are the common ground of the sports world – everyone enjoys them, no matter their interest level for the rest of the year. Mathematicians are no exception to this (despite their geeky reputation) and while like everyone else I enjoy cheering for athletes and becoming invested in the competition, I can’t help but appreciate some of the beautiful maths that’s present across every event! As we wait with anticipation for Tokyo 2021, here’s a look at some of the sums, shapes and stats that will come along with it!

FIGURES AND FORMULA

Throughout the Games, numbers are quite literally everywhere you look. From the overall medal table, the scores and points awarded in each event to the attendance of the crowd (remember those?) you simply can’t get away from them. And of course, with these figures comes formula. For example, knowing that the women’s 100m breaststroke world record is 1:04:35 is interesting, but what creates the excitement when watching the event is seeing the athletes chase that little red line in the pool (only visible on tv, obviously...). This is possible thanks to the differential equation that calculates the speed and displacement at any given point in the race needed to achieve the record – clearly calculus is everywhere, even Olympic swimming pools…

THE OLYMPIC RINGS

The iconic symbol of the Games dates back over 100 years and features five uniquely coloured circles, one to represent each of the competing continents. While the geometry behind five circles isn’t too complex, the use of a mathematical concept in such a high-profile way shows that the appreciation of its beauty is not just shared amongst mathematicians.

LOGISTICS AND SCHEDULING

With over 339 medal events planned for Tokyo 2021, featuring over 14,000 athletes from about 200 countries, organising an event on this scale is clearly extremely complex, and that’s before you even consider spectators (fingers crossed for next year...) Most of these timetables will be written using the help of a computer system; however, as the task boils down to an optimisation problem, the algorithms behind the machines are heavily reliant on areas of mathematics such as combinatorics and numerical analysis. Take simply assigning a bed to each of the 14,000 athletes. Clearly you can’t just match Athlete 1 to Bed 1 as teams, sports and countries will need to be kept near each other for logistical reasons. By using graph theory and modelling these constraints, it’s possible to find solutions using some beautiful principles such as Kőnig's theorem on bipartite graphs.

 - Lucy Chats Maths