The Olympics are very proprietary about the rings and the name and any and all tie ins. The knitting social media site, Ravelry was sent a cease and desist letter for an event called the Ravelympics and caused so much kerfuffle that the US Olympic Committee apologized not just once but twice...and yet knitting and the Olympics still have found some links. Like this yarn bombing in North Yorkshire (do click that link it is impressive a bit of what you'll see.
In Lincolnshire they knit 200 meter running track that is being displayed at the Olympic village.
So if you have forgiven the Olympic Committee and are knitting while watching the Olympics take some inspiration from these great feats of knitting.