Mathematical Gymnastics

For the long days of ICM 2014 lectures, and long flights to and from Seoul, some mathematical gymnastics is needed. And this is precisely what Omer Angel taught us in his recent visit. Combining gymnastic with a demonstration of parallel transport and deep insights on human physiology!

You want to move from this  position

hands1

to this position

hands2

without simply rotating your hand.

Here are two video-demonstrations by some HUJI top people

parallel trasposrt

Click on the picture to see the video. (The drill  is a sequence of five moves and the video skipped the first.)

Some other mathematical gymnastics is demonstrated in the post the ultimate riddle. And for a futurist mathematical application to sport (soccer) see this post.

The Intermediate Value Theorem Applied to Football

My idea (in my teenage years) of how to become a professional basketball player was a bit desperate. To cover for my height and my athletic (dis)abilities, I would simply practice how to shoot perfectly from every corner of the court. I would not have to run or jump. My team could pass the ball to me at the right moment and I would shoot. (I was a little worried that once I mastered this ability they would change the rules of the game.)

But this idea did not work. As much as I practiced, I could not shoot perfectly from all corners of the court, and not even from the usual places. In fact, my shooting was below average (although not as much below average as my other basketball skills.)

Next came my idea how to become a professional football (soccer) player. This idea was based on mathematics, an area where I had some advantage over other ambitious sports people; more precisely, my idea was based on the intermediate value theorem. (We had a post about this theorem.)

The idea is this: If you put a football on your head and start running the ball will fall from behind. But if you put the ball on your forehead and start running the ball will fall in front of you. By the intermediate value theorem, there must be a point, in between, such that if you run with the ball at this point, the ball will not fall at all. In fact you can find such a point for every way you would like to run. And you can even learn to adjust it if you change your route!  The plan was now simple. At the right moment I would get the ball from my team, put it on the right point on my forehead  start running and slalom my way towards the goal. (I was a little worried that once I mastered this ability they would  change the rules of the game.) I practiced it for several weeks, Continue reading