CLUMSY WAGON

It's not the day-to-day of railroads, but it can be a problem when giant beams are transported on winding roads: what if the car is too big in relation to the curve of the tracks?

If the entrance and exit of the winding region are on the same straight line, and whatever the size of the wagon, will it always be possible to make the crossing? See in the figure the problem of making the hypothesis about the input and the output. Note that the wagon in the figure is too big to get out, as it needs to be perpendicular to the entry and exit directions at some point, but this is impossible, because of its size.

So far, the only known examples that fail are only possible in the mathematical world. It is also known that, in a sense, the wagon can make the crossing in most situations. An abstract problem that has not yet been completely solved by mathematicians.

Take a look at this stop-motion video that shows how to cross the train in one of the exhibitions of Matemateca's collection. Did you feel like trying too?

Video: Rodrigo Tetsuo Argenton.

This Wikipedia page talks a little about the clumsy wagon, explaining what it is and what the goal of this "game" is. He also briefly mentions the study of functions and the role of games like this in mathematics education.

In fact, the clunky wagon part was created based on the problem reported in this Conan Wu page. Can you see the similarities? Take the opportunity to look at other interesting things in his blog.