Are there any restrictions on the angle the length sits within the tunnel?
This seems pretty fundamental to me, however I was not able to find information about this particular problem on the net, so I'm writing here seeking your knowledge
Let's say we have two connected perpendicular "tunnels" like in this picture:
Widths are x and y respectively. Question is, what is the maximum length of an indefinitely narrow object, which is able to move from one end to another?
Sorry for possible awkward presentation, English is obviously not my native language.
I mean, imagine black lines being "walls" and red line being a narrow "car" (couldn't think of a less lame comparison) - "car" will eventually have to make a nearly 90 degrees turn, but I do not know which particular moment will be the most complicated for the "car" to fit within the "walls"...
Of course we are minimizing (you wrote maximizing) the quantity. Nevertheless, your method is very graceful and correct, while my initial idea using coordinates was way too complicated.
I am able to approach
as long as it seems the same as
I am not quite able to reach this wonderful expression. Could someone please give me a hint?