The Fishing Rod
Sam finished making this very beautiful fishing rod, 1.4 m long:
On the weekend Sam takes the new fishing rod to the train station on the way to a great fishing spot.
Not Allowed
But the Station Master says "Sorry Sam, but it is longer than 1 m. No one is allowed to take things on the train that are more than 1 m long. New rules you know."
Sam thinks for a bit, then asks "when is the next train?"
"In half an hour" says the Station Master.
Half an hour later Sam is back again, with the same fishing rod. It is not altered at all, not cut or shrunk or pulled apart or anything. But the Station Master measures it and says "OK Sam you can get on the train with that."
What did Sam do?
Don't go any further until you have a solution!
Sam's Solution
Sam cut a piece of cardboard into a 1 m square and placed the fishing rod along the diagonal and covered it all in wrapping paper.
In fact the diagonal of a 1 m square is slightly longer:
it is actually √2 = 1.4142...
Read Pythagoras Theorem to learn more.
The Station Master measured its length and width and found them both "not more than 1 m" and so all was satisfactory.
Such are the ways of the world.
Daydreaming at the River
Sam enjoyed a lovely day at the river, and daydreamed about a new fishing rod, but this one will be longer!
In fact it will be 1.7m long.
Is there any way Sam could get such a fishing rod past the friendly (but stubborn) Station Master?