This is a Country and Western song that tries to get across the idea of a radian to young mathematicians who've never met this idea before. There is a version on Youtube also.
Joe stood up at the Sunday lunch, in the bosom of his loving family,
With a slice in his hand, for the apple pie,
To serve his wife, and his daughter, and his fine sons three.
He said “How much?” to each in turn, and they each said “Sixty degrees!”
“Now six times sixty makes an empty plate,” thought Joe,
“That’s my kind of maths, yes please!”
But then he came to his youngest son, who loved to get his father mad.
When Joe said “How much?”, this is what he heard, “I’d like a radian, Dad!”
What’s the point in a radian? If you know, please won’t you tell?
Who needs a new-fangled unit? When degrees have served us so well?
You say it’ll make things easier, and I suppose that pigs might fly.
So how do I get an empty plate, when I’m cutting up my Sunday lunch pie?
His son piped up, “Let me tell you, radians are cool, and here’s why.
Just look what they do to your formulae, remembering them’s as easy as pie.
I like the crust, and to find its length the radius times the angle will do,
And the area’s easy to find as well, it’s theta r squared over two.
So come on Dad, get with it, degrees are a little passe
Okay, so the plate won’t be empty, but that’s some more for another day.
Let’s all use a radian yes, a radian, why not risk it?
Nothing against the good old degree, but the radian takes the biscuit,
Those formulae look just nice and neat, make ‘em yours! You’ll be in clover.
And the best thing about a radian, is that it leaves a bit of pie left over!