### Oh! Triangle (The Square Root of Two Song)

*Lyrics by Philip Carl
Sung to the tune of “Oh! Susanna” by Stephen Foster*

If you take a right triangle

With sides *a* and *b* and *c*

Then “*a*” squared summed with “*b*” squared

Equals “*c*” squared don’t you see?

If *a* and *b* have unit length

When squared and summed it’s true

Your third side simply has to be

That strange square root of two

**CHORUS**

Oh! Triangle

What problems you let loose

If you are right then something’s wrong

With the hypotenuse

What is the length of that third side?

Oh how I wish I knew

It’s a number that when squared becomes

Precisely two

We write your value equal to

A “*p*” that’s over “*q*”

So *p* squared over *q* squared

Must exactly equal two

*Chorus*

If *p* and *q* are integers

We write in lowest terms

A reduction to absurdity

The paradox confirms

For you can see that *p* is even

So indeed is *q*

So they can’t be in lowest terms

Which we assumed was true

*Chorus*

So the length of the hypotenuse

Is irrational you see

Which drove Pythagoras to drink

And sort of bothers me

Oh! Triangle

What problems you let loose

If you are right then something’s wrong

Yes something’s very very wrong

And I’ve tried to tell you in this song

Which has probably gone on much too long

With the hypotenuse!