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To prove Pythagoras' theorem would be easy to do:
You need a, b
and c and some Greek letters too.
You see Pytha' was a Greek, with a strange
based an entire math-based cult on a wrong supposition.
this theorem bears his name: misplaced credit it may be,
It is named after a
man who thought beans unhealty.
Though the proof requires squares, we
shall need a triangle,
One that is blessed with a straight ninety degree
For the shortest of the sides, the letters a and b we'll use,
the last letter c marks the hypothenuse.
We shall employ alpha and beta to
name the angles not straight-
It won't matter which goes where- you will see
if you wait.
A squared plus b squared equals c squared, we shall
So the proof will employ a few squares, don't you know.
But first, I
have to tell, we need not one triangle but more,
All exactly the same; we
shall need at least four.
Now that we have what we need, you might need pen
For from here on will start the great Pythagorasian
As we've all learned back at school, it is basic math to
That the sum of alpha and beta is exactly ninety.
Place corner alpha
of one triangle against corner beta of another;
It is hard to envision, but
well worth the bother.
Now we repeat the process with the other triangles to
That they've curled back into each other into a square with sides
Now the surface of this square, with basic math you can see,
it equals c squared, that is, c multiplied by c.
But this is not all, for as
you may recall,
This square is actually formed by four triangles and
Four triangles, but that's not all, for in the largest square's
We find we must allow a smaller square to enter.
it is there, because the triangles, you see,
Were too small to cover the
surface of square c.
Let us say the the shortest side was assigned letter
Then the sides of this square equal b minus a.
The surface of this
square, much fun this will be,
Thus equals a squared plus b squared minus two
But wait, what of the triangles, four in number they
Well, their surface (basic math!) proves to be a half a times b.
don't forget there were four, or things will go amiss!
So if we seek their
collective surface, then 2ab it is.
Now we add the inner square, cross some
And we will find the outer square's surface, of that there's no
What is this? A squared plus b squared, is that what we
Our previous answer c squared comes to mind.
One conclusion can be
drawn, and that is that it's no ruse,
The sum of the squares of the other
sides equals the square of the hypothenuse!
Now smile and nod at the scary
geek and tell him that you get it,
For if you don't, and ask for more, you
WILL live to regret it.
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