Why does Scarecrow in The Wizard Of Oz get the Pythagorean Theorem wrong?

Question

After receiving a "brain," the Scarecrow in The Wizard of Oz famously says the following:

“The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side!”

Which as generations of know-it-alls have noted, is incorrect. That's a right triangle, you idiot!

Over the years I have a number of conflicting explanations for the mistake, all treated as the real reason. Among them:

• this was intentional, and is intended to show the scarecrow is in fact as dim as always
• this was intentional, because the filmmakers thought the word isosceles sounded "smarter"
• this was mistake on the part of the actor, and the script said "right triangle."
• this was a mistake on the part of the filmmakers

Is there any firm evidence or statements from those involved about which explanation is correct?

Answer 1

There is a version of the script that had more to say to make it obvious that it was intentional, according to:

Hollywood Science: The Next Generation, From Spaceships to Microchips

(ISBN 331954215X, 9783319542157; Kevin R. Grazier, Stephen Cass; Springer, 2017)

So I went back to the scripts I’ve got here, and we can specially credit Noel Langley with that part of the script. I’ve got a draft dated April 18, 1938 and these are changes to a script he already did.

           SCARECROW
The sum of the square roots of any 
two sides of an isosceles triangle
 is equal to the square root of the
 remaining side: H-2-O plus H-2-S-
O-4 equals H-2-S-O-3 using pi-r
 squared as a common denominator. 
Oh joy! Oh rapture! What a brain!

—perhaps the blend of chemistry with geometry in that manner was too obvious. That line does, however, remove much of the doubt that the Scarecrow’s faulty exposition on the nature of the isosceles triangle is intentional on the part of the writers, and it also makes it clear that, in essence, the Wizard did very little.

Answer 2

Seem pretty obvious that the Wizard, being a fake himself, could only give fake gifts -- he sort of says this. The scarecrow obviously did have brains and perhaps armed with a belief in his own abilities would eventually become genuinely educated. Of course the Tin Man had a heart or he would not have wanted one. The Cowardly Lion just, like the others, needed to believe in himself.

Dorothy was given a real magical gift because the witches of Oz were magical. Why they put up with the Wizard I'll never know; perhaps the Good Witch was just being kind or needed someone to rule Oz although she would step in if necessary as she indeed did in Dorothy's case.

Answer 3

I don't think it's a invalidation of the scarecrow. I think it's saying in fantasy land that math is fantasy too. Or it's being not serious about math, when the moral of the story was the part that was supposed to shine.