The Scarecrow's math being wrong was intentional

In 2009 I had a post about Movie mistakes (see here). One of them was the Scarecrow in The Wizard of Oz after he got a Diploma (AH- but not a brain) he said

The sum of the square roots of any two sides of an isoscles triangle is equal to the square root of the remaining side. Oh joy! Rapture! I have a brain!

I wrote that either this mistake was (1) a mistake, (2) on purpose and shows the Scarecrow really didn't gain any intelligence (or actually he was always smart, just not in math), or (3) It was Dorothy's dream so it Dorothy was not good at math.

Some of the comments claimed it was (2).  One of the comments said it was on the audio commentary.

We now have further proof AND a longer story: In the book Hollywood Science: The Next Generation, From Spaceships to Microchips (see here) they discuss the issue (page 90). The point to our blog as having discussed it (the first book not written by Lance or Lipton-Regan to mention our blog?) and then give evidence that YES it was intentional.

They got a hold of the original script. The Scarecrow originally had a longer even more incoherent speech that was so over the top that of course it was intentional. Here it is:

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 rapture! What a brain!

While I am sure the point was that the Scarecrow was no smarter, I'm amused at the thought of Dorothy not knowing math or chemistry and jumbling them up in her dream.