[FRIAM] square land math question

[cody dooderson]

A kid momentarily convinced me of something that must be wrong today.
We were working on a math problem called Squareland (
https://docs.google.com/presentation/d/1q3qr65tzau8lLGWKxWssXimrSdqwCQnovt0vgHhw7ro/edit#slide=id.p).
It basically involved dividing big squares into smaller squares.
I volunteered to tell the kids the rules of the problem. I made a fairly
strong argument for why a square can not be divided into 2 smaller squares,
when a kid stumped me with a calculus argument. She drew a tiny square in
the corner of a bigger one and said that "as the tiny square area
approaches zero, the big outer square would become increasingly square-like
and the smaller one would still be a square".
I had to admit that I did not know, and that the argument might hold water
with more knowledgeable mathematicians.

The calculus trick of taking the limit of something as it gets
infinitely small always seemed like magic to me.


Cody Smith
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