[FRIAM] square land math question

[Frank Wimberly]

Off the top off my head.  As long as the small square isn't of zero area
the larger square isn't a square.  When the smaller square reaches area
zero there is only one square.

What do you think?
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Tue, Jul 21, 2020, 5:59 PM cody dooderson <d00d3rs0n at gmail.com> wrote:

> 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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