[FRIAM] square land math question

[Eric Charles]

This is a Zeno's Paradox styled challenge, right? I sometimes describe
calculus as a solution to Zeno's paradoxes, based on the assumption that
paradoxes are false.

The solution, while clever, doesn't' work if we assert either of the
following:

A) When the small-square reaches the limit it stops being a square (as it
is just a point).

B) You can never actually reach the limit, therefore the small square
always removes a square-sized corner of the large square, rendering the
large bit no-longer-square.

The solution works only if we allow the infinitely small square to still be
a square, while removing nothing from the larger square. But if we are
allowing infinitely small still-square objects, so small that they don't
stop an object they are in from also being a square, then there's no
Squareland problem at all: *Any *arbitrary number of squares can be fit
inside any other given square.



-----------
Eric P. Charles, Ph.D.
Department of Justice - Personnel Psychologist
American University - Adjunct Instructor
<echarles at american.edu>


On Tue, Jul 21, 2020 at 7:59 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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