[FRIAM] square land math question

[Frank Wimberly]

Incidentally, people are used to seeing limits that aren't reached such a
limit as x goes to infinity of 1/x = 0.  But there are limits such as limit
as x goes to 3 of x/3 = 1.  The question of the squares is the latter
type.  There is no reason the area of the small square doesn't reach 0.

On Wed, Jul 22, 2020 at 7:36 PM Eric Charles <eric.phillip.charles at gmail.com>
wrote:

> 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
>> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
>> FRIAM Applied Complexity Group listserv
>> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
>> archives: http://friam.471366.n2.nabble.com/
>> FRIAM-COMIC http://friam-comic.blogspot.com/
>>
> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. .
> FRIAM Applied Complexity Group listserv
> Zoom Fridays 9:30a-12p Mtn GMT-6  bit.ly/virtualfriam
> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> archives: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/
>


-- 
Frank Wimberly
140 Calle Ojo Feliz
Santa Fe, NM 87505
505 670-9918
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20200722/bf0a32cf/attachment.html>