[FRIAM] square land math question

[Frank Wimberly]

p.s.  Zeno's Paradox is related to

1/2 + 1/4 + 1/8 +...

= Sum(1/(2^n)) for n = 1 to infinity

= 1

(Note:  Sum(1/(2^n)) for n = 0 to infinity

= 1/(1 - (1/2)) = 2)

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Wed, Jul 22, 2020, 8:49 PM Frank Wimberly <wimberly3 at gmail.com> wrote:

> 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/20200723/4b109ecc/attachment.html>