[FRIAM] square land math question

Thu Jul 23 11:17:46 EDT 2020

Right.  When its area reaches zero it's not a square.  That is, there is
only one square then.

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

505 670-9918
Santa Fe, NM

On Thu, Jul 23, 2020, 9:10 AM Edward Angel <angel at cs.unm.edu> wrote:

> Why would you call the limit of the increasing smaller squares a “square”?
> Would you still say it has a dimension of 2? It has no area and no
> perimeter. In fractal geometry we can create objects with only slightly
> different constructions that in the limit have a zero area and an infinite
> perimeter.
>
> Ed
> _______________________
>
> Ed Angel
>
> Founding Director, Art, Research, Technology and Science Laboratory
> (ARTS Lab)
> Professor Emeritus of Computer Science, University of New Mexico
>
> 1017 Sierra Pinon
> Santa Fe, NM 87501
> 505-984-0136 (home)   angel at cs.unm.edu
> 505-453-4944 (cell)  http://www.cs.unm.edu/~angel
>
> On Jul 23, 2020, at 9:03 AM, Frank Wimberly <wimberly3 at gmail.com> wrote:
>
> 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
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>>
>>
>> --
>> Frank Wimberly
>> 140 Calle Ojo Feliz
>> Santa Fe, NM 87505
>> 505 670-9918
>>
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