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 <an...@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) an...@cs.unm.edu > 505-453-4944 (cell) http://www.cs.unm.edu/~angel > > On Jul 23, 2020, at 9:03 AM, Frank Wimberly <wimber...@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 <wimber...@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.char...@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 >>> <echar...@american.edu> >>> >>> >>> On Tue, Jul 21, 2020 at 7:59 PM cody dooderson <d00d3r...@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 >> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > 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/ >
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