The point is there is no way to partition a square into two squares. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505
505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 9:17 AM Frank Wimberly <wimber...@gmail.com> wrote: > 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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