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 >
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