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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