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/ >
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