Quote (Snyft2 @ Jan 23 2020 04:17pm)
it does work, you can draw a circle by chunking a square. imagine you have to draw a circle on a computer screen. you will use little squares because the screen is made of pixels. and using those you can create a circle. observe:
https://www.mathopenref.com/images/constructions/constcirclecenter2/step0.png
see, a circle :cry: ! and if you zoom in, you will see its made of little squares, so why is the total length of the circumference not 4* R but 3.14 * R :unsure: ?
exactly :cry: i need mathematical proof! something is wrong but i dont know what :wacko: !
The key to this problem is to realize it doesn't matter how closely / many times we approximate the circle by chipping away (you'd still have wedged corners), the orthogonal lines of the approximation formed by inverting the square corners will never be tangential to the circle. You need to think conceptually, as everything on the computer screen is pixelated (i.e: made out of tiny squares). Obviously the higher resolution screen will have more "believable" circle, but it's still made out of pixels :P I remember somebody in my undergrad calculus class asking the same question to the prof and he did manage to explain it - although I didn't really pay attention / cared enough to listen lol.