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Say you're at one corner of a rectangle and you need to get to the opposite one. A diagonal path is faster than going on the edges. If you look at the edge path and fold the corner in such that it touches the diagonal path, it's still the same distance. However, if you keep doing that infinite times(a limit as it tends to infinity) it eventually becomes a diagonal line. Since the distance never changes, how did this happen?

Ryan Vaughn
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    Welcome to [math.se] SE. Take a [tour]. You'll find that simple "Here's the statement of my question, solve it for me" posts will be poorly received. What is better is for you to add context (with an [edit]): What you understand about the problem, what you've tried so far, etc.; something both to show you are part of the learning experience and to help us guide you to the appropriate help. You can consult this link for further guidance. – Another User Aug 20 '22 at 22:03
  • possible duplicate of https://math.stackexchange.com/questions/859800/computing-diagonal-length-of-a-square The short answer is -- "length" is not continuous with respect to taking limits in $R^2$. – Peter Franek Aug 20 '22 at 22:05
  • also here https://www.stackubuntu.com/what-is-the-concept-theory-behind-the-fact-that-when-two-shapes-approximate-each or here https://en.wikipedia.org/wiki/Staircase_paradox – Peter Franek Aug 20 '22 at 22:09

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