How to use the intermedate value theorem show that every smo

How to use the intermedate value theorem show that every smooth closed curve can be put in a square frame tangent to the curve??

Solution

I think this is a form of the famous Square Peg problem/conjecture. There are certain proves given by mathematcians only under the consideration that the curve is \"smooth enough\". This conjecture was given by Otto Toeplitz. Since, the proof you are asking for involves a research paper/papers, it can\'t be discussed here. I suggest you take a look at this: http://people.mpim-bonn.mpg.de/matschke/SurveyOnSquarePeg_extension14.pdf