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Does every closed loop always pass through corners of some square?

Question asked by Kaustubh Katdare in #Coffee Room on Feb 24, 2019
Kaustubh Katdare
Kaustubh Katdare · Feb 24, 2019
Rank A1 - PRO

I recently discovered this post on Twitter and was amazed. I tried to draw a few curves myself and this seems to be working. I'm however open to opinions and comments from fellow CEans. Do you think this is actually true and if yes, what could be the reason? 

Look at this image, for example -

Zofq-closed-loop-corners-of-square.jpg

Tagging @Ramani Aswath , @Harshad Italiya, @Ambarish Ganesh , @Ankita Katdare , @Manish Goyal , @Anoop Mathew . Could you give this a try? 

Posted in: #Coffee Room
Ramani Aswath
Ramani Aswath · Feb 24, 2019
Rank A1 - PRO

Why a closed curve? It will be true of open curves. In the very example shown any one of the three outside loops can be absent.

Why square? Maybe the thing is true for other regular polygons?

It may not be true also. I shall revert.

Kaustubh Katdare
Kaustubh Katdare · Feb 24, 2019
Rank A1 - PRO

... I think the criteria for open curve holds. I'm trying to figure this out; but won't deny possibilities. Let's see. 

Update: 

I found this link that talks about the subject: https://www.webpages.uidaho.edu/~markn/squares/

Ramani Aswath
Ramani Aswath · Feb 25, 2019
Rank A1 - PRO

@Kaustubh Katdare , I must qualify what I said about open curves. The statement is true for some (not all) open curves. I took an isosceles right triangle and theoretically proved that a square can be inscribed in it. I presume that the original staement that you posted may be true.

I shall revert if I work out or find any rigorous proof.

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