Comments by "John Berry" (@user-ud6ui7zt3r) on "What's the curse of the Schwarz lantern?" video.

  1. Didn't our host promise to reveal how to properly resolve the π=4 conundrum?
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  2.  @Mathologer  As a person who chooses to reason carefully, I didn't want to rely upon assumptions. Thank you for your wonderful videos! I do notice, however, in the process of "folding-down-corners", with each iteration, you are keeping to the lantern rules of... • ever increasing (break) points; as • the length of the lines between the (break) points heads towards zero. Apparently, the rate at which the number of (break) points increases has to be carefully balanced against the rate at which line lengths tend towards zero. With the right balance, π should successfully be achieved. With the wrong balance (of the two rates), numbers such as 4 can be achieved. This "rate balancing" sort of suggests that an important theorem might be hiding within all of this. Such a theorem would probably apply to determining the total length of the perimeter of shapes such as a Koch "snowflake."
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