There was a fallacious explanation for this floating around a long time ago basically starting with a triangle and adding sides to the polygon 1 at a time, making the claim that it gets closer to being a circle each time but never actually becomes a perfect circle. It then made the claim that a perfect circle, therefore, is a polygon with infinite sides and as a result has infinite surface area. If someone is just... really gullible, gave it zero actual thought, and hasn't taken middle school level math, it could have been convincing.

But is a perfectly straight section of coastline infinite?