Thick and thin

Mar 5, 2021
Jordan curve illustrations: drawing the curve

There is a Jordan curve such that every piecewise-linear path from the inside to the outside intersects the curve infinitely many times. I describe how to draw such a curve here, and do so.
Mar 5, 2021
Jordan curve illustrations: wiggling a course

There is a Jordan curve such that every piecewise-linear path from the inside to the outside intersects the curve infinitely many times. I define the wiggling precisely here in terms of courses (turn-type sequences).
Mar 4, 2021
Jordan curve illustrations: a triangular example

There is a Jordan curve such that every piecewise-linear path from the inside to the outside intersects the curve infinitely many times. I sketch the construction of such a curve here.