Robert C. Haraway, III
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Thick and thin

  • Mar 10, 2021

    Representing permutations relatively compactly

    Here is a more relative way to represent a permutation with the same economical number of bits.

  • Mar 6, 2021

    Representing permutations compactly

    Here is a way to represent a permutation with a fairly economical number of bits.

  • 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.

  • Sep 18, 2020

    Jordan curve illustrations: better pictures

    This post has pictures suggesting a better example of a Jordan curve, using the isotopies suggested last time.

  • Jul 11, 2020

    Jordan curve illustrations: idea for a better example

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

  • Jul 3, 2020

    Jordan curve illustrations: attempts

    The Jordan curve theorem is famously simple to state and tricky to prove. I want to explain why the Jordan curve theorem ought to be difficult to prove, by showing some pictures of very complicated Jordan curves.

  • Jun 26, 2020

    Whence topology: main concepts

    Having introduced you to the swamp and the monsters, let me finish by sketching the structures used to make some sense out of it all.

  • Jun 16, 2020

    Whence topology: monsters

    The swamp of topology has monsters lurking inside.

  • Jun 15, 2020

    Whence topology: the swamp

    One is lured into the field of topology by the beauty of the previous problems. But serious attention to the subject reveals a swamp of difficulty with definitions.

  • Jun 12, 2020

    Whence topology: problems

    I like to study topology. These first few blog posts will explain what it’s about. This first discusses some motivating problems.

Thick and thin

  • Robert C. Haraway, III
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