Socks and Puppets | website | Bluesky | @ahdok@ttrpg.network

Transcript

An informational diagram showing different (bad) ways to cut a circular pizza.

  1. A grid cut, labelled “Tic-Tac-Toe”
  2. a regular 8-way cut, but the middle is very off center, labelled “Off-Center Inequality.”
  3. A six-slice cut where each cut is a sinusoidal curve, labelled “Apple Beachball”
  4. A spiral that goes all the way to the middle, labelled “Spiral Cut”
  5. Looks normal, but is labelled “Just draw the lines on with a sharpie”
  6. Regular shaped slices cut out of the middle of the pizza in random positions, labelled “Why”
  7. A side view, showing two long horizontal cuts through the entire disc, labelled “Layer Cake”
  8. Mostly diagonal lines splitting the pizza into shapes, labelled “Tangram”
  9. Two identical pizzas, labelled “Banach-Tarski”
  • palordrolap@fedia.io
    10·
    1 day ago

    It’s pretty simple, really. There’s a mathematical way of creating a complete cover of all points within a sphere in a finite number of subsets in such a way that those finite subsets can be rearranged into two complete spheres of the same size.

    It’s kind of like how there are exactly as many points between 0 and 1 on a number line as there are between 0 and 2, so if you take a 0 to 1 segment, and then multiply all distances by 2, you can cut it into two pieces with exactly as many points as the original 0 to 1.

    This is the sort of thing that only works with mathematical abstractions, which is why it’s paradoxical. You sure as heck can’t do this with a pizza, even if it’s technically isomorphic to a sphere.

      • palordrolap@fedia.io
        1·
        22 hours ago

        Imagine a stretchy piece of elastic that doesn’t change cross-section when pulled and doesn’t snap back. (This is mathemagic elastic. A regular rubber band gets thinner and narrower in cross-section when pulled. Also they tend to snap back.)

        Stretch it to twice its length and then cut it at the halfway point. You now have two stretchy pieces of elastic just like the first one.

        If this bothers you that something is apparently being created from nothing, that’s why Banach-Tarski is called a paradox.