4 ms·

I wrote about this years ago, and submitted it here on HN where I think it sank without trace. It's on this page: https://www.solipsys.co.uk/new/ConsideringASp

• defrost 3y ago
  Many moons ago, twixt primary school and high school, I enjoyed coming up with two derivations of the volume of a sphere remaining after removing the volume of a hole drilled from pole to pole (cylinder plus end caps). These things can get a little addictive :-)
  • recursive 3y ago
    Those end caps sound difficult.
    • defrost 3y ago
      There's a "surprising twist" on analysis. The question above is typically posed as (say) a hole of 2 units in length. That's all you get, the lip to lip length of the hole. Not the radius of the sphere, not the diameter of the hole - just the hole length. Nothing else (save the implication that it's solvable). There's a lengthy formula laden proof approach, and there's an Aha!! lighbulb moment solution.
      • deleted 3y ago
        [deleted]
• zem 3y ago
  that's very nicely done, as was the linked proof of archimedes' hatbox theorem