Hacker News Reader

I think OP is thinking about covering the sphere of directions in 3D space, not just directions in a 2D plane. No matter how hard you spin the pencil, you're drawing a one-dimensional curve that has no area, so any finite amount you draw will cover zero percent of the area of the two-dimensional sphere surface.

> No matter how hard you spin the pencil, you're drawing a one-dimensional curve that has no area

The object doesn’t matter, using pencil as the example was what threw you off - it’s not about what the pencil “draws”. Consider a thin cylinder, or rectangular prism, or just a stick - if you spin it around, its endpoints trace out a circle whose diameter is the length of the stick. You can move and spin such an object in another way where the shape traced out by its endpoints has smaller area than that circle.

Yes, and spinning the pencil on its centre like that shows that the circle (of pencil length diameter) is such a set. (I think you're thinking about it the wrong way around: it's which containing shapes allow this, not how can it be done at all.)

in 2d, but not in 3d though (like in the video on top of the article)!