Earlier quoted context omitted.
People don't tend to find that unintuitive. The Greeks had a nice geometric example in a square of side length 1: ┌┬┬─┬───┬───────┐ ├┘│3│ │ │ ├─┘-│ │ │ │ 64│ │ │ ├───┘ │ │ │ │ │ │ 3/16 │ │ │ │ │ ├───────┘ │ │ │ │ │ │ │ │ 3/4 │ │ │ │ │ │ │ └───────────────┘ 3/4 + 3/16 + 3/64 + 3/256 + ... is easy to visualize as successively filling in three quarters of an ever-smaller residual square. Intuitively, no matter how finel…
Now squeeze the top-left piece so it's half as wide but twice as tall (i.e. the same height as the full rectangle), and do this recursively. Same area, right? Then stack the L shapes on top of each other. Then you have one of these horns.
Huh? The horn is a three-dimensional object; the square exists in 2-space. You can't make the horn from pieces of the square even if you allow deformation.