Matpic
mathematics, in pictures
Ladder

Arc length — the ladder

One essay so far against this idea. A ladder is the distinct arguments that stand against one idea, and this one has room to grow.
  1. 1 steplength 2.00gap 0.7072 stepslength 2.00gap 0.2584 stepslength 2.00gap 0.14316 stepslength 2.00gap 0.035every staircase is exactly 2 long; a quarter circle is 1.5708 longthe finest one here is never more than 0.035 away from the curve, and it is still 2 long

    The staircase that is not the diagonal

    A staircase can be made to follow a quarter circle as closely as anyone likes. Its length is 2 at every stage and the arc's length is 1.5708, and no amount of refinement closes the gap — which is a fact about length rather than about staircases.

    rung 1 · analysis

All ladders