Ladder

Ballrecovery — the ladder

2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
  1. the eyecorrect from 9 cm, at 160 mm wideoutlines agree to 6e-12 px

    One picture of a ball

    The outline of a ball in a photograph fixes the cone of rays that graze it, so the cone's axis is the direction of the ball's centre and its half-angle is the arcsine of radius over distance — both exactly, and neither of them separately. A ball a hundred and thirty-seven times larger, a hundred and thirty-seven times further away, draws the identical conic. And the drawn ellipse's own centre is not the image of the ball's.

    rung 4 · metrology
  2. 020406012345the baseline between the two eyes (metres)angle between the cone axes (°)42.6°two cones, one ballcentre to 9e-7°

    Two pictures of a ball

    Two outlines give two tangent cones, and where their axes cross is the ball's centre — with the radius following from either half-angle. There is no correspondence problem, because a ball's outline in one picture and its outline in another are guaranteed to be the same ball; and there is a degeneracy, which is the two eyes and the ball in a line, and the solver refuses it rather than returning something plausible.

    rung 5 · metrology

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