Series

Poleandpolar — the series

2 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. the pointone point, one conicconstructed and computed agree to 2e-13

    The polar with a straightedge

    Two secants through a point cut a conic at four places; the complete quadrangle they make has two more diagonal points; the line through those is the polar. Not one length, angle or midpoint is used, so the whole construction survives the projection that made the picture — and three unrelated pairs of secants land on the same line to 4.3e-13, while moving the point moves it by fifteen orders of magnitude more.

    part 4 · foundations
  2. the photographv1v2v3orthocentre = principal pointcorrect from 4 cm, at 30 mm wideself-polar to 3.1e-13 px · orthocentre 1.4e-13 px

    The triangle a camera cannot move

    Three mutually perpendicular directions give three vanishing points, and that triangle is self-polar with respect to the image of the absolute conic — to 3.1e-13 px, with no length and no angle anywhere in the statement. Turn one direction two degrees out of square and the polars miss their sides by 65.8 px. The statistic this collection has been printing as evidence for the same claim, meanwhile, is an identity that cannot fail.

    part 5 · foundations

All series