Series

Taughtratio — the series

3 essays on one idea, from the one that introduces it to the one that assumes the rest.
  1. the pavement implies a horizon 171 px off the topthe horizon the panel drewcorrect from 12 cm at 160 mm wide9.2 px from the truth, 0.17 px from a perspective

    The rule that draws another room

    The taught rule for spacing receding boards — each gap a fixed fraction of the last — is not a projection of anything, and it produces a pavement that is a correct perspective to within a fifth of a pixel. Of a room whose horizon is a hundred and seventy pixels from the one the panel drew. The error is not incoherence; it is a disagreement between two halves of one drawing.

    part 1 · wrong
  2. 00.50011.5000.5001the lens's radial coefficient, −k₁the worst transversal's distance from a correct perspective, in pxa reader's ruler, 0.2 pxk₁ = −0.40a photographed pavement, against its lens5.7 px of bow at the threshold

    The lens a pavement can hide

    A photographed pavement reads as a correct drawing up to a radial coefficient of about four tenths — a lens strong enough to bow a straight edge across the page by nearly six pixels and to print as twenty per cent distortion at the frame's corner. The reason is that a pavement sits near the principal point, which is the one part of the frame a radial map barely touches.

    part 2 · lens
  3. 0.050.10.20.5125105101520braccia in the pavement, drawn to one page widthpixelsthe diagonal, by straightedgethe transversals, by fittingboth read on one pavement47× at eight braccia

    The rule is exact for a floor that lengthens

    The constant-ratio rule for spacing receding boards is an exact perspective — to the last digit, on the panel's own horizon — of a floor whose boards grow by the inverse of the ratio, 0.74 braccia deep at the front and 1.31 at the back on an eight-braccio pavement. The orthogonals agree with that floor. What says the tiles were meant to be square is a diagonal, which bends 8.1 pixels off straight where the reader's fitting test finds a sixth of one.

    part 3 · wrong

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