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Parallel Lines

Six long slanting lines, crossed with short strokes, and a question about whether they run side by side.

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Six long slanting lines, crossed with short strokes, and a question about whether they run side by side.

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Angles that grow

The long lines are exactly parallel. Each short stroke meets its long line at a sharp angle, and a sharp angle tends to be seen as wider than it is; the strokes on neighbouring lines lean opposite ways, so every line is pushed the opposite way from its neighbour and they seem to splay apart and close together.

The astrophysicist Johann Karl Friedrich Zöllner came across the effect in 1860 in a pattern printed on fabric. It is one of a family — Hering’s bowed lines and Poggendorff’s hidden line belong to it too.

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