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Graeme J. Kennedy, Harry S. Orbach, Gunter Loffler; Shape can bias angle perception: An angle illusion. Journal of Vision 2006;6(6):22. doi: 10.1167/6.6.22.
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© ARVO (1962-2015); The Authors (2016-present)
Introduction: There are numerous examples of geometric illusions based on the distortion of angles (e.g. Zöllner Illusion). We present evidence for what we believe to be a novel illusion where angles are misjudged depending on the triangular shape containing the angle.
Methods: A temporal 2AFC paradigm was used to measure angle discrimination. Individual trials showed an isosceles and a scalene triangle (various scalene shapes given by different side length ratios) and subjects were asked to judge which of the two contained the more obtuse angle. The point of subjective equality, defined as the angle that yielded a judgement of “more obtuse” in 50% of the trials, was determined from psychometric functions. Five reference angles were tested.
Results: For a reference angle of 60 degrees, angles embedded in isosceles triangles were judged to be 7.3, 15.2 and 17.4 degrees larger than angles embedded in scalene triangles with side length ratios of 1.7:1, 3.0:1 and 5.7:1, respectively. This illusion holds for different reference angles: for angles of 30, 50, 60, 90 and 120 degrees respectively, angles in isosceles triangles were judged to be 10.4, 18.0, 15.2, 12.3 and 11.9 degrees larger than angles in scalene triangles (side length ratio 3:1).
Conclusions: An angle embedded in an isosceles triangle is judged substantially larger than the same angle embedded in a scalene triangle. The effect that the global triangular shape has on the local angle judgement is paradoxical: a shorter side opposite the angle yields a larger angle judgement.
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