Sugihara's Impossible Circle/Square Illusion
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This example demonstrates Kokichi Sugihara's geometric illusion that appears as a circular cylinder from one angle and a square cylinder from another. It involves core math concepts like parametric curves, coordinate geometry, solid geometry, and optical illusions. Constructed using GeoGebra's CurveCartesian command with parameters a, b, A, B, C, D. Suitable for high school students and above exploring geometric transformations, visual arts, and the intersection of mathematics.
GeoGebra Commands & Parameters
CurveCartesian(t, (1 / 2 * (1 - abs(t) + sqrt(1 - t^(2)))), (1 / 2 * (sqrt(1 - t^(2)) - 1 + abs(t))), t, -1, 1) → aCurveCartesian(t, (1 / 2 * (-1 + abs(t) - sqrt(1 - t^(2)))), (1 / 2 * ((-sqrt(1 - t^(2))) + 1 - abs(t))), t, -1, 1) → b
AI Drawing Prompt Reference
Create a geometric illusion that appears as a cylindrical shape from one angle and a square cylindrical shape from another. First, draw a parametric curve with the equation t, (1/2 * (1 - abs(t) + sqrt(1 - t^2))), (1/2 * (sqrt(1 - t^2) - 1 + abs(t))), from -1 to 1, then draw another parametric curve with the equation t, (1/2 * (-1 + abs(t) - sqrt(1 - t^2))), (1/2 * ((-sqrt(1 - t^2)) + 1 - abs(t))), also from -1 to 1.
The prompt above was compiled from the original drawing commands and is for reference only.