Sugihara’s Circle/Square Optical Illusion

David Richeson: Division by Zero

[Update: Check out my second post in which I provide a template so you can make your own Sugihara circle/square object out of paper.]

Kokichi Sugihara created a video called Ambiguous Optical Illusion: Rectangles and Circles. In it he shows a variety of 3-dimensional objects that look like one shape when viewed from the front but look like a different shape in the mirror behind it.

In this blog post we show how he achieved the effect. For simplicity, we will show how he made a shape that looks like a circular cylinder from the front and a square cylinder in the mirror.

The following applet shows our final product (clicking the image links to the GeoGebra applet). It is a closed curve that represents the top rim of Sugihara’s shape. You can rotate the axes with your mouse. If you view the coordinate system with the positive green and…

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