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In this illusion, the vertical lines in the above figure are parallel, but appear to be tilted at an angle. In 1860, F. Zöllner sent his discovery in a letter to physicist ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

A regular two-dimensional arrangement of squares separated by vertical and horizontal "canals." Looking at the grid produces the illusion of gray spots in the white area ...

Radial line segments whose inward-pointing end produce the illusion of a circle or other figure. The apparent figure has the same color as the background, but appears ...

The illusion due to psychologist Edward Bradford Titchener that a circle surrounded by other circles will appear smaller if the surrounding circles are enlarged. This effect ...

The tribox, also called the Penrose rectangle or Penrose square, is an impossible figure that is the generalization of the Penrose triangle from a triangle to a square. ...

The 4-polyhex illustrated above (Gardner 1978, p. 147).

A polyhex consisting of hexagons arranged along a line.

The 4-polyhex illustrated above.