Paradoxical Elastic Squares

A math-magic article I wrote for the German magazine Zeit Wissen: with the 13 triangular and square pieces (fig. 1) it is possible to form two large squares shown in fig. 2. Though the second large square has an extra piece the dimensions of the squares seem to be the same! Can you explain why this is possible?

This puzzle is available as greeting cards from my online store.

Moona Lisa

In 1997, I remixed the Leonardo da Vinci’s famous painting Mona Lisa into 142 perfectly spaced color beads placed at the intersections of an imaginary two-dimensional triangular network. Close up, the picture of the set of beads makes no sense, but if you see it from a distance you will perceive (or at least ‘guess’?) the portrait of Mona Lisa, the most famous Leonardo Da Vinci’s painting.

hidden mona lisa
Hidden Mona Lisa (1997), © Gianni A. Sarcone

Ghost Colors

This is one of my earliest color optical illusions. There is no yellow or green in the diamond shapes, just vertical black lines! (If you don’t believe it, use a eyedropper tool to check it.) This intriguing visual effect is mainly due to “color contrast induction“.

Illusive colors
Ghost Squares / Black Diamonds (2002 – 2007)
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Scintillating Starburst: Seeing rays that aren’t there…

This is one of my oldest illusions I created in the 90s. In the picture you may see ghostlike dark radial beams. This illusion is a variant of the Herman’s scintillating grid illusion. I designed this illusion just by turning 45 degrees the Herman grid and then by applying a polar transformation.

From my book “Eye Tricks“, 2001-2007.
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