At some point in your life, you've probably played this game of logic known as the
missing square puzzle, or
Curry's paradox - named after its inventor Paul Curry. This optical illusion is commonly used in mathematics classes to help students reason about geometrical figures, or rather to teach them to not reason using figures, but only using the textual description thereof and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle, but one has a 1×1 hole in it.
As depicted in the animation, the illusion works because the diagonal of the two internal triangles is
not a continuous slope from corner to corner. The overall connected shape is not a geometric triangle with 3 sides, but an arbitrary 4-sided quadrilateral. The first has a depression (concave), the second a bulge (convex). Thus, the area of the vacant square is equal to the area between the two bent slopes.
