# Missing square illusion - Optical Illusions

## Missing square illusion

The missing square puzzle is an optical illusion used in mathematics classes, to
help students reason about geometrical figures. It depicts two arrangements of
shapes, each of which apparently forms a 13x5 right-angled triangle, but one of
which has a 1x1 "hole" in it.

The key to the puzzle is the fact that neither of the 13x5 "triangles" has the
same area as its component parts.

The four figures (the yellow, red, blue and green shapes) total 32 units of
area, but the triangles are 13 wide and 5 tall, which equals 32.5 units. The
blue triangle has a ratio of 5:2, while the red triangle has the ratio 8:3, and
these are not the same ratio. So the apparent combined hypotenuse in each figure
is actually bent.

The amount of bending is around 1/28th of a unit, which is very difficult to see
on the diagram of this puzzle, though just about possible.

According to Martin Gardner, the puzzle has been invented by a New York city
amateur magician Paul Curry in 1953. Ever since it has been known as Curry's
paradox.

You may have noticed that the integer dimensions of the parts of the puzzle (2,
3, 5, 8, 13) are successive Fibonacci numbers. Many other geometric dissection
puzzles are based on a few simple properties of the famous Fibonacci sequence.