Triangle puzzle – How can the following be true?

Some people refer to this as “Curry’s Paradox,” but this illusion is actually listed on Wikipedia as “the missing square puzzle.” It is an optical illusion created by Paul Curry, and used in mathematics classes to help students reason about geometrical figures.

It depicts two arrangements of shapes, each of which apparently forms a 13×5 right-angled triangle, but one of which has a 1×1 hole in it.

The solution: The key to the puzzle is the fact that neither of the 13×5 “triangles” is truly a triangle, because what would mean the hypotenuse is bent. In other words, the hypotenuse does not maintain a consistent slope, even though it may appear that way to the human eye. A true 13×5 triangle cannot be created from the given component parts.

Click on the following picture to see the animation.

By the way, Curry’s paradox is named after the logician Haskell Curry, while the missing square puzzle is by Paul Curry.

Animation via imgur.