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 rightangled triangle, but one of which has a 1x1 "hole" in it. A optical illusion is a type of illusion characterized by visually perceived images that are deceptive or misleading [1]. Information gathered by the eye is interpreted by the brain to give the perception that something is present when it is not. ...
Euclid, detail from The School of Athens by Raphael. ...
A triangle is one of the basic shapes of geometry: a twodimensional figure with three vertices and three sides which are straight line segments. ...
The key to the puzzle is the fact that neither of the 13x5 "triangles" has the same area as its component parts. Missing Square Puzzle, my own drawing of it File links The following pages link to this file: Missing square puzzle Categories: GFDL images ...
An example of a simple puzzle. ...
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. For alternate meanings, such as the musical instrument, see triangle (disambiguation). ...
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 was invented by a New York city amateur magician Paul Curry in 1953. Ever since it has been known as Curry's paradox. The principle of a dissection paradox has however been known since the 1860s. Martin Gardner (born October 21, 1914) is an American recreational mathematician, magician, skeptic, and author of the longrunning but now discontinued Mathematical Games column in Scientific American. ...
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. In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ...
In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ...
External links
 How can this be true?
 Curry's Paradox: How Is It Possible? at cuttheknot
 A Faulty Dissection: What Is Wrong? at cuttheknot
