FACTOID # 10: The total number of state executions in 2005 was 60: 19 in Texas and 41 elsewhere. The racial split was 19 Black and 41 White.
 
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Encyclopedia > Missing square puzzle

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. 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 two-dimensional 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 long-running 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 cut-the-knot
  • A Faulty Dissection: What Is Wrong? at cut-the-knot

  Results from FactBites:
 
Missing square puzzle - Wikipedia, the free encyclopedia (274 words)
The key to the puzzle is the fact that neither of the 13x5 "triangles" has the same area as its component parts.
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.
The Five Square Puzzle (854 words)
Puzzle addicts are familiar with the type that appears in The Age each Saturday.
The central square is blank but has a value equal to one of the letters, which we must find; let us call it "x" initially.
Comments are very useful in keeping track of which row/col you have used; also, it helps to mark in the puzzle table which letters you have already involved by putting a dot near them, ie.
  More results at FactBites »

 
 

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