Proof without Words
A proof that is only based on visual elements, without any comments.
An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical quantities. The above figure shows that the difference between
the 
th pentagonal
number and 
is equal to three times the 
th triangular
number. Of course, the situation depicted is a particular case of the formula
(here it corresponds to 
), but it is
presented in a way that can be immediately generalized.
Another form of proof without words frequently used in elementary geometry is the dissection proof.
This entry contributed by Margherita Barile
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.
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Barile, Margherita. "Proof without Words." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. http://mathworld.wolfram.com/ProofwithoutWords.html
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