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.
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