Proof without words

Proof without words of the Nicomachus theorem (Gulley (2010)) that the sum of the first n cubes is the square of the nth triangular number

In mathematics, a proof without words (or visual proof) is an illustration of an identity or mathematical statement which can be demonstrated as self-evident by a diagram without any accompanying explanatory text. Such proofs can be considered more elegant than formal or mathematically rigorous proofs due to their self-evident nature.[1] When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.[2]

A proof without words is not the same as a mathematical proof, because it omits the details of the logical argument it illustrates. However, it can provide valuable intuitions to the viewer that can help them formulate or better understand a true proof.

  1. ^ Dunham 1994, p. 120
  2. ^ Weisstein, Eric W. "Proof without Words". MathWorld. Retrieved on 2008-6-20