In mathematics, a proof without words is a proof 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 more formal and mathematically rigorous proofs due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be able to be generalised.
Famous quotes containing the words proof and/or words:
“If any doubt has arisen as to me, my country [Virginia] will have my political creed in the form of a “Declaration &c.” which I was lately directed to draw. This will give decisive proof that my own sentiment concurred with the vote they instructed us to give.”
—Thomas Jefferson (1743–1826)
“and the words never said,
And the ominous, ominous dancing ahead.
We sat in the car park till twenty to one
And now I’m engaged to Miss Joan Hunter Dunn.”
—Sir John Betjeman (1906–1984)