Questions tagged [proof-without-words]

For questions concerning the creation and understanding of pictorial proofs.

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 formal or mathematically rigorous due to their self-evident nature. When the diagram demonstrates a particular case of a general statement, to be a proof, it must be generalisable.

For example, the following is a proof of the Pythagorean Theorem due to Martin Gardner.

Explain this calculus proof without words

This demonstrates that $\int_0^1 t^{p/q} + t^{q/p} dt = 1$. Could you please explain how the proof without words shows that?

proof-without-words

asked Oct 27 '13 at 03:52

user103493

vote

1 answer

Is there a dissection proof of the Pythagorean Theorem, such that a single cut makes the needed pieces from the squares?

Can you cut the squares of a right triangle with one cut (cutting all three pieces at the same time) so that it’s possible to arrange them and prove Pythagoras’ theorem?

proof-without-words

asked Nov 08 '18 at 08:34

lukejanicke