Talk:Proof without words

Proof of Pythagorean theorem
I'm having some difficulty seeing how the diagram constitutes a proof of the Pythagorean theorem. Perhaps it is too subtle for me. But even if it is a proof, does it apply to all right angled triangles, or only 3-4-5 ones? Rjm at sleepers (talk) 04:40, 24 June 2008 (UTC)
 * All of them. Try to express the area of the square in two different ways. It seems self-evident to me, and apparently to the author of my reference. Nousernamesleft copper, not wood 19:45, 24 June 2008 (UTC)
 * It is an evergreen that has graced more than one cover of a maths book. 2A01:CB0C:CD:D800:D987:899A:3E01:2296 (talk) 08:21, 30 October 2022 (UTC)

The article said to "see" the historical Chinese-text diagram File:Chinese pythagoras.jpg in 2008, with no explanation in all this time of what was happening. Great if you already know it, not so much if you don't. I've rewritten the section to give a clearer explanation, and used a different illustration. --Belbury (talk) 09:03, 30 October 2022 (UTC)

Suggestion for a subsection topic
In rewriting systems one ca do diagrammatic proofs (without words) that have a precise meaning. Take a look at one of the books listed in references there. Sadly, no such proof appears in any of the related articles yet. Pcap ping  06:27, 23 August 2009 (UTC)

Assessment comment
Substituted at 02:31, 5 May 2016 (UTC)

Being clear about proofs without words vs. formal proofs
I added some material to make it more obvious that mathematicians typically would not accept a proof without words as a genuine proof of something. Pictures can easily be misleading, by glossing over important details that come to light when you approach the argument deductively. I really would not want a casual reader to come across this page and get the idea that they can substitute a picture or informal thought experiment for a rigorous argument when they want to prove something mathematical—as long as they hang onto that idea it will harm their mathematical development. I don't think many people get much experience with proofs in their grade school math classes (definitely not in the U.S. where I live) so it seems to me like there's a real risk of that happening if we're not careful to avoid it. Mesocarp (talk) 03:16, 27 October 2022 (UTC)


 * Yes, the layperson should understand that these are classroom demonstration objects. It is just fun to point out to the student that everything is right there in the picture. In maths folklore we have a zoo of jocular "proof principles" that are not proofs at all, e.g. proof by obfuscation, proof by mutual attrition, proof by total intimidation. Also, "without words" is itself a bit tongue in cheek. I find I do need to talk myself through the bits and pieces that are on display before I understand what is going on. 2A01:CB0C:CD:D800:D987:899A:3E01:2296 (talk) 08:19, 30 October 2022 (UTC)

Proof by Lego/Meccano
Sometimes considerable clarity is gained in a proof without words by having moving parts in the graphical representation. This can be achieved with construction toy and the modern overhead projector which illuminates from above (and which actually gives a depth of focus of a good few inches --- it's not just for display on paper). 2A01:CB0C:CD:D800:D987:899A:3E01:2296 (talk) 08:15, 30 October 2022 (UTC)