Timeline for Proofs without words
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 17, 2022 at 21:09 | comment | added | Honest Abe |
This is not a proof without words: It's a trick question invented by an "amateur magician" which exploits the fact that the combined geometry looks like a 13x5 triangle. For us it's an exercise in exposing an optical illusion. Why would we try to prove that a statement that is explicitly false (e.g. 32.5 = 31.5) is in fact true?
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| Dec 7, 2020 at 18:21 | comment | added | Toby Bartels | And if you use the actual area of the figure, it proves that 31.5 and 32.5 are both also equal to 32. | |
| Oct 15, 2019 at 12:26 | comment | added | pseudosudo | This argument against proofs by picture is itself a proof by picture. | |
| Sep 26, 2017 at 7:20 | history | edited | Peter Heinig | CC BY-SA 3.0 |
In the process of searching for something else, I stumbled over this and took the liberty of adding an animated gif, with a reference. The colors match the static illustrations. This seems a valuable addition. Style of answer respected. In particular: did not explain the 'paradox'.
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| Jan 23, 2015 at 2:53 | comment | added | Todd Trimble | It might be noted that the success of the illusion partly depends on the fact this uses Fibonacci numbers (it is a coincidence I guess that the next newest answer is also about Fibonacci numbers!). | |
| Oct 25, 2014 at 7:17 | comment | added | PKumar | +1 , Here is the wiki page for this. en.wikipedia.org/wiki/Missing_square_puzzle | |
| Jun 17, 2014 at 2:40 | history | edited | senshin | CC BY-SA 3.0 |
rehost to imgur to prevent linkrot
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| Nov 29, 2010 at 1:04 | comment | added | Peter LeFanu Lumsdaine | @Pietro: “there is a very strong sense in which written proofs may be formalised”? Formalisation is a highly non-trivial task, and typically depends on quite a lot of mathematical background. What affects the difficulty is not whether the proof is written or graphical, but whether it’s detailed or highly abstracted. Formalising a good proof-by-picture is no harder than formalising a high-level written proof. Insofar as there’s a difference, I’d say it’s just that written proofs can be made detailed enough that formalising them is straightforward, whereas picture proofs perhaps can’t. | |
| May 15, 2010 at 20:22 | comment | added | Pietro | @Steven: I think there is some truth to your claim, but I don't agree fully. First, we may notice that most proofs rely much more on writing than on pictures, and so mathematicians have developed a better radar for "written gaps". Second, there is a very strong sense in which written proofs may be formalized and checked by computer. Picture proofs, unless they share quite a bit of the "discrete" character of written proofs, usually are not amenable to such treatment. (And the notions of discreteness I can think of pretty much ensure that the picture proof could be turned into words.) | |
| Mar 7, 2010 at 23:41 | comment | added | Steven Gubkin | I think it is just as easy to introduce some kind of logical gap in a written proof as in a graphical one. | |
| Mar 7, 2010 at 2:16 | history | answered | Russell O'Connor | CC BY-SA 2.5 |