Talk:Compass equivalence theorem
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Reference to a false proof
editThe external link to http://web.mnstate.edu/peil/geometry/C2EuclidNonEuclid/1Compass.htm, present from the very first version of the article until now, actually points to a fallacious proof.
The proof has a heading line 'Exercise 2.2. The Rusty Compass Theorem'. Why is it an exercise?! Textbooks usually present some problems to be solved as exercises; sometimes it is some theorem to prove. But a proof itself? It might be a solution, an answer to an exercise, not an exercise itself. Am I right...?
Yes, I am. The exercise is announced on the previous page:
- 2.1.1 Introduction to Euclidean and Non-Euclidean Geometry
- http://web.mnstate.edu/peil/geometry/C2EuclidNonEuclid/1introduction.htm
in these words:
- Exercise 2.2. Identify the error or errors in the proof of the Rusty Compass Theorem.
Can you see? Identify the error or errors in the proof...! It is deliberately spoiled as an exercise in rigorous, precise proving techniques. And we have it as a reference proof...
I'm removing it. Right now. --CiaPan (talk) 21:10, 17 September 2015 (UTC)
False proof still presented as correct
editThis article still contains an incorrect proof, CiaPan removed the reference to it, but the representation still remains, even the image for it has the name of "rusty compass". I've improved the citation given by Dmcq, which contains the proof as it would appear in THE BOOK (;)) and I'll add an expert attention needed tag to this soon, and a subject matter classification. --No identd (talk) 18:12, 6 November 2018 (UTC)
- I'm not so sure that there is a problem here. The fallacious proof (but not its citation) was removed in 2010 and replaced by the current one. The rusty compass reference is clearly a misnomer (also due to that fallacious reference) as this proof has nothing to do with "rusty" (fixed aperture) compasses. The current proof appears to be a modernization of Euclid's proof, but I haven't checked the details. I can find several references for the construction in the second proof, but they don't include the proof of validity (this is left to the reader). --Bill Cherowitzo (talk) 22:42, 6 November 2018 (UTC)
- I just had a look and I saw the problem with the original proof straight away and I can't see any problem with the proofs in the article. I wouldn't have called the original proof fallacious, just it doesn't work when the radius is too big so I'd have called it incomplete. However I see the external link has the invalid proof and passes it as valid! I'll remove the external link. We really need citations on the two proofs. Dmcq (talk) 23:42, 6 November 2018 (UTC)
- I only used "fallacious" since that was the word that CiaPan used above. I've added references and removed the tags since there is nothing wrong with these proofs. I will also replace the diagram for the first proof with a less cluttered and easier to read one when I get a chance. --Bill Cherowitzo (talk) 19:52, 8 November 2018 (UTC)
- Thanks that looks good. Dmcq (talk) 23:00, 8 November 2018 (UTC)
- I only used "fallacious" since that was the word that CiaPan used above. I've added references and removed the tags since there is nothing wrong with these proofs. I will also replace the diagram for the first proof with a less cluttered and easier to read one when I get a chance. --Bill Cherowitzo (talk) 19:52, 8 November 2018 (UTC)