Timeline for Proofs without words
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Dec 6, 2019 at 14:36 | history | edited | Denis Serre | CC BY-SA 4.0 |
I avoid the use of $A$ for the area, when it also denotes a vertex.
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| Jun 8, 2016 at 14:44 | comment | added | Yaakov Baruch | This same proof also appears at the very opening of this paper: arxiv.org/abs/1301.0352 | |
| Jun 17, 2014 at 2:59 | history | edited | senshin | CC BY-SA 3.0 |
rehost to imgur to prevent linkrot
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| Nov 13, 2012 at 1:22 | history | edited | Igor Khavkine | CC BY-SA 3.0 |
Fixed image links again.
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| Mar 12, 2011 at 11:51 | history | edited | Igor Khavkine | CC BY-SA 2.5 |
Fixed broken image links.
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| May 18, 2010 at 19:04 | comment | added | Vaughn Climenhaga | There is an analogous proof using the fact that although the hyperbolic plane has infinite area, a triply asymptotic triangle has finite area, so once you pick one of the two triply asymptotic triangles containing your triangle, you're in business. The relevant picture's in my answer posted separately (I posted it before I had the reputation to leave comments): mathoverflow.net/questions/8846/proofs-without-words/… | |
| Apr 26, 2010 at 20:57 | comment | added | Igor Khavkine | Incidentally, I tried to find a similar proof for the area formula for hyperbolic triangles. Unfortunately, that did not work due to non-compactness of hyperbolic space. If anyone knows whether such a proof exists, I'd be happy to see it. | |
| Apr 26, 2010 at 20:55 | comment | added | Igor Khavkine | Haha, I'm happy to see these illustrations useful to someone! I created them some years ago, mainly to crystalize what I saw in my minds eye after finding some simple proofs of this identity online. The words accompanying these images can be found at planetmath.org/encyclopedia/AreaOfASphericalTriangle.html Also, original MetaPost source can be obtained from this unfortunately obscure link: images.planetmath.org:8080/cache/objects/5841/src/sph-tri.mp | |
| Feb 22, 2010 at 22:31 | comment | added | John Stillwell | Thomas Harriot first proved this formula in 1603, apparently by a similar argument, though I have not seen his picture(s). | |
| Feb 22, 2010 at 15:25 | history | answered | CuriousUser | CC BY-SA 2.5 |