# Talk:2042: Rolle's Theorem

Now we wait for https://en.wikipedia.org/wiki/Munroes_theorem. 172.69.54.165 15:51, 5 September 2018 (UTC)

- Can't wait to see how long it takes to remove the article. Linker (talk) 17:05, 5 September 2018 (UTC)

- Proposed ideas for Munroe's Law:
- - Any seemingly simple idea will be difficult to prove; the simpler it seems, the harder the proof.
- - Any proof which is discovered by a layperson will have been previously discovered by an expert (or an "expert") in the field.

- Raj-a-Kiit (talk) 17:57, 5 September 2018 (UTC)
- I do not have the time to do it good, so here a suggestion: Would someone go to the wikipedia page of Rolle's theorem and add a "in popular culture" section? may be a first? Not even "Nash equilibrum" has that :-) 162.158.234.16 08:13, 6 September 2018 (UTC)
- Speaking of popular culture, there's a (moderately) well known Ballad of Rolle's theorem Balada o vete Rolleovej ("moderately" meaning some people who studied at Faculty of mathematics in Bratislava might have heard (of) it) --Kventin (talk) 07:41, 7 September 2018 (UTC)

I feel like Euclid beat Randall to the punch here, a couple millennia. 162.158.155.146 16:54, 5 September 2018 (UTC)

I don't see that Thales has proven Randall's theorem. Do not to be confused with Thales's theorem, that's about right angles. Maybe I'm blind or just dumb, but if so it has to be explained with more traceable background. I just believe that this diagonal is so trivial that even the ancient Greeks weren't engaged on a proof. --Dgbrt (talk) 21:38, 5 September 2018 (UTC)

- From Wikipedia: Other quotes from Proclus list more of Thales' mathematical achievements: "They say that Thales was the first to demonstrate that the circle is bisected by the diameter, the cause of the bisection being the unimpeded passage of the straight line through the centre." Alexei Kopylov (talk) 05:39, 6 September 2018 (UTC)
- On the other hand not all historian believe Proclus. But van der Waerden does: [1]. Alexei Kopylov (talk) 05:49, 6 September 2018 (UTC)

**Rolle's Theorem counterexample?**

Isn't the TAN(x) function a counterexample to this? Starting at a given point, it rises to infinity, then returns from negative infinity to the same point without ever having a slope of zero. 172.68.58.89 06:58, 6 September 2018 (UTC)

- TAN(x) isn't differentiable at pi/2, hence the theorem doesn't apply--162.158.92.40 07:48, 6 September 2018 (UTC)
- And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. Fabian42 (talk) 08:01, 6 September 2018 (UTC)
- Nope: tan(x) has a slope of 1 at pi, and its slope is never less than 1. Of course, that doesn't make it a counterexample. Zetfr 09:17, 6 September 2018 (UTC)

- And tan(x) has a slope of 0 at pi, so even if it applied, it wouldn't prove it wrong. A better example would be 1/x, but still invalid. Fabian42 (talk) 08:01, 6 September 2018 (UTC)

**Clueless Museum Visitor**

The math in the comic is well explained, but shouldn't there be something about the "math equivalent of the clueless art museum visitor..." part? Zetfr 09:17, 6 September 2018 (UTC)

- Seconded, all the argument here is about math that isn't even *in* the comic, whereas the bit that confuses me is the cultural metaphor... 162.158.154.235 07:16, 7 September 2018 (UTC)
- I had a go.162.158.154.103 08:35, 7 September 2018 (UTC)

Just so we're on the same page, while the proof of Rolle's theorem is not completely trivial, neither is it difficult by any means. Proving it seems to be a pretty common homework assignment in undergrad math classes, for example, so one might legitimately ask why it deserved to be named. Perhaps it's simply that it's old enough that the methods at the time were crappy, and so modern proofs are much easier. 172.69.22.140

- It is named because it's a very important theorem in calculus, used to prove many other theorems or results. So when you need to prove something using this property, instead of re-demonstrating it or merely saying "it is well known that..." (which often raises alarm bells in the mind of the reader/corrector), all you have to do is reference Rolle's theorem.162.158.155.158 11:08, 6 September 2018 (UTC)
- It could almost be called "Rolle's lemma". 162.158.154.103 12:28, 6 September 2018 (UTC)

- When I am teaching Rolle's theorem, I always make it a point to draw the link to reals. Rolle's theorem fails when the output is complex valued. Then you can see for yourself how non-trivial this is. 162.158.165.124 04:40, 7 September 2018 (UTC)

Has anyone else noted the irony of having a wiki page to explain a comic whose subject is how some things are self-evident? JamesCurran (talk) 20:13, 6 September 2018 (UTC)

Does the Kepler Conjecture actually belong on that list at the end? Most of the others are "derp" level intuitively obvious and/or essentially tautological on a very basic level, but the Kepler Conjecture couldn't actually be exhaustively proven until machine computation, nor is it intuitively definitive--if you've ever stacked round things into a box you've noticed that it feels like you're wasting a lot of space at the edges. So...? AtrumMessor (talk) 21:37, 6 September 2018 (UTC)

- I would also argue against most of the other examples. Neither the isoperimetric inequality nor the hairy ball theorem are obviously true and their proof is quite a bit more involved than the one of Rolle's theorem. The Jordan curve theorem sounds obvious but then the proof definitely isn't. The parallel postulate isn't even a theorem. The only real good example in the list is the pigeonhole principle.162.158.91.155 12:35, 7 September 2018 (UTC)

I also suggest that Fundamental Theorem of Calculus be removed from this list. Firstly, the beginner student, just introduced to derivatives and antiderivatives, will not easily see that antiderivatives are the same as finding areas under curves. Instead, it is only obvious upon hindsight, after instruction. More importantly, a restriction of the FTC to better-behaved spaces shows a far greater insanity: the restricted FTC is a consequence of generalised Stokes's theorem **applied twice**. This operation is so highly unintuitive, that one simply cannot claim that this is in any way, shape, or form, trivial. I think that trying to pretend that anything in beginning calculus is obvious to students is just going to alienate them rather than soothe their worries. 162.158.165.124 04:40, 7 September 2018 (UTC)

"Munroe's theorem" should definitely refer to the circle thing in the alt text 162.158.62.57 (talk) *(please sign your comments with ~~~~)*

Since I'm half a mathematician, I did the math. I looked up Rolle's theorem and it uses the theorem of Weierstraß. I looked up the theorem of Weierstraß (better known as extreme value theorem) and it uses the theorem of Bolzano-Weierstraß. I looked up...why am I suddenly reminded of https://xkcd.com/609 ? :-) 141.101.104.71 08:36, 7 September 2018 (UTC)