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| | :[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|talk]]) 17:57, 5 September 2018 (UTC) | | :[[User:Rajakiit|Raj-a-Kiit]] ([[User talk:Rajakiit|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 :-) [[Special:Contributions/162.158.234.16|162.158.234.16]] 08:13, 6 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 :-) [[Special:Contributions/162.158.234.16|162.158.234.16]] 08:13, 6 September 2018 (UTC) |
| − | ::Done. [[User:Kmote|Kmote]] ([[User talk:Kmote|talk]]) 17:56, 10 September 2018 (UTC)
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| | ::Speaking of popular culture, there's a (moderately) well known Ballad of Rolle's theorem [https://www.youtube.com/watch?v=S0BXv90MlhA Balada o vete Rolleovej] ("moderately" meaning some people who studied at Faculty of mathematics in Bratislava might have heard (of) it) --[[User:Kventin|Kventin]] ([[User talk:Kventin|talk]]) 07:41, 7 September 2018 (UTC) | | ::Speaking of popular culture, there's a (moderately) well known Ballad of Rolle's theorem [https://www.youtube.com/watch?v=S0BXv90MlhA Balada o vete Rolleovej] ("moderately" meaning some people who studied at Faculty of mathematics in Bratislava might have heard (of) it) --[[User:Kventin|Kventin]] ([[User talk:Kventin|talk]]) 07:41, 7 September 2018 (UTC) |
| | ::Proposed idea for Munroe[[wikipedia:Apostrophe#Smart quotes|’]]<nowiki/>s Law: | | ::Proposed idea for Munroe[[wikipedia:Apostrophe#Smart quotes|’]]<nowiki/>s Law: |
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| | :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.[[Special:Contributions/162.158.91.155|162.158.91.155]] 12:35, 7 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.[[Special:Contributions/162.158.91.155|162.158.91.155]] 12:35, 7 September 2018 (UTC) |
| | :I have removed all but that, as it is the only one comparable to Rolle's in simplicity to understand without understanding math. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 14:04, 7 September 2018 (UTC) | | :I have removed all but that, as it is the only one comparable to Rolle's in simplicity to understand without understanding math. --[[User:Kynde|Kynde]] ([[User talk:Kynde|talk]]) 14:04, 7 September 2018 (UTC) |
| − | ::I agree, Randall mentions nothing like that and a simple parallel is enough. --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 14:25, 7 September 2018 (UTC)
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| − | ::I would argue that a lot of them could have stayed. Just because some of the examples given do have a lot of "hidden" mathematical complexity and are important bases for mathematical fields does not mean they are not useful parallels to the comic's example. In fact, one that comes to mind is the infamous 300-page Russell/Whitehead proof of 1+1=2. If anything, the more axiomatically complex but intuitively, even stupidly obvious something is, the BETTER it fits. My original point was that the Kepler Conjecture felt like a "which one of these things is not like the others" situation in the original list, as it was not at all easily proven, nor is it intuitively obvious. Some of these were actually pretty useful examples and should have been left, no matter how foundational they are to calculus ;) [[User:AtrumMessor|AtrumMessor]] ([[User talk:AtrumMessor|talk]]) 06:46, 9 September 2018 (UTC)
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| | 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. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 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. [[Special:Contributions/162.158.165.124|162.158.165.124]] 04:40, 7 September 2018 (UTC) |
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| | :Ehh what? No, FTC restricted to smooth functions is simply a special-case of Stokes' Theorem. This is explained [https://en.wikipedia.org/wiki/Stokes%27_theorem#Introduction here]. I don't even know what you could possibly mean by applying Stokes' theorem twice, in any context. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 13:23, 7 September 2018 (UTC) | | :Ehh what? No, FTC restricted to smooth functions is simply a special-case of Stokes' Theorem. This is explained [https://en.wikipedia.org/wiki/Stokes%27_theorem#Introduction here]. I don't even know what you could possibly mean by applying Stokes' theorem twice, in any context. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 13:23, 7 September 2018 (UTC) |
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| − | :: ``FTC restricted to smooth function is simply a special case of Stokes's theorem"" is basically what I said, although FTC proper applies to a wider range of functions. As to applying Stokes's theorem twice, remember that the differential form for areas is A = iint dw, where dw = dx ^ dy. You apply once to get that A = oint w, where oint runs around the entire boundary of the area to be considered. Then you have to use some smarts to zero the contributions from 3 of the 4 sides, leaving just the contribution from the x-axis. Then the boundary, which is supposed to have no boundary itself, gets two new boundaries, of which then you can apply another Stokes's theorem to get the F(b)-F(a) result. Again, this process is highly non-trivial, as evidenced by your failure to see what I meant from the first time talking about it. Pardon if the IP changed, it is me. [[Special:Contributions/162.158.167.60|162.158.167.60]] 04:48, 9 September 2018 (UTC)
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| − | ::: No it isn't "basically" what you said. I know FTC applies to a wider range of functions, that's why I said "restricted to smooth functions". I have not even the slightest idea what process you're trying to explain or why you're talking about 2D integrals. FTC restricted to smooth functions ''is exactly'' Stokes restricted to a line-segment, there is no "process". Again, [https://en.wikipedia.org/wiki/Stokes%27_theorem#Introduction this wikipedia section] explains this quite well, albeit informally. [[User:Zmatt|Zmatt]] ([[User talk:Zmatt|talk]]) 11:01, 10 September 2018 (UTC)
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| − | :::: You seem to be missing what I am referring to. There are at least two parts. Let's start with the main one. You keep referring to the same place of the same article. That is not under contention, so it is irrelevant. So I checked Wikipedia's article on FTC itself and I think I see why you don't see my point. When I learnt FTC from textbooks, the definition of integrals is via the area under curve, i.e. the relevant bit in the FTC article is the geometric intuition. The FTC article, however, quite much like you seem to be, however, only covers the anti-derivative part. In a sense, it comes down to the definition of what an ``integral" means. AFAIK, for beginners, there is only 3 definitions in common use, the directed area under curve, limit of a certain sum, and anti-derivatives. When I teach, I tend to define the directed area under curve, just because students like to see things. Because of that, my FTC has to cover the area under curve. And that is the 2D integral known to Leibniz. If you want the 2D integral, then you ought to integrate the fundamental differential form I was talking about---you don't talk about generalised Stokes's theorem without differential geometry, and I am trying to say that the identification of a definite integral with the area under curve is what is taught to beginning students, but is highly non-trivial under differential geometry! I hope this is clearer. Of course, the moment the 2D integral is reduced to a 1D integral with new boundaries, then the part you keep referring to is relevant, and again, not under any contention. I am simply saying I am not happy with that being the sole content of FTC. The FTC I respect is the one that includes the geometrical intuition. Finally, just the quibble---what part of my ``the restricted FTC is a consequence of generalised Stokes's theorem" is different from your ``FTC restricted to smooth functions is simply a special case of Stokes' theorem"? Even if you disagreed with my ``applied twice", you should not be disagreeing with my ``basically what I said". [[Special:Contributions/162.158.166.191|162.158.166.191]] 16:55, 10 September 2018 (UTC)
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| | "Munroe's theorem" should definitely refer to the circle thing in the alt text {{unsigned ip|162.158.62.57}} | | "Munroe's theorem" should definitely refer to the circle thing in the alt text {{unsigned ip|162.158.62.57}} |
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| | 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 ? :-) [[Special:Contributions/141.101.104.71|141.101.104.71]] 08:36, 7 September 2018 (UTC) | | 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 ? :-) [[Special:Contributions/141.101.104.71|141.101.104.71]] 08:36, 7 September 2018 (UTC) |
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| − | What goes up must come down. [[Special:Contributions/198.41.238.64|198.41.238.64]] 05:53, 8 September 2018 (UTC)
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| − | '''Going in the opposite direction.'''
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| − | Sure, some seemingly obvious things can be made theorems, but there's a point of view that the most complex theorems may seem obvious to a sufficiently smart entity, that we have such hard time studying mathematics simply because it's difficult for us to grasp long sequences of obvious connections in our insufficiently powerful imagination, so we need to break it down into manageable pieces.
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| − | "I have come to believe, though very reluctantly, that it [mathematics] consists of tautologies. I fear that, to a mind of sufficient intellectual power, the whole of mathematics would appear trivial, as trivial as the statement that a four-legged animal is an animal." ---Bertrand Russell (1957) {{unsigned ip|162.158.74.231}}
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| − | "This is what f'(c) = 0 means, as f' is a common notation for the derivative of the function f in differential calculus." Is it? I took both calculus and differential equations as an undergraduate (in the United States in the 1970s/1980s) and never saw that notation.[[User:Nitpicking|Nitpicking]] ([[User talk:Nitpicking|talk]]) 17:57, 1 August 2022 (UTC)
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| − | :Coming from a UK background, myself, I recognise it as such. Not really much experience the '70s, but definitely across the early '80s and beyond. For Secondary Education, in the first instance where the initial "Number machines" idea led straight into algebra, and differentiation/integration was in the second or third year (whatever that is in 'K-12'-style numbering that's in use today, seemingly imported from the US). Not sure what system dominated beyond secondary and tertiary/college levels and into my own university years (heading towards the '90s). It might have depended on whether it was the physics or the maths lectures and workshops (or indeed the given lecturer/workshopper of the moment) as to which of the many possible conventions we could have used and be considered correct. dFoo/dBar probably was used a lot, but obviously got messier than ''f''unctioning things when going far into that sort of thing (either direction!). Though whether curly-ds or primes, it does get more difficult to differentiate the number of differentiations once you get into higher realms of notation... ;)
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| − | :I went a-looking and it ''is'' fairly common, even unto {{w|Derivative#Higher_derivatives|higher derivatives with multiple marks}} (which I've used, well... to no more than the third degree, probably).
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| − | :Looking further still, I now know (have reminded myself?) that {{w|Notation for differentiation#Lagrange's notation|it's 'Lagrangian' notation}}, at least as far as it stays unawkward before going into the numeric form rather than repeated Prime-marks towards a sublime ridiculousness.
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| − | :Of course, elsewhere on that latter link you might find your own learnt system. Or various others more familiar to you and which I ''may'' as readily recognise, unprompted. [[Special:Contributions/162.158.159.133|162.158.159.133]] 18:23, 1 August 2022 (UTC)
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