Editing Talk:2042: Rolle's Theorem
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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) | ||
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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 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) | ::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 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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:: ``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) | :: ``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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"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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What goes up must come down. [[Special:Contributions/198.41.238.64|198.41.238.64]] 05:53, 8 September 2018 (UTC) | 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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