Talk:1047: Approximations - Revision history

Psychoticpotato at 13:15, 28 May 2024

2024-05-28T13:15:46Z

ColorfulGalaxy: OEIS Citation

2023-01-16T11:40:39Z

OEIS Citation

ColorfulGalaxy: Ordinal numbers

2022-12-11T20:35:40Z

Ordinal numbers

Mumingpo at 13:36, 6 May 2021

2021-05-06T13:36:15Z

162.158.158.87 at 20:47, 28 November 2019

2019-11-28T20:47:25Z

Yosei: Yet another proof of cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2

2019-02-17T08:19:44Z

Yet another proof of cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2

Dgbrt: Please sign your comments.

2018-09-03T12:27:03Z

Please sign your comments.

Redbelly98: World population discussion

2018-09-03T00:48:50Z

World population discussion

625571b7-aa66-4f98-ac5c-92464cfb4ed8: comic is wrong now?

2018-01-19T00:54:24Z

comic is wrong now?

162.158.63.28 at 13:41, 5 May 2017

2017-05-05T13:41:13Z

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	The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)		The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)
		+	:Same here in 2024! [[User:Psychoticpotato\|Psychoticpotato]] ([[User talk:Psychoticpotato\|talk]]) 13:15, 28 May 2024 (UTC)

	They're actually quite accurate. I've used these in calculations, and they seem to give close enough answers. '''[[User:Davidy22\|<span title="I want you."><u><font color="purple" size="2px">David</font><font color="green" size="3px">y</font></u><sup><font color="indigo" size="1px">22</font></sup></span>]]'''[[User talk:Davidy22\|<tt>[talk]</tt>]] 14:03, 8 January 2013 (UTC)		They're actually quite accurate. I've used these in calculations, and they seem to give close enough answers. '''[[User:Davidy22\|<span title="I want you."><u><font color="purple" size="2px">David</font><font color="green" size="3px">y</font></u><sup><font color="indigo" size="1px">22</font></sup></span>]]'''[[User talk:Davidy22\|<tt>[talk]</tt>]] 14:03, 8 January 2013 (UTC)

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 In searching for an error correction term of the Taylor expansion of -x log(x) at degree n around 1, I found the term (1 - x)^(n * e)/n. It felt so close to having an actual log(x)^e appearing in a useful equation...
 Hope I would be able to see one someday. [[User:Mumingpo|Mumingpo]] ([[User talk:Mumingpo|talk]]) 13:36, 6 May 2021 (UTC)
 == E in title text ==
 The number  e typically appears in the basis of a power (forming the exponential function), not in the exponent. However, Ordinal numbers in le francais are usually formed by adding a superscript "e" to a number, such as "5<sup>e</sup>". Furthermore, ordinal numbers in le francais can also denote denominators (unlike ordinal numbers in German), so "1 x 5<sup>e</sup>" would literally mean “1/5”. {{citation needed}} [[User:ColorfulGalaxy|ColorfulGalaxy]] ([[User talk:ColorfulGalaxy|talk]]) 20:35, 11 December 2022 (UTC)

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 How could he forget 1 gallon ≈ 0.1337 ft³?! [[Special:Contributions/67.188.195.182|67.188.195.182]] 00:51, 8 September 2013 (UTC)
 Worth mentioning that Wolfram Alpha now officially recognizes the [http://www.wolframalpha.com/input/?i=e%5E-%28%281%2B8%5E%281%2F%28e-1%29%29%29%5E%281%2Fpi%29%29 White House switchboard constant] and the [http://www.wolframalpha.com/input/?i=%287%5E%28e-1%2Fe%29-9%29*pi%5E2 Jenny constant]. [[Special:Contributions/86.164.243.91|86.164.243.91]] 18:28, 8 October 2013 (UTC)
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 :Dgbrt, please see my answer from 11 May 2014 up there. Any odd integer will do, as long as you sum enough of cos(pi/[thing]).
 :*Let's try with 5 : cos(pi/5) + cos (3pi/5) = 1/2.
-:*With 9 : cos(pi/9)+ cos(3pi/9) + cos (5pi/9) + cos(7pi/9) = 1/2
+::: cos(pi/5) is actually (1+sqrt(5))/4. Additionally, sin(pi/10) is very close to (1 foot/1 meter).
 : No big mystery around here. Just a beautiful formula :) I think there are similar formulas with cosines and even integers. I'll post them here if I have time. [[User:Varal7|Varal7]] ([[User talk:Varal7|talk]]) 09:56, 17 May 2014 (UTC)
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 In searching for an error correction term of the Taylor expansion of -x log(x) at degree n around 1, I found the term (1 - x)^(n * e)/n. It felt so close to having an actual log(x)^e appearing in a useful equation...
 Hope I would be able to see one someday. [[User:Mumingpo|Mumingpo]] ([[User talk:Mumingpo|talk]]) 13:36, 6 May 2021 (UTC)

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	and so (using the relationship of the roots and the coefficients) their sum is −(−4)/8 = 1/2.		and so (using the relationship of the roots and the coefficients) their sum is −(−4)/8 = 1/2.
	[[User:Yosei\|Yosei]] ([[User talk:Yosei\|talk]]) 08:19, 17 February 2019 (UTC)		[[User:Yosei\|Yosei]] ([[User talk:Yosei\|talk]]) 08:19, 17 February 2019 (UTC)
		+
		+	'''One step closer to the elusive log(x)^e
		+	In searching for an error correction term of the Taylor expansion of -x log(x) at degree n around 1, I found the term (1 - x)^(n * e)/n. It felt so close to having an actual log(x)^e appearing in a useful equation...
		+	Hope I would be able to see one someday. [[User:Mumingpo\|Mumingpo]] ([[User talk:Mumingpo\|talk]]) 13:36, 6 May 2021 (UTC)

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	:: This explanation covers 42 adequately, and would probably be made slightly worse if such information were added. The very widely known cultural reference is to Adams's interpretation, not Dodgson's original obsession. Adding it would be akin to introducing the MPLM into the explanation for the hijacking of Renaissance artists' names by the TMNT. I definitely concede that it does not cover 42 exhaustively, but I think it can be considered complete and in working order without such an addition. If it really irks you, be bold and add it! --[[User:Quicksilver\|Quicksilver]] ([[User talk:Quicksilver\|talk]]) 00:37, 30 August 2013 (UTC)		:: This explanation covers 42 adequately, and would probably be made slightly worse if such information were added. The very widely known cultural reference is to Adams's interpretation, not Dodgson's original obsession. Adding it would be akin to introducing the MPLM into the explanation for the hijacking of Renaissance artists' names by the TMNT. I definitely concede that it does not cover 42 exhaustively, but I think it can be considered complete and in working order without such an addition. If it really irks you, be bold and add it! --[[User:Quicksilver\|Quicksilver]] ([[User talk:Quicksilver\|talk]]) 00:37, 30 August 2013 (UTC)
		+
		+	::: Additionally, the Lewis Carroll idea is only one of several theories about where Douglas Adams got the number from. [[Special:Contributions/162.158.158.87\|162.158.158.87]] 20:47, 28 November 2019 (UTC)

	"sqrt(2) is not even algebraic in the quotient field of Z[pi]" is not correct. Q is part of the quotient field of Z[pi] and sqrt(2) is algebraic of it. The needed facts are that pi is not algebraic, but the formula implies it is in Q(sqrt(2)). --DrMath 06:47, 7 September 2013 (UTC)		"sqrt(2) is not even algebraic in the quotient field of Z[pi]" is not correct. Q is part of the quotient field of Z[pi] and sqrt(2) is algebraic of it. The needed facts are that pi is not algebraic, but the formula implies it is in Q(sqrt(2)). --DrMath 06:47, 7 September 2013 (UTC)

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	I'd add pi = (9^2 + (19^2)/22)^(1/4) [[Special:Contributions/198.41.230.73\|198.41.230.73]] 02:41, 13 May 2015 (UTC)		I'd add pi = (9^2 + (19^2)/22)^(1/4) [[Special:Contributions/198.41.230.73\|198.41.230.73]] 02:41, 13 May 2015 (UTC)
		+
		+	'''Yet another proof of cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2''' — Use the multi-angle formula cos(7θ) = 64(cos θ)^7 − 112(cos θ)^5 + 56(cos θ)^3 − 7(cos θ),
		+	and assume cos(7θ)=−1; then 7θ=π, 3π, 5π, 7π, etc.
		+	Let x=cos θ, then x = cos(π/7), cos(3π/7), cos(5π/7), cos(7π/7), etc.<br />
		+	Now one could actually solve 64x^7 − 112x^5 + 56x^3 − 7x + 1 = (x+1)(8x^3 − 4x^2 − 4x + 1)^2 = 0,
		+	but it’s easier to argue that cos(π/7), cos(3π/7), cos(5π/7) are the 3 roots of the cubic equation 8x^3 − 4x^2 − 4x + 1,
		+	and so (using the relationship of the roots and the coefficients) their sum is −(−4)/8 = 1/2.
		+	[[User:Yosei\|Yosei]] ([[User talk:Yosei\|talk]]) 08:19, 17 February 2019 (UTC)

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 The US population estimate is now off by 7 million, although 2018 just started. Even so, in December 2017, it would have been 4 million off. [[User:625571b7-aa66-4f98-ac5c-92464cfb4ed8|625571b7-aa66-4f98-ac5c-92464cfb4ed8]] ([[User talk:625571b7-aa66-4f98-ac5c-92464cfb4ed8|talk]]) 00:54, 19 January 2018 (UTC)
-: Off by 7 million out of 7-8 billion means that it's accurate to one part in 1,000. That's consistent with it's location in the chart -- next to other values that are accurate to 1 in 1,000.
+: Off by 7 million out of 7-8 billion means that it's accurate to one part in 1,000. That's consistent with it's location in the chart -- next to other values that are accurate to 1 in 1,000. {{unsigned|Redbelly98}}
 The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28|162.158.63.28]] 13:41, 5 May 2017 (UTC)

← Older revision		Revision as of 00:48, 3 September 2018
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	The US population estimate is now off by 7 million, although 2018 just started. Even so, in December 2017, it would have been 4 million off. [[User:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|625571b7-aa66-4f98-ac5c-92464cfb4ed8]] ([[User talk:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|talk]]) 00:54, 19 January 2018 (UTC)		The US population estimate is now off by 7 million, although 2018 just started. Even so, in December 2017, it would have been 4 million off. [[User:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|625571b7-aa66-4f98-ac5c-92464cfb4ed8]] ([[User talk:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|talk]]) 00:54, 19 January 2018 (UTC)
		+
		+	: Off by 7 million out of 7-8 billion means that it's accurate to one part in 1,000. That's consistent with it's location in the chart -- next to other values that are accurate to 1 in 1,000.

	The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)		The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)

← Older revision		Revision as of 00:54, 19 January 2018
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		+	The US population estimate is now off by 7 million, although 2018 just started. Even so, in December 2017, it would have been 4 million off. [[User:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|625571b7-aa66-4f98-ac5c-92464cfb4ed8]] ([[User talk:625571b7-aa66-4f98-ac5c-92464cfb4ed8\|talk]]) 00:54, 19 January 2018 (UTC)
		+
	The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)		The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)

← Older revision		Revision as of 13:41, 5 May 2017
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		+	The world population estimate is still accurate to within .1 billion. [[Special:Contributions/162.158.63.28\|162.158.63.28]] 13:41, 5 May 2017 (UTC)
		+
	They're actually quite accurate. I've used these in calculations, and they seem to give close enough answers. '''[[User:Davidy22\|<span title="I want you."><u><font color="purple" size="2px">David</font><font color="green" size="3px">y</font></u><sup><font color="indigo" size="1px">22</font></sup></span>]]'''[[User talk:Davidy22\|<tt>[talk]</tt>]] 14:03, 8 January 2013 (UTC)		They're actually quite accurate. I've used these in calculations, and they seem to give close enough answers. '''[[User:Davidy22\|<span title="I want you."><u><font color="purple" size="2px">David</font><font color="green" size="3px">y</font></u><sup><font color="indigo" size="1px">22</font></sup></span>]]'''[[User talk:Davidy22\|<tt>[talk]</tt>]] 14:03, 8 January 2013 (UTC)