# Difference between revisions of "Talk:1047: Approximations"

(Correct formula and associated computation.) |
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Maybe [[:Category:Comics featuring Miss Lenhart|Miss Lenhart]] can help. | Maybe [[:Category:Comics featuring Miss Lenhart|Miss Lenhart]] can help. | ||

--[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:41, 17 December 2013 (UTC) | --[[User:Dgbrt|Dgbrt]] ([[User talk:Dgbrt|talk]]) 21:41, 17 December 2013 (UTC) | ||

+ | |||

+ | cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2 is exactly correct. | ||

+ | |||

+ | Let a=π/7, b=3π/7, and c=5π/7, then | ||

+ | (cosa+cosb+cosc)⋅2sina=2cosasina+2cosbsina+2coscsina=sin2a+sin(b+a)−sin(b−a)+sin(c+a)−sin(c−a)=sin(2π/7)+sin(4π/7)−sin(2π/7)+sin(6π/7)−sin(4π/7)=sin(6π/7)=sin(π/7)=sina | ||

+ | |||

+ | Hence, cos(π/7) + cos(3π/7) + cos(5π/7) = sin(π/7) / 2sin(π/7) = 1/2 | ||

+ | [[Special:Contributions/108.162.216.74|108.162.216.74]] 01:57, 16 January 2014 (UTC) | ||

;So, still incomplete? | ;So, still incomplete? |

## Revision as of 01:57, 16 January 2014

They're actually quite accurate. I've used these in calculations, and they seem to give close enough answers. __Davidy__^{22}`[talk]` 14:03, 8 January 2013 (UTC)

I only see a use for the liters in a gallon one. The rest are for trolling or simple amusement. The cosine identity bit our math team in the butt at a competition. It was painful. --Quicksilver (talk) 05:27, 17 August 2013 (UTC)

Annoyingly this explanation does not cover 42 properly, it does not say that Douglas Adams got the number 42 from Lewis Carroll, who is more relevant to the page because he was a mathematician named Charles Lutwidge Dodgson. He was obsessed with the number forty-two. The original plate illustrations of Alice in Wonderland drawn by him numbered forty-two. Rule Forty-Two in Alice in Wonderland is "All persons more than a mile high to leave the court", There is also a Code of Honour in the preface of The Hunting of the Snark, an extremely long poem written by him when he was 42 years old, in which rule forty-two is "No one shall speak to the Man at the Helm". The queens in Alice Through the Looking Glass the White Queen announces her age as "one hundred and one, five months and a day", which - if the best possible date is assumed for the action of Through the Looking-Glass - gives a total of 37,044 days. With the further (textually unconfirmed) assumption that both Queens were born on the same day their combined age becomes 74,088 days, which is 42 x 42 x 42. --139.216.242.254 02:43, 29 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! --Quicksilver (talk) 00:37, 30 August 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)

13/15 is a better approximation to sqrt(3)/2 than is e/pi. Continued fraction approximations are great! --DrMath 07:23, 7 September 2013 (UTC)

How could he forget 1 gallon ≈ 0.1337 ft³?! 67.188.195.182 00:51, 8 September 2013 (UTC)

Worth mentioning that Wolfram Alpha now officially recognizes the White House switchboard constant and the Jenny constant. 86.164.243.91 18:28, 8 October 2013 (UTC)

Maybe we should add the [Extension:LaTeXSVG LaTeX extension] to make it easier to transcribe these equations. -- 108.162.219.220 23:02, 16 December 2013 (UTC)

- Protip - Does anyone see the correct equation?

Maybe this is just an other Wolfram Alpha error, like we recently have had here: 1292: Pi vs. Tau. All equations still look invalid to me.

*√2 = 3/5 + π/(7-π)*: is impossible because √2 is an irrational number and no equation can match.*cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2*: could only match if*cos(x) + cos(3x) + cos(5x) = 1/2*would be valid, because*π/7*is also an irrational number.*γ = e/3*: would mean that a sum of two irrational numbers do fit to the Gamma Constant. Impossible.^{4}+ e/5 or γ = e/54 + e/5*√5 = 13 + 4π / 24 - 4π*: √5 and π are irrational numbers, there is no way to match them in any equation like this.*Σ 1/n*: doesn't make any sense either.^{n}= ln(3)^{e}

Maybe Miss Lenhart can help. --Dgbrt (talk) 21:41, 17 December 2013 (UTC)

cos(π/7) + cos(3π/7) + cos(5π/7) = 1/2 is exactly correct.

Let a=π/7, b=3π/7, and c=5π/7, then (cosa+cosb+cosc)⋅2sina=2cosasina+2cosbsina+2coscsina=sin2a+sin(b+a)−sin(b−a)+sin(c+a)−sin(c−a)=sin(2π/7)+sin(4π/7)−sin(2π/7)+sin(6π/7)−sin(4π/7)=sin(6π/7)=sin(π/7)=sina

Hence, cos(π/7) + cos(3π/7) + cos(5π/7) = sin(π/7) / 2sin(π/7) = 1/2 108.162.216.74 01:57, 16 January 2014 (UTC)

- So, still incomplete?

Where's our (in)complete judge? 199.27.128.186 19:21, 18 December 2013 (UTC)