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Title: cos(ln(pi+20)) Post by Grimbal on Nov 21st, 2004, 2:15pm What is the value of cos(ln(pi+20)) ? |
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Title: Re: cos(ln(pi+20)) Post by towr on Nov 21st, 2004, 3:03pm interesting.. |
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Title: Re: cos(ln(pi+20)) Post by Icarus on Nov 21st, 2004, 3:20pm Approximately [hide]-0.99999999924[/hide]. A nice little coincidence. |
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Title: Re: cos(ln(pi+20)) Post by Sir Col on Nov 21st, 2004, 3:40pm I can do better... how about cos(ln(4605/199))? Or if you want an "exact" form, try cos(ln(239432496618343/10346816338556))? ::) |
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Title: Re: cos(ln(pi+20)) Post by THUDandBLUNDER on Nov 21st, 2004, 7:13pm 262537412640768744 - epi*sqrt(163) |
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Title: Re: cos(ln(pi+20)) Post by Barukh on Nov 22nd, 2004, 5:42am on 11/21/04 at 15:20:24, Icarus wrote:
Sometimes, it's not a coincidence. Read the first and the beginning of the second page of this article (http://algo.epfl.ch/~gerard/Articles/MazeMinder.pdf). The relation between e and [pi] is nice, but the approximation of 18,000 digits is simply stunning! |
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Title: Bubble or GUM? Post by JocK on Nov 24th, 2004, 1:22pm So I met this guy the other day. You know the type, but you never get to know the person. An absolute weirdo and a loner. Lives on a different planet. Since ages busy with some PhD that nobody believes will ever be completed. When he saw me, he immediately approached me. Kind of strange, as I don't know the guy really. He seemed nervous, but sounded very excited when he started talking. "Forget all the stuff you learned!" he exclaimed. "Yeah right" I repied. "Really, listen...." He stopped talking and scribled something on a tiny piece of paper. He handed me the paper and disappeared. I put the paper in my pocket, and didn't look at it till this morning. The equations written on this piece of paper half the size of an envelope seemed futile, but somehow captured my attention. The equations are deceivingly simple, but after having played with them I am really stunned. Is this GUM, the holy grail of Grand Unified Mathematics? Or is it a bubble? For you to decide: --------------------------------------------------------- xy - y = z x5 - y4 - y3 = z Set the GUM parameter z = 20 and calculate xiy. --------------------------------------------------------- |
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Title: Re: Bubble or GUM? Post by BNC on Nov 24th, 2004, 10:44pm on 11/24/04 at 13:22:08, JocK wrote:
What am I missing? ::[hide] x=10.87; y=-20 => xiy=-0.823+i0.567 [/hide]:: ??? |
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Title: Re: cos(ln(pi+20)) Post by towr on Nov 25th, 2004, 12:13am You're missing the second solution |
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Title: Re: cos(ln(pi+20)) Post by THUDandBLUNDER on Nov 30th, 2004, 7:51am An interesting quotient: 117441919232813531727425565815319808042793430457803809016804183046894566787292800844355644360850267694083886151344689499579001360114390469381999 97085476755 DIVIDED BY 154869850584491050531644084747671856047860810846796338034518794614003549805894953276361189463850906775276855316001248612140851476810180855882711 408487828 EQUALS 75.83265483215645321082105463287643218128653187326587421674213675984632187599999900000000000000000000001111111111000000000100000010000000000100000010000000000100000010000000000100000010000000000000000000000099999999932614761832548321584765321845328586326499999999999999999999999999999999999999999999999999997716926789172533458522475044349516024604083677867120133343721921422849679050222504698158268486127965468404988633838738053870962305711117793867481832862345979729718899223868793839031484514844173097 ... |
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Title: Re: cos(ln(pi+20)) Post by aldron on Jan 1st, 2005, 5:19pm on 11/25/04 at 00:13:23, towr wrote:
what is the second solution? |
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Title: Re: cos(ln(pi+20)) Post by JocK on Jan 2nd, 2005, 8:02am Hint: A graphical solution (plotting both x = (20 + y)1/y and x = (20 + y3 + y4)1/5 as function of y) yields the following picture: |
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Title: Re: cos(ln(pi+20)) Post by BNC on Jan 2nd, 2005, 8:47am on 11/25/04 at 00:13:23, towr wrote:
A-Ha!! |
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