Author |
Topic: cos(ln(pi+20)) (Read 692 times) |
|
Grimbal
wu::riddles Moderator
Uberpuzzler
Gender: 
Posts: 7527
|
 |
cos(ln(pi+20))
« on: Nov 21st, 2004, 2:15pm » |
 Quote  Modify
|
What is the value of cos(ln(pi+20)) ?
|
|
 IP Logged |
|
|
|
Icarus
wu::riddles Moderator
Uberpuzzler
Boldly going where even angels fear to tread.
Gender:
Posts: 4863
|
|
Re: cos(ln(pi+20))
« Reply #2 on: Nov 21st, 2004, 3:20pm » |
Quote Modify
|
Approximately -0.99999999924. A nice little coincidence.
|
|
IP Logged |
"Pi goes on and on and on ...
And e is just as cursed.
I wonder: Which is larger
When their digits are reversed? " - Anonymous
|
|
|
Sir Col
Uberpuzzler
impudens simia et macrologus profundus fabulae
Gender:
Posts: 1825
|
|
Re: cos(ln(pi+20))
« Reply #3 on: Nov 21st, 2004, 3:40pm » |
Quote Modify
|
I can do better... how about cos(ln(4605/199))?
Or if you want an "exact" form, try cos(ln(239432496618343/10346816338556))? 
|
|
IP Logged |
mathschallenge.net / projecteuler.net
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: cos(ln(pi+20))
« Reply #4 on: Nov 21st, 2004, 7:13pm » |
Quote Modify
|
262537412640768744 - epi*sqrt(163)
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
Barukh
Uberpuzzler
Gender:
Posts: 2276
|
|
Re: cos(ln(pi+20))
« Reply #5 on: Nov 22nd, 2004, 5:42am » |
Quote Modify
|
on Nov 21st, 2004, 3:20pm, Icarus wrote:| Approximately -0.99999999924. A nice little coincidence. |
|
Sometimes, it's not a coincidence. Read the first and the beginning of the second page of this article. The relation between e and [pi] is nice, but the approximation of 18,000 digits is simply stunning!
|
|
IP Logged |
|
|
|
JocK
Uberpuzzler
Gender:
Posts: 877
|
|
Bubble or GUM?
« Reply #6 on: Nov 24th, 2004, 1:22pm » |
Quote Modify
|
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.
---------------------------------------------------------
|
|
IP Logged |
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
|
|
|
BNC
Uberpuzzler
Gender:
Posts: 1732
|
|
Re: Bubble or GUM?
« Reply #7 on: Nov 24th, 2004, 10:44pm » |
Quote Modify
|
on Nov 24th, 2004, 1:22pm, JocK wrote:
---------------------------------------------------------
xy - y = z
x5 - y4 - y3 = z
Set the GUM parameter z = 20 and calculate xiy.
---------------------------------------------------------
|
|
What am I missing?
::
x=10.87; y=-20 => xiy=-0.823+i0.567
::
|
|
IP Logged |
How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
|
|
|
ThudnBlunder
wu::riddles Moderator
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489
|
|
Re: cos(ln(pi+20))
« Reply #9 on: Nov 30th, 2004, 7:51am » |
Quote Modify
|
An interesting quotient:
117441919232813531727425565815319808042793430457803809016804183046894566 787292800844355644360850267694083886151344689499579001360114390469381999
97085476755
DIVIDED BY
154869850584491050531644084747671856047860810846796338034518794614003549 805894953276361189463850906775276855316001248612140851476810180855882711
408487828
EQUALS
75.832654832156453210821054632876432181286531873265874216742136759846321 875999999000000000000000000000011111111110000000001000000100000000001000 000100000000001000000100000000001000000100000000000000000000000999999999 326147618325483215847653218453285863264999999999999999999999999999999999 999999999999999999977169267891725334585224750443495160246040836778671201 333437219214228496790502225046981582684861279654684049886338387380538709 62305711117793867481832862345979729718899223868793839031484514844173097 ...
|
|
IP Logged |
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.
|
|
|
aldron
Guest
|
on Nov 25th, 2004, 12:13am, towr wrote:| You're missing the second solution |
|
what is the second solution?
|
|
IP Logged |
|
|
|
JocK
Uberpuzzler
Gender:
Posts: 877
|
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:
|
|
IP Logged |
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
|
|
|
BNC
Uberpuzzler
Gender:
Posts: 1732
|
|
Re: cos(ln(pi+20))
« Reply #12 on: Jan 2nd, 2005, 8:47am » |
Quote Modify
|
on Nov 25th, 2004, 12:13am, towr wrote:| You're missing the second solution |
|
A-Ha!!
|
|
IP Logged |
How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print
Remove