Needing irrational help

[room208]

It would suprise me to no degree if this topic has already been discussed, but I would like to know if there are any proven correlations between pi, phi, and eulers constant? If anyone could help me with this I would be much obliged.

[lqg]

there is approximatiom of pi with phi:
1/√(φ)= 3.144605511~π as you can see it's only 2 decimals accurate.

[dave]

There's quite a nice formula for calculating pi using the Fibonacci numbers;

pi/4 = sum(k=1 to infinity)(arctan(1/F2k+1))

(I'd use mimeTeX but for some reason, it hates \arctan).

[dave]

You can find this, and a few others, at http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibpi.html

[Kedas]

Just wanted to say that the subject line is funny:
"Needing irrational help"

I just did my part ;)

[wolfson]

e^i*pi = -(phi)^0

[dave]

e^i*pi = -(phi)^0

Nice one :-p

As of yet, I haven't been able to find any equations linking euler's constant to pi and phi directly, I'm not sure whether there is a connection or not.

[bloodhound]

this is a famous limit

F(n)/F(n-1) tends to phi as n tends to infinity where F(n) is the nth fibonacci number

also

http://mathworld.wolfram.com/fimg1233.gif

find loads . i mean tons and tons of exciting equations and recurrence relations for fibonacci at

http://mathworld.wolfram.com/FibonacciNumber.html

[dave]

Yeah, mathworld in general has a hell of a lot of articles about most of the major functions in mathematics.

[bloodhound]

i think i have read everything in there!!! they start simple and go into the most hard stuff