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Hurkyl
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I meant phi+(phi)^2 = phi^3, and it is the only number that has this property.
Actually, three numbers have that property...
0, φ, and (1-φ)
I meant phi+(phi)^2 = phi^3, and it is the only number that has this property.
Originally posted by lavalamp
I assume that you guys are American, since HallsofIvy & Hurkyl effectively don't have profiles.
So I want to know, at what age did you guys learn about the golden ratio, the sin, sinh, cos, and cosh identities and the e^i[pi] thing? And did you learn it in school or just reading in and around Maths?
i found that there is an approximation that 4/(phi)^0.5=pi.Originally posted by HallsofIvy
Well, they are real numbers! Any other relationship I suspect is more "number mysticism" than mathematics. (Phi, in any case, is an algebraic number while e and pi are not.)
Originally posted by loop quantum gravity
i found that there is an approximation that 4/(phi)^0.5=pi.
i checked in my calculator and it's precise only from 2 place after the point of a decimal.
i stumbled upon this equation in this webpage:http://www.innerx.net/personal/tsmith/Gpyr.html
is it a reliable approximation?
this feature can be attribute to any base (different than 1 and 0) because it is simply pi^(phi^2)=pi^(phi+1) and then phi^2-Phi-1=0 which is ofcourse the equation for calculating the solution to the golden number, it doesn't say they have any relations which can only be attributed to these number only.moshek said:pi ^ (phi^2)=pi * pi ^( phi)
KingNothing said:Is that golden ratio constant the actual number, or an approximation?
i think i did it in first two pages of this thread.moshek said:Than you should reply to me
in some different way like:
Now i have more exact way
to ask my original question !
Best
Moshek
I invite you to read:
www.physicsforums.com/showthread.php?t=17243
he doesn't say how he arrived at the e proportion.epii10 said:Thought you guys might appreciate a little math I found concerning the numbers; Pi, e, and Phi as they relate to three unique right triangles. I call it the "Triple-Triangle-Theory" (TTT). I'm no mathematician so if anyone could tell me "why" the TTT works please feel free. (I think it has to do with the imaginary unit ie. "sqrt -1").
Here's the link:
http://www.gizapyramid.com/rick_howard research.htm
Rick Howard