I asked for you to define your point. Why is this the only way to understand it? It is not my friend. Again, the definitions of these functions are not absolute. You can define it as exp(sqrt(2)*log(2)) and worry about your definitions of e and ln, or you can define it as (2^sqrt(2)) and worry...
I could further comment however I feel this sums it up quite nicely.
One could also write Pi as 4*ArcTan(1) or Ln(-1)/i
I am asking for a non recursive method to define pi in terms of algebraic expression. The sqrt(x) is a none integer coefficient. Furthermore, the method that you bring up is...
For example:
Sin(X) = \sum^{\infty}_{N=0}\ (-1)^N \frac{X^{2N+1}}{(2N+1)!}
Cos(X) = \sum^{\infty}_{N=0}\ (-1)^N \frac{X^{2N}}{(2N)!}
eX = \sum^{\infty}_{N=0} \frac{X^N}{N!}
Sine and Cosine may also be expressed in terms of e and so on, so forth.
Pi may be a symbolic representation, but it...
Howdy folks.
The Gelfond-Schneider Constant 221/2 is transcendental. Of my understanding, transcendental numbers are a special case of irrational numbers in the sense of how they may or may not be derrived. This being the case, how is it that many infinite series are stated with such...
Ah, and so you see, this much I understand as well. I'm not refuting that. For you see, you can square the Euclidean circle if you were to treat it in Hyperbolic space, or so I believe I've seen a proof on that aforementioned topic. Even so, the analogy doesn't work here. I'm not talking about a...
Of course, this much I understand. But those values are nonetheless irrational. Described by method of measurement. If we knew the exact value of the circumference of a euclidean circle, and described it as say 2, we wouldn't know the irrational value of 2pi. We wouldn't be able to describe it...
Howdy ho. No reason for a welcome around here, it's not about me it's about the Mathematical Anti-Telharsic Harfatum Septomin, eh!? (I hope at least one of you are familiar with that guy) Nonetheless, I've become obsessed with the transcendental property, and thusly therein my familiarization...