![]() ![]() To be transcendental, but is generally believed to be.) Period-doubling bifurcation parameters approaches the numberĪnd it has been discovered in many physical systems before The ratio of successive differences between (These are related to properties of dynamical systems with Take the ith power of both sides, the right side being i^i andĥ. Then e^(iPi/2) = i = Cos Pi/2 + i Sin Pi/2 since Cos Pi/2 = Cosĩ0 deg. Since e^(ix) = Cos x + i Sin x, then let x = Pi/2.Ģ. Here is how you can compute the value of i i = 0.207879576.ġ. Since log is multivalued, there are other possible values for Is algebraic but irrational, the theorem applies. Isn't this a real beauty? How many people have actually ![]() Trigonometric or hyperbolic functions of non-zero algebraic numbers In fact, according to the Gelfond-Schneider theorem, any number Not it is transcendental was one of Hilbert's (This is called Hilbert's number because the proof of whether or Transcendental results at rational points.) (Transcendental functions can usually be expected to give Special values of the zeta function, such as.This is constructed by concatenating the digits of the positive ![]() Transcendental but it is also incomputable.) (Noam Elkies of Harvard notes that not only is this
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