Another day, another guess at a mathematical constant.
The Embree-Trefethen Constant is closely related to Viswanath's Constant, so the fact that my equation-crunching program would find a similar expression for it is not altogether surprising. The constant arises from a special constraint placed on the Random Fibonacci Sequence.
Embree-Trefethen ~= asin((ln(MRB)*ln(Khinchin))/(ln(2)*(ln(Feigenbaum Alpha) - 2*ln(5) - 2*ln(2))))
{MRB = 0.18785964246206712024851793405427323; Khinchin = 2.68545200111950741674; Feigenbaum Alpha = 2.50290787509589282228390287321821578}
Or:
β* ~= sin-1(log2(MRB) * log(α/102)(K0))
~= 0.70258000015353862646252912388969476230829130717359666148292521633...
Also, a brief disclaimer: I will make no guarantees as to the accuracy of the numbers that I'm sharing, or the equations I used to compute them. They're probably woefully incomplete. The point is to demonstrate the capability a computer algorithm has of helping to discover mathematical formulas and proofs, which has been a hotly debated subject among computer scientists.
Your next question might be: how do you know that an equation generated by an algorithm is even accurate? Couldn't the very next decimal place you failed to compute be off by a small amount, and you would never know it?
My response is that this is the nature of mathematics. No theory in its field has ever been proven beyond any doubt; not even the simplest of equations. We can calculate Pi to a billion decimal places, and still not be 100% sure the next digit isn't the end of the sequence. That is quite simply the way things work in the world of science.
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