"pressure equals a third of energy density" -- really?... well, a tetrahedron is a third of the volume of the parallelopiped that it's inscribed in; so, there.
"spacetime" is a totally useless word for concepts, since it is merely phase-space of ordinary space; just use quaternions, real part as time. (funny thing: I just read that Hoagland's "hyperdimensional physics" was nothing but quaternions .-)
> The problem with the em-force for me is/was, that is should somehow fill > the atom with a strong forcefield, that should have nodes within the > particles. But that would mean for a pointlike particle infinite > field-strength inside. > So I tried something different, where the particles are nodes of a > three-dimensional standing wave. These are build as kind of interference > pattern of two antagonistic forces, that rotate in opposite directions, > where the 'real thing' are not the patterns, but the 'medium' in > between. This would generate also inertia. as this standing wave has a > center and we could ascribe the stability to that center, while the > electron is the center of a smaller circle, that swirls around the > proton. But in this picture both particles are 'one thing', because > 'real' is that kind of abstract medium in between.
thusNso: I don't see any neccesary resaon for *any* irrational number to have a maximum run of any digit in what ever integral base; so, rake one coal over yourself for propitiating such a silly idea!
on the wayside, 0.999.... does not = 1; it equals 1.000...., the "real"number, one; take a hop, a skip & a jump over Tony Robinson's bed (of coals).
> Many irrational numbers have this property that there is a maximum run of > one or all digits. Despite the fact that the probability of this occuring is
thusNso: the second part of the question is clearly trivial, and the first part seems to be its inverse, or what ever.
have Farey sequences ever been used for continued fractions, or does that make any sense, at all?
> Example: The fraction 4 / 97 occur in the place 197 of > the Farey's sequence of order 113. How can I know it > without calculate all the smaller terms?
--Pi, the surfer's canonical value -- good to at least one place! http://wlym.com