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Ryan Matthew Ferris 10:26 PM Thursday, November 19, 2015, 2015 Bellingham, WA
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Updated 7/10/2018
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*Notes on 187.5/16 or 11.71875*
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In this code, I introduce 'xi' (11.71875) a constant with strong relationships
to both pi and # exp(1).
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'Xi' (11.71875 or (187.5/16)) is a 'translator constant' between powers of 2
and 16.
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Search google for "11.71875mhz" and you can see this. 11.71875mhz is
a widely used frequency in 'crystal resonators'.
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More than simply being an efficient means to compute pi or exp(1) (e.g. 'Eulers
number'), 'xi' may
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'interpolate' between pi and e, giving science the means to measure logarithmic
growth patterns of
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increasing radii. This may make it useful for gravitational and rotational
calculations. It is
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possible that the 187.5 cm-3 pc represents some fixed attenuation limit (see
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http://arxiv.org/abs/1503.05245) for radio waves signal that require either
boosting or
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chirping. The relationships between pi, e, and xi(187.5./16 = 11.71875) may
represent fixed
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constants descriptive of all EM signaling. In addition, the constants that
describe the
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circumscription of an octahedron (sqrt(1/2) and sqrt(1/6) can also be used to
derive xi with a
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factor close to 9/16.
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A number of constants and function names are used. Some are reused:
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[1] "almost2" "aR" "c2"
"cR" "eR" "F_pe" "F_pi"
"findpi" "i" "j" "k"
"k1"
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[13] "k2" "l" "l1"
"mm1" "p1" "p2" "piR"
"pR" "pX" "s4" "seqe"
"seqpi"
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[25] "seqpi_e" "t1" "t2"
"t3" "Vx" "x" "xi"
"xi_sqrt" "xif" "y"
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Set your graphics device to record history if desired. 86 graphs are produced.
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You may want par(mfrow=c(1,2))
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NB : In R 3.5 there is no bigint by default,however there are 22 digits of
accuracy.
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See my usage of BIGINT in Powershell
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For this work I used Microsoft Open R 3.5 with Intel's MKL (Math Kernel
Library)