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