ThepurposeofthisMathematicaNotebookistocomputetheFineStructureConstant[α]to60+significantdigitsusingonly[π]andthenumber[b=22+6.
13
].Notethenumberb*πisnearlyequalto-1
α
ThefundamentalassumptioninthiscomputationisthatatleastoneinfiniteseriesF[b,π,α]==0existswhichconvergestozeroandsatisfiestheRatioTest.MostofthetermsofFareoftheformandeachsuccessivetermgenerallyincreasesμby1.Thevaluesofκandλareadjustedmanuallytomakethesumofalltermsconvergetozeroandmaketheabsolutevalueofeachtermgenerallysmallerthanthepreviousone.Afereachtermisinserted,anewequationF[b,π,α]==0canbesolvedforα.Usingapproximately77terms,αwascomputedtohavethevalue
κ
b
λ
π
μ
α
0.00729735256429999992416860274723885002506940170167664094552769
Thepreviousbestknownvalueforαis
0.0072973525643
SECTION I
SECTION I
The extraction,of the matrices defined below,from the first verse of Genesis has been described in the article entitled Genesis of the Reciprocal Fine Structure Constant which can be found at https://christianapologetic.org/encrypted-in-genesis/genesis-of-reciprocal-fine-structure-constant
The value of [b] was first detected as an eigenvalue for a 3rd order, 3 dimensional tensor based on the Spectral Theory of Tensors developed by Guimei Zhang, Shenglong Hu and others.
"A11"A11=0"A12"A12=2"A13"A13=0"A21"A21=0"A22"A22=0"A23"A23=0"A31"A31=1"A32"A32=1"A33"A33=0"B11"B11=2"B12"B12=1"B13"B13=2"B21"B21=0"B22"B22=0"B23"B23=1"B31"B31=2"B32"B32=0"B33"B33=0"C11"C11=0"C12"C12=2"C13"C13=0"C21"C21=0"C22"C22=0"C23"C23=0"C31"C31=1"C32"C32=1"C33"C33=0(*------------------------------*)
"Ayz"Ayz={{A11,A12,A13},{A21,A22,A23},{A31,A32,A33}}MatrixForm[Ayz]"Byz"Byz={{B11,B12,B13},{B21,B22,B23},{B31,B32,B33}}MatrixForm[Byz]"Cyz"Cyz={{C11,C12,C13},{C21,C22,C23},{C31,C32,C33}}MatrixForm[Cyz]"Azx"Azx={{A13,B13,C13},{A23,B23,C23},{A33,B33,C33}}MatrixForm[Azx]"Bzx"Bzx={{A12,B12,C12},{A22,B22,C22},{A32,B32,C32}}MatrixForm[Bzx]"Czx"Czx={{A11,B11,C11},{A21,B21,C21},{A31,B31,C31}}MatrixForm[Czx]"Axy"Axy={{C11,C12,C13},{B11,B12,B13},{A11,A12,A13}}MatrixForm[Axy]"Bxy"Bxy={{C21,C22,C23},{B21,B22,B23},{A21,A22,A23}}MatrixForm[Bxy]"Cxy"Cxy={{C31,C32,C33},{B31,B32,B33},{A31,A32,A33}}MatrixForm[Cxy]"Xxz"Xxz={{C31,C32,C33},{B21,B22,B23},{A11,A12,A13}}MatrixForm[Xxz]"Xzx"Xzx={{C11,C12,C13},{B21,B22,B23},{A31,A32,A33}}MatrixForm[Xzx]"Xzy"Xzy={{A11,B11,C11},{A22,B22,C22},{A33,B33,C33}}MatrixForm[Xzy]"Xyz"Xyz={{A31,B31,C31},{A22,B22,C22},{A13,B13,C13}}MatrixForm[Xyz]"Xyx"Xyx={{A31,A21,A11},{B32,B22,B12},{C33,C23,C13}}MatrixForm[Xyx]"Xxy"Xxy={{C31,C21,C11},{B32,B22,B12},{A33,A23,A13}}MatrixForm[Xxy](*------------------------------*)
"yz=Ayz.Byz.Cyz.Xyz.Xzy"yz=Ayz.Byz.Cyz.Xyz.XzyMatrixForm[yz]"zx=Azx.Bzx.Czx.Xzx.Xxz"zx=Azx.Bzx.Czx.Xzx.XxzMatrixForm[zx]"xy=Axy.Bxy.Cxy.Xxy.Xyx"xy=Axy.Bxy.Cxy.Xxy.XyxMatrixForm[xy](*------------------------------*)
"x=yz.Transpose[yz]"x=yz.Transpose[yz]MatrixForm[x]"y=zx.Transpose[zx]"y=zx.Transpose[zx]MatrixForm[y]"z=xy.Transpose[xy]"z=xy.Transpose[xy]MatrixForm[z](*------------------------------*)"a1=x[[1,1]]"a1=x[[1,1]]"a2=x[[2,2]]"a2=x[[2,2]]"a3=x[[3,3]]"a3=x[[3,3]]"a4=2*x[[1,2]]"a4=2*x[[1,2]]"a5=2*x[[1,3]]"a5=2*x[[1,3]]"a6=2*x[[2,3]]"a6=2*x[[2,3]]"b1=y[[1,1]]"b1=y[[1,1]]"b2=y[[2,2]]"b2=y[[2,2]]"b3=y[[3,3]]"b3=y[[3,3]]"b4=2*y[[1,2]]"b4=2*y[[1,2]]"b5=2*y[[1,3]]"b5=2*y[[1,3]]"b6=2*y[[2,3]]"b6=2*y[[2,3]]"c1=z[[1,1]]"c1=z[[1,1]]"c2=z[[2,2]]"c2=z[[2,2]]"c3=z[[3,3]]"c3=z[[3,3]]"c4=2*z[[1,2]]"c4=2*z[[1,2]]"c5=2*z[[1,3]]"c5=2*z[[1,3]]"c6=2*z[[2,3]]"c6=2*z[[2,3]](*------------------------------*)
The following 6 by 6 matrix was defined by Guimei Zhang and Shenglong Hu in Characteristic Polynomial and Higher Order Traces of Third Order Three Dimensional Tensors
SECTION II
SECTION II
In the remainder of Section II, it is shown that various unitless numbers, of physics and mathematics, can be expressed in terms of JJ, KK, LL and MM to any required level of precision
SECTION III
SECTION III