Update index.html

index.html

@@ -305,6 +305,28 @@ <h3>1 / log(2) is a transcendental number</h3>
 
 <h4>1.442695040888963 = log2(e)</h4>
 
+-0.0450174147692956119367488822382 * ((0.81007883)^2 - (10 * ( 1 / log(2)^2)) = 
+
+=   11.035206267601980662683842299568
+
+  == -109.69583496520563772683842299568
+
+  4.9382229011404647012246185768126
+
+0.97027011439203392574025601921001
+<h2>continued fraction theorem</h2>
+  Let x be an irrational number where 0<x<1 and
+d_n (x) = 10^(-n) floor(10^n x)
+e_n (x) = 10^(-n) (floor(10^n x) + 1)
+be decimal approximations of x, m be a Lebesgue measure set, x = continued fraction k _(n=1)^∞ 1/a_n
+be the regular continued fraction of x, d_n(x) = continued fraction k _(n=1)^∞ 1/(b_1(n))
+be the regular continued fraction of d_n(x), e_n(x) = continued fraction k _(n=1)^∞ 1/(b_2(n))
+be the regular continued fraction of e_n(x), and
+k_n(x) = sup({i: for all i<=n, b_1(i) = b_2(i)}).
+Then
+for almost all x, lim_(n->∞) k_n/n = (6ln 2 ln 10)/π^2.
+
+  https://scipp.ucsc.edu/~haber/ph222/One%20Loop%20Renormalization%20of%20the%20Electroweak%20SM.pdf
 
 
 
@@ -352,3 +374,5 @@ <h4>Sources:</h4>
 - https://en.wikipedia.org/wiki/Green%27s_theorem
 - https://en.wikipedia.org/wiki/Stokes%27_theorem
 - https://sprott.physics.wisc.edu/pickover/trans.html
+
+- https://scipp.ucsc.edu/~haber/ph222/One%20Loop%20Renormalization%20of%20the%20Electroweak%20SM.pdf