A hint of the Gauss constant

I wrote earlier why 1.414 .... And not 0.414... So also for why 1.732.... And not 0.732.... in my "The other day" blog.
Below I present 2 screenshots. First is the continued fractions of
 1+ 1/(root(2)+1/(root(3)+.....
The second is 1.53... divided by 0.8346 which is the Gauss constant. The result is 1.83....
So in a way I have shown why 1 is added. Using Gauss constant.

How about this ?

(It is a privilege to see Gauss constant. Gauss is really too good and very high. Gauss is considered the greatest mathematician by many guys over internet. He won the Copley medal too. Wow !! I feel honored to see Gauss constant...... though partly !!)

I feel there are many criticism on 0.8346 and 1.8346 results with continued fraction of the type root (n). 

Why it is not accurate? 

It is not meant to be. Ceiling and floor are to be used.

My result demonstrates the enormity of the Gauss's constant G. It includes the explanation of initial value in continued fractions and also the ceiling and floor functions.

In fact 0.8346 and 1.8346 result is as beautiful as 22/7 of pi.