If 0.0819949771411335541326 lived in the best of all possible worlds,
while 0.07043106849242149001936 stood on the shoulders of giants,
then who is represented by 0.045317973977950402535096?

The answer is: the author of Candide, as

  5   point 10
 10      Alpha$="abcdefghijklmnopqrstuvwxyz"
 20      N=0.0819949771411335541326
 30      for I=1 to 7
 40        N=1/N
 50        L=int(N)
 60        print mid(Alpha$,L,1);
 70        N=N-L
 80      next
100      print
120      N=0.07043106849242149001936
130      for I=1 to 6
140        N=1/N
150        L=int(N)
160        print mid(Alpha$,L,1);
170        N=N-L
180      next
200      print
220      N=0.045317973977950402535096
230      for I=1 to 8
240        N=1/N
250        L=int(N)
260        print mid(Alpha$,L,1);
270        N=N-L
280      next

finds

Words for fractionals 10 (Decimals for display 48)
leibniz
newton
voltaire

The title of the current puzzle led back, via the search box, to the original Odd Men puzzle, who's solution was indeed the continued fraction expansion of fractions. Beyong that lookup, the computer merely assisted in the arithmetic involved.