Short Simple Continued Fractions
Short Simple Continued Fractions
Play with the continued fraction:
u+
1
v+
1
w+
1
x+
1
y
Notice that it increases with , , and decreases with and .
u
w
y
v
x
The numbers π, ϕ, , are given by the sequences .
2
e
u,v,w,x,y,…=3,7,15,1,292,…,1,1,1,1,1,…,1,2,2,2,2,…,2,1,2,1,1,…