# 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,…