WOLFRAM|DEMONSTRATIONS PROJECT

Short Simple Continued Fractions

u

20

v

20

w

20

x

20

y

14

20+

1

20+

1

20+

1

20+

1

14

=

2264854

112961

≈ 20.0498756208

Play with the continued fraction:

u+

1

v+

1

w+

1

x+

1

y

Notice that it increases with

u

,

w

,

y

and decreases with

v

and

x

.

The numbers π, ϕ,

2

,

e

are given by the sequences

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,…

.