Symmetry of a Mystery Curve

This Demonstration shows graphs of the function

f(t)=a

i

n

1

t

e

+b

i

n

2

t

e

+c

i

n

3

t

e

, where

a

,

b

, and

c

are complex coefficients and the frequencies

n

1

,

n

2

, and

n

3

are integers. In particular, for the frequencies 1, 6, and -14, the curve has five-fold symmetry.