Trigonometric Sums as Parametric Curves
Trigonometric Sums as Parametric Curves
Using trigonometric sums like , you can generate very different curves in the plane.
m
∑
n=1
sin[t]
2
n
2
n
The following four examples are used:
;
x(t,m,1)=,y[t,m,1)=
m
∑
n=1
sin[t]
2
n
2
n
m
∑
n=1
cos[t]
2
n
2
n
;
x(t,m,2)=,y(t,m,2)=
m
∑
n=1
n
(-1)
sint
n
(-1)
2
n
2
n
m
∑
n=1
n
(-1)
cost
n
(-1)
2
n
2
n
;
x(t,m,3)=0.4,y(t,m,3)=0.4
m
∑
n=1
sin[nt]
n
(-1)
n
m
∑
n=1
cos[nt]
n
(-1)
n
.
x(t,m,4)=0.4,y(t,m,4)=0.4
m
∑
n=1
sin[nt]
n
m
∑
n=1
cos[nt]
n
The first two examples are the interesting ones.