Trigonometric Sums as Parametric Curves

example

1

2

3

4

sum index

51

sample points

100

x

min

-1.3

x

max

1.3

y

min

-1.3

y

max

1.7

frame

Using trigonometric sums like

m

∑

n=1

sin[

2

n

t]

2

n

, you can generate very different curves in the plane.

The following four examples are used:

x(t,m,1)=

m

∑

n=1

sin[

2

n

t]

2

n

,y[t,m,1)=

m

∑

n=1

cos[

2

n

t]

2

n

;

x(t,m,2)=

m

∑

n=1

n

(-1)

sin

n

(-1)

2

n

t

2

n

,y(t,m,2)=

m

∑

n=1

n

(-1)

cos

n

(-1)

2

n

t

2

n

;

x(t,m,3)=0.4

m

∑

n=1

sin[

n

(-1)

nt]

n

,y(t,m,3)=0.4

m

∑

n=1

cos[

n

(-1)

nt]

n

;

x(t,m,4)=0.4

m

∑

n=1

sin[nt]

n

,y(t,m,4)=0.4

m

∑

n=1

cos[nt]

n

.

The first two examples are the interesting ones.