Four Space Curves

curve

circle

Archimedes's spiral

helix

conical spiral

box

a

3

c

0

T

2π

xacos(t), yasin(t), zc

Some space curves can be defined by a parametric representation

x=x(t)

,

y=y(t)

,

z=z(t)

, where

t

takes values within the interval

I=[0,T]

. This Demonstration shows the parametric equations of the circle, the spiral of Archimedes, the helix, and the conical spiral, and then plots them.