Möbius (Moebius) strip

Written by Paul Bourke
May 1996

The Möbius stip is the simplest geometric shape which has only one surface and only one edge. It can be created by taking a strip of paper, giving it a half twist along its long axis, and then joining the two narrow ends together.

The Möbius strip in 3 dimensions can be represented parameterically f(s,t) as follows


where s ranges from 0 to 2*pi and t ranges typically from -0.4 to 0.4

An example of such a strip is shown below.



Featured in "mama 27", November 2000, pp 91, Figure 17.

The band for different values of t are illustrated below.

t = -1 -> 1

t = -0.1 -> 0.1

t = -0.5 -> 0.5

Increasing the range of t even further yields interesting folded and increasingly convoluted forms.




Pisot Triaxial

By Roger Bagula
Graphics by Paul Bourke
August 2002

x = 0.655866 cos(1.03002 + u) (2 + cos(v))
y = 0.754878 cos(1.40772 - u) (2 + 0.868837 cos(2.43773 + v))
z = 0.868837 cos(2.43773 + u) (2 + 0.495098 cos(0.377696 - v))
0 <= u <= 2 pi, 0 <= v <= 2 pi