Moebius Strip

Mathematically, it can be parametrised by:

${\displaystyle x=\cos u+v\cos {\frac {nu}{2}}\cos u}$

${\displaystyle y=\sin u+v\cos {\frac {nu}{2}}\sin u}$

${\displaystyle z=v\sin {\frac {nu}{2}}}$,

where n is the number of half-twists, u runs from 0 to 4π and v from 0 to 0.3 (this can be varied to alter the width). n=1 gives the standard Möbius Strip, while any integer gives a continous strip with n half twists in it. If n is not an integer, the surface may be discontinuous (depending on how far u runs).

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By setting n to non-integer values between 0 and 1, we can see a flat band "unwrap" into a Möbius strip:

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  n=0
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  n=0.1
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  n=0.2
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  n=0.3
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  n=0.4
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  n=0.5
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  n=0.6
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  n=0.7
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  n=0.8
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  n=0.9
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  n=1 (This is off-centre to align with the others - use the version at the top if used by itself)