Mobius Surfaces

In the last week I became interested in the more mathematical approach to parametric surfaces, ie. a surface (or curve) where the points that describe its coordinates can be expressed in functions of a variable.

The simplest parametric equation perhaps is that which forms the circle which comes in the form:

x = cos(t)
y = sin(t)

where this becomes more interesting is when we introduce a z function and we can evaluate t (or some other parameter) within a specified range to produce a surface or something more complex.

And one of the areas I found most interesting was that of mobius and klein surfaces, surfaces which turn on themselves to bend our perception of the geometry.

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