MATHEMATICS IN
'DEPENDENT BEINGS'
The Möbius Band is made up of a thin strip
(think of a strip of paper). But what if we thickened this strip so that
it had a square cross section? If this were to happen then the Möbius
Band becomes John Robinson's DEPENDENT
BEINGS, which he made from a fibre
bundle with a square fibre.
We have produced a rotating model of this sculpture by gluing two twisted
Bands together (one gold, one black). These are created from two offset lines
(as we have shown in the "How we did the
pictures" section).
These two lines are rotated through 360 degrees in their plane about the
origin while the origin itself follows the path of a circle twice. Thus the
resulting two twisted bands are not Möbius bands.
In GEOMVIEW it is then possible to combine these two pictures and
rotate the result. Using "screen grabs" we can create a series of pictures,
and so go on to produce a multiple gif file giving the moving picture effect
below.
THE MATHEMATICAL THEMES

Borromean Rings  what
they are and why they don't exist!

The Möbius Band  what
one looks like, experiments to try, amd a beautiful rotating golden one enabling
you to really see what one looks like in 3D (this is optional as 90Kb).

Bernard Morin and the Brehm Model
 how Bernard Morin showed John Robinson the Brehm Model of the
Möbius Band and how to make one!

The Projective Plane 
how to create and understand the projective plane when it is not possible
to physically construct.(this relates to the Brehm Model in the Projective
Plane.

Fibre Bundles  what
they are, how to make them, and examples of them in John Robinson's Work.

Knots and Links  rotating
3D model the Gordian Knot and what was used to construct it.

Torus Knots  two pages
explaining the basics about torus knots with the help of excellent colourful
graphics. There are also 3D moving images of John Robinson's sculptures of
the Gordian Knot and the Rhythm of Life.

Ronnie
Brown's Homepage

John Robinson's Symbolic
Sculpture

About the Centre for the Popularisation
of Mathematics
©Mathematics and
Knots/Edition Limitee 1996
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