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