# MATHEMATICS IN JOHN ROBINSON'S SYMBOLIC SCULPTURE

## INTRODUCTION

The mathematician, a member of the wide mathematical community, studies forms and patterns for their own sake, for the sense of structure, logic and truth which they bring, and for the simple delight in the discovery of amazing new forms and patterns, which often also reveal new features of the world around us.

The artist has his sense of proportion and line, his precise visual imagination, his feeling for emotion and wider significance, and his ability to realise these in a beautifully crafted object.

John Robinson's Symbolic Sculptures have brought together the artist and mathematicians.

Through this association, both sides have been enriched, and Robinson's striking works have been brought to the attention of a wider public.

Some of his work can be visualised in a Brochure produced by The University of Wales, Bangor which gives a guided tour around the university grounds and his sculptures.

## THE MATHEMATICAL THEMES

• Borromean Rings (50Kb) - what they are and why they don't exist!
• The Möbius Band (53Kb) - what one looks like, experiments to try, and 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 (25Kb) - how Bernard Morin showed John Robinson the Brehm Model of the Möbius Band and how to make one!
• The Projective Plane (88Kb), (95Kb) - two pages explaining how to create and understand the projective plane although it is not possible physically to construct it. Also, the relation to the Brehm Model of the Möbius Band, and the Dirac String Trick.
• Fibre Bundles (8Kb) - what they are, how to make them, and examples of them in John Robinson's Work.
• Knots and Links - (30Kb) Introduction to the subject of Knot Theory, includes history of the subject, and a rotating mathematically constructed version of Immortality, which is the most basic of knots, namely a trefoil knot, made from a Möbius Band.
• Torus Knots (95Kb), (96Kb) - two pages explaining the basics about torus knots with the help of full colour graphics. There are also 3D moving images of John Robinson's sculptures of the Gordian Knot and the Rhythm of Life.
• Fractals 3 pages, introducing Fractals, considering iteration, The Sierpinski Gasket and the applications of the subject.
• How we made the pictures (10kb) Details of the construction of the computer graphics.