### Where Do We Get Our Feet Wet?

Professor Korner has generously supported school mathematics for more than 30 years and has been a good friend to NRICH since it started.

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots, prime knots, crossing numbers and knot arithmetic.

### Earth Shapes

What if the Earth's shape was a cube or a cone or a pyramid or a saddle ... See some curious worlds here.

# Exhibition of Knots

##### Stage: 5

A visit to this site opens a door to a new world and beautifully illustrates how mathematics may be used to explore and understand the seemingly commonplace knot. The site is clearly set out as an exhibition, presented by the School of Mathematics of the University of Wales, Bangor, and designed by Professor R.Brown, Nick Gilbert and Tim Porter. If you follow the pages or sections under the Contents title, the site will carefully take you through the introduction, definitions, understanding and application of knots.

I have but one slight criticism. In the section titled 'Mirror Images' a rather sudden jump to notation of the image and its invariants is made without defining what the terms meant in $l^2 m^2-2l^2-l^4$. This did rather stop my education in knots for the moment. However, links with other sites did allow me to continue to peruse knots to a greater depth. I would have liked a little more about the theory of colouring than was provided by the site, but here again to quote the designers; 'We are not interested in conveying technique '. This would seem to agree with their stated aim of 'suggesting that the making of mathematics is a natural human activity, part and parcel of the usual methods by which man has explored, discovered and understood the world'. In this last aim, I think the designers have most definitely succeeded.