# TORUS KNOTS

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**Torus** is the mathematical name for an inner tube or doughnut.

It is obtained by rotating a circle a fixed distance from the origin (see
**Fibre Bundles** ). John
Robinson's **BONDS OF FRIENDSHIP**
consists of two linked toruses.

John describes how he made **RHYTHM OF LIFE
** by wrapping ribbon around an inner tube and was totally
surprised when it met up with itself. (We have produced a
**rotating version** of his sculpture for you to look
at). Here is a picture of what he did using a tube rather than a ribbon. We
show it with and without the torus and in different positions. It is called a
**(15,4) torus knot**, because it is wrapped 15 times one way and 4 times the
other. Check how these numbers arise in the picture.

**Without Torus**

**With Torus**

Here is what a **(4,15) torus knot** looks like !

You can make a torus knot **T(p,q)** with any numbers
**p, q** provided they are **coprime**, i.e. have no
common divisor - so **(2,6)** will not do. The pair **(15,4)** is interesting
because it uses the three prime numbers **2, 3, 5**.

Here are some pictures of an **(8,3) torus knot**.
The **GORDIAN KNOT** is also
an **(8,3) torus knot**, but with a thick tube, and an invisible inner torus!
(There is a **3D rotating picture**
of the **GORDIAN KNOT** to see in these pages!).

**| SECOND PAGE OF TORUS KNOTS |**

**©Mathematics and Knots/Edition Limitee 1996**

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