**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.- see the **animation** too. 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 is an animation (120k) and 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 an **animation** of the **GORDIAN KNOT** here and also Nick Mee's **animation** in the sculpture section.)

**© Mathematics and Knots/Edition Limitee 1996 - 2002**

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