**Knots and their polynomials**

Figure-Eight Knot

- Calculate the Jones polynomial of the Figure-Eight Knot.
- What happens to the polynomial when you change the crossings?
- How should this be interpreted?

Square Knot

- Show that when two knots are spliced together, the Jones polynomial
of the splice is the product of the two Jones polynomials.
- Calculate the Jones polynomial of (Left-trefoil) splice (Right-trefoil)
= Square knot.
- Calculate the Jones polynomials of (Left-trefoil) splice (Left-trefoil)
and (Right-trefoil) splice (Right-trefoil) = the two Granny knots.

Back to the previous knot page.Back to the first knot page.