By a mathematical knot we mean the continuous image of the unit circle embedded in three dimensional Euclidean space (or the 3-sphere).

• A unit circle (the unknot)
• An overhand knot (the trefoil)
• A granny knot (the connected sum of two trefoils)
• A torus knot (a knot who lives on the surface of a torus)

A \((p,q)\)-torus knot can be parametrized as follows: \[ k(t) = (x(\theta), y(\theta), z(\theta)) \] where \[ x(\theta) = ((\cos(q\theta) + 2)\cos(p\theta)\\ y(\theta) = (\cos(q\theta) + 2)\sin(p\theta))\\ z(\theta) = -\sin(q\theta)) \]

Here we see an example of a \((3,2)\)-torus knot. My shiny app will allow the user to visualize a \((p,q)\)-torus knot. One needs only provide the number of times the knot should travel the long way around the torus \(p\) (longitude) and the number of times the knot travels around the shorter direction around the torus \(q\) (meridian).