Vassiliev defined a holonomic knot as a curve (-f(t),f'(t),-f''(t)) for a smooth, periodic function f:\mathbb{R}\to\mathbb{R}. These knots, while they are explicity defined, capture all the structure of classical knot theory and give us a computational tool to explore properties of knots. In the first part of this talk, we will consider some of the geometric aspects of holonomic knots and describe a way to model these properties using planar diagrams. We will also consider some connections to contact structures on jet bundles. In the second part of the talk, we will see how holonomic knots, planimeters and other computational tools can be used effectively in teaching. The focus will be the use of technology to explore concepts at various levels of mathematics and how research level mathematics can enrich teaching in service courses.