Math, Paper, Pencil, Graphene, Carbon Nanotubes, and Buckyballs


Joanne Rowe, Math, Northwest School of the Arts

Curriculum Unit (pdf)


The purpose of this unit is to introduce students to the world of nanoscience, where the significant unit of measure is the nanometer which is one billionth of a meter. This unit can be used as a review at the end of the year for rational expressions which can be used to convert standard measurements to nanometers and make comparisons using scientific notation and order of magnitude. The unit focuses on different allotropes, or forms, of carbon which have been discovered in the last 40 years which include fullerenes, specifically buckyballs, which self-assemble from vaporized carbon. One problem posed to students is to determine the number of carbon bonds in a buckyball.   Geometric sequences and solving exponential functions using logarithms are reviewed when comparing human hair to carbon nanotubes which are formed from graphene. Graphene is composed of a single layer of carbon atoms which form a regular hexagonal pattern. Trigonometry, vectors, and radical functions are reviewed when examining the diameters of carbon nanotubes and the possible ways they can be formed from graphene.