Using animal trails to illustrate mathematical functions: from beach bivalves to moth larvae

Connecting mathematics to real-world examples is considered a valuable and informative way to teach students at various educational levels. Typically, this begins at the earlier levels of education entailing skills such as simple numeracy and shape identification. Nature provides a plethora of examples for mathematics and science educators to explore simple and more complex mathematical concepts and patterns. In this paper, we explore the use of real-life examples found in nature to illustrate a range of shapes/functions. Specifically, we use animal trails formed by a bivalve, polychaete, nematode and moth larvae to illustrate a variety of mathematical functions. These include sinusoidal curves, triangular wave functions, parameterisation of a loopy curve and rose curves.