Solving Hardy-Weinberg with Geometry: An Integration of Biology and Math

Introducing Hardy-Weinberg equilibrium into the high school or college classroom can be difficult because many students struggle with the mathematical formalism of the Hardy-Weinberg equations. Despite the potential difficulties, incorporating Hardy-Weinberg into the curriculum can provide students with the opportunity to investigate a scientific theory using data and integrate across the disciplines of biology and mathematics. We present a geometric way to interpret and visualize Hardy-Weinberg equilibrium, allowing students to focus on the core ideas without algebraic baggage. We also introduce interactive applets that draw on the distributive property of mathematics to allow students to experiment in real time. With the applets, students can observe the effects of changing allele frequencies on genotype frequencies in a population at Hardy-Weinberg equilibrium. Anecdotally, we found use of the geometric interpretation led to deeper student understanding of the concepts and improved the students' ability to solve Hardy-Weinberg-related problems. Students can use the ideas and tools provided here to draw connections between the biology and mathematics, as well as between algebra and geometry.