Heron’s Formula: A Visual Proof in the Style of Oliver Byrne

In this undergraduate student research project, I applied Oliver Byrne’s visual methodology to proving Heron of Alexandria’s famous formula for triangular area. Heron’s proof, although rich and intriguing in its approach, requires a considerable amount of effort by the reader to fully understand and appreciate. To expedite comprehension of the underlying principles, I drew from the primary historical source for Heron’s proof to create an original visual proof in the style of Byrne. My goal in this project was to make Heron’s proof more widely accessible to mathematics students, as well as to celebrate the artistry in Byrne’s approach. Mathematics instructors may find it useful to apply Byrne’s techniques to other propositions in geometry and trigonometry.